Past Probability and Statistics Research Seminars
1st Semester 2011/20122nd Semester 2010/2011
1st Semester 2010/2011
2nd Semester 2009/2010
1st Semester 2009/2010
2nd Semester 2008/2009
1st Semester 2008/2009
2nd Semester 2007/2008
1st Semester 2007/2008
2nd Semester 2006/2007
1st Semester 2006/2007
2nd Semester 2005/2006
1st Semester 2005/2006
1st Semester 2011/2012
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5 OctoberSolving the KPZ Equation
2011
Professor Martin Hairer (University of Warwick)
2:15pm, Frank Adams 1 -
12 OctoberCapped optimal stopping problems for the maximum process
2011
Curdin Ott (University of Bath)
2:15pm, Frank Adams 1 -
20 OctoberRecent results on optimality of designs under the interference model
2011
Katarzyna Filipiak and Augustyn Markiewicz (University of Life Sciences, Poland)
2:00pm, 2.217, University PlaceAbstractWe consider optimality of circular block designs under the interference model. The only so far known optimal designs under this model are circular neighbor balanced designs (CNBDs). Their universal optimality under fixed model is proved in Druilhet (1999) and under mixed model in Filipiak and Markiewicz (2003, 2007). However, when the number of blocks is not proportional to the number of treatments minus one then CNBDs cannot exist. Therefore our aim is to characterize D- and E-optimal designs as well as universally optimal designs in classes of complete designs with specific numbers of blocks.
26 OctoberSolving optimal stopping problems for Levy processes by fluctuation theory
2011
Erik Baurdoux (London School of Economics)
2:15pm, Frank Adams 19 NovemberStochastic control, robust portfolio choice, and BSDEs
2011
Martin Schweizer (ETH Zürich)
2:00pm - University Place 4.204AbstractPortfolio choice is one of the classical problems from mathematical finance. One typical formulation is that none considers an agent who invests in a financial market to maximise his expected utility from consumption and/or terminal wealth. This problem and its solution are by now well understood at the conceptual level, although explicit solutions are rather rare. Robust portfolio choice is concerned with the same problem when the investor is no longer certain about the underlying model. Hence he cannot take "the" expected utility, but must consider, for each possible model, the corresponding expected utility and try to find something which is optimal with respect to the model as well. A more precise formulation leads to a maximin (or minimax) problem where one maximises over strategies and minimises with respect to models. One approach tom study these problems is via convex duality. But if one wants more information about the dynamic behaviour of a solution, one will rather turn to stochastic control methods, and this leads to some interesting connections to backward stochastic differential equations. In the talk, we give an outline of this subject and try to explain how and where the different ideas come in. We also present some results which are based on joint works with G. Bordigoni, A. Matoussi and Y. Hu.
9 NovemberComparison based tests for nonlinear time series
2011
Suhasini Subba Rao (Texas A&M University)
3:15pm - Frank Adams 2AbstractThis talk addresses the issue of tests for nonlinear time series. In the case that a time series is linear, tests, such as goodness of fit tests, can be constructed using the spectral density function. However, such tests can lead to unreliable conclusions if applied to nonlinear time series, a classical example is how observations from an ARCH model can be miconstrued as either iid or from an autoregressive process, depending on how the test is constructed. In this talk, we consider tests based on comparisons with the quantile spectral density, which can be considered as a quantile version of the usual spectral density function.
The quantile spectral density `measures' sequential dependence structure of a time series, and is well defined under relatively weak conditions. We use the quantile spectral density to construct a goodness of fit test for time series and explain how this test can also be used for comparing the sequential dependence structure of two time series and classification. The method is illustrated with simulations and some real data examples.16 NovemberStationary Solutions of Retarded Linear Equations with Additive Noise
2011
Kai Liu (University of Liverpool)
2:15pm - Frank Adams 123 NovemberMixed-effects GPFR Models with Application to Management of Renal Anaemia
2011
Bo Wang (Leicester University )
2.15pm - Frank Adams 2AbstractThis talk will introduce a new semiparametric model for functional regression analysis, combining a parametric mixed-effects model with a nonparametric Gaussian process regression (GPR) model, namely a mixed-effects GPFR (Gaussian process functional regression) model. The parametric component can provide explanatory information between the response and the covariates, while the nonparametric component can add nonlinearity, thus the model benefits from increased interpretability and flexibility. The model is applied to dose-response curves in the management of renal anaemia which describes changes in the responses of subjects for differing levels of the dose of a drug or agent. Individual dose-response curves can be improved when more information is included by this mechanism from the subject/patient over time, enabling a patient-specific treatment regime.
30 NovemberShape constrained additive models.
2011
Natalya Pya (Bath University)
2.15pm - G.108, Alan Turing BuildingAbstractIn many practical situations when analyzing a dependence of one or more explanatory variables on a response variable it is essential to assume that the relationship of interest obeys certain shape constraints, such as monotonicity or monotonicity and convexity/concavity. In this talk a framework is presented for generalized additive modelling under shape constraints on the smooth terms of the linear predictor. Shape constrained terms representation is based on re-parameterized P-splines. Smoothing methods under monotonicity together with convexity/concavity for univariate smooths, and multi-dimensional smoothing with monotonicity restrictions are developed. The proposed smoothers make it possible to develop a penalized likelihood maximization method for fitting a shape constrained additive model (SCAM) based on the Newton-Raphson method. A numerically robust algorithm for efficient estimation of smoothing parameters is presented as an integral part of model estimation. To assess the performance of the proposed procedure SCAM has been compared with other approaches to shape preserving smoothing on simulated examples. The simulation studies show that the new method has practical advantages over the alternatives considered. Applications are presented using real data examples including the risk of disease in relation to proximity to municipal incinerators and the association between air pollution and health.
7 DecemberCubature and splitting schemes for stochastic differential equations.
2011
Christian Bayer (University of Vienna)
2.15pm - Frank Adams 2, Alan Turing BuildingAbstractAbstract will appear here
7 DecemberMulti-resolution inference of stochastic models from partially observed data.
2011
Sam Kou (Harvard University)
4.00pm - Frank Adams 2AbstractStochastic models, diffusion models in particular, are widely used in science, engineering and economics. Inferring the parameter values from data is often complicated by the fact that the underlying stochastic processes are only partially observed. Examples include inference of discretely observed diffusion processes, stochastic volatility models, and double stochastic Poisson (Cox) processes. Likelihood based inference faces the difficulty that the likelihood is usually not available even numerically. Conventional approach discretizes the stochastic model to approximate the likelihood. In order to have desirable accuracy, one has to use highly dense discretization. However, dense discretization usually imposes unbearable computation burden. In this talk we will introduce the framework of Bayesian multi-resolution inference to address this difficulty. By working on different resolution (discretization) levels simultaneously and by letting the resolutions talk to each other, we substantially improve not only the computational efficiency, but also the estimation accuracy. We will illustrate the strength of the multi-resolution approach by examples.
14 DecemberNature-Inspired Metaheuristic Algorithms for Generating Optimal Experimental Designs
2011
Weng Kee Wong (UCLA)
2.15pm - Frank Adams 2AbstractParticle swarm optimization (PSO) is a relatively new, simple and powerful way to search for an optimal solution. It is widely used in many applied fields. The method works quite magically and frequently finds the optimal solution or a nearly optimal solution after a few iterations. There is virtually no assumption required for the method to perform well and the user only needs to input a few easy to work with tuning parameters.
After a brief review of the fundamentals of optimal design of experiments and recent advances in the field, I use several nonlinear regression models to demonstrate that PSO can find different kinds of optimal designs quickly, including mini-max types of optimal designs where effective algorithms to find such designs have remained elusive until now. To promote use of optimal design ideas in practice, I also introduce a website that freely generates a variety of tailor-made optimal designs for popular models in the biological sciences.2nd Semester 2010/2011
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2 FebruarySequential Importance Sampling for Continuous-time Markov processes
2011
Paul Fearnhead (University of Lancaster)
2.15pm - G.205, Alan Turing BuildingAbstractMany continuous-time Markov processes, such as diffusion models, have an intractable transition density. In these cases either simulating the process, or making inference about the process, cannot be done directly. A common approach is then to approximate the continuous-time process by a suitable discrete-time process, and then simulate from (or perform inference for) this discrete-time approximation.
Here we present a novel approach, which uses sequential importance sampling to generate weighted samples from the distribution of the process at any time-point. The weighted samples can then be used to get unbiased estimates of properties of the process. As such they can enable inferences for the process which avoid any time-discretisation error.
Our method can be viewed as a generalisation of recent work for simulation and inference of diffusions, which is based on the Exact Algorithm of Beskos, Papaspiliopoulos and Roberts. The new approach is more general, as it can be applied to almost all diffusion processes as well as other continuous-time Markov processes.16 FebruaryThree Topics in Non-linear Time Series Analysis and Modelling
2011
Tony Lawrance (Warwick University)
2.15pm - G.205, Alan Turing BuildingAbstractThree Topics in Non-linear Time Series Analysis and Modelling
2 MarchEM, Variational Bayes and Expectation Propagation
2011
Mike Titterington (University of Glasgow)
2.15pm - G.205, Alan Turing BuildingAbstractThe main aim of the talk will be to discuss the Expectation Propagation (EP) approach of T. Minka. This will follow a preamble based on the EM algorithm and the variational approximation approach. The relationship between EP and other parts of the literature will be outlined and some semi-theoretical investigation of its properties in some very simple problems will be presented.
9 MarchFactor Modelling for High-Dimensional Time Series: A Dimension-Reduction Approach
2011
Clifford Lam (London School of Economics)
2.15pm - G.205, Alan Turing BuildingAbstractAbstract : In this talk we deal with the dimension reduction of high-dimensional time series based on a lower-dimensional factor process. In particular we allow the dimension of time series N to be as large as, or even larger than, the length of observed time series (also refereed as the sample size) T. The estimation of the factor loading matrix and the factor process itself is carried out via an eigenanalysis of a N * N non-negative definite matrix. We spell out explicitly the rates of convergence for various estimators including the factor loading matrix and the common component. We also introduce a method in estimating the number of factors r, and look at the theoretical background of this method. Throughout this talk our motivating example is an analysis of a set of real environmental data, where results of our analysis will be given at the end.
9 MarchFirst exit times of solutions of SDEs driven by multiplicative Levy noise with heavy tails
2011
Ilya Pavlyukevich (University of Jena)
2.15pm - G.110, Alan Turing BuildingAbstractWe study first exit times from a bounded domain of a gradient dynamical system perturbed by a small multiplicative Levy noise with heavy tails. A special attention is paid to the way the multiplicative noise is introduced. In particular we determine the asymptotics of the first exit time of solutions of Ito, Stratonovich and Marcus canonical SDEs.
16 MarchA Ciesielski-Taylor type identity for positive self-similar Markov processes
2011
Andreas E. Kyprianou (University of Bath)
2.15pm - G.205, Alan Turing BuildingAbstractThe aim of this talk is to give a straightforward proof of a general version of the Ciesielski-Taylor identity for positive self-similar Markov processes of the spectrally negative type which umbrellas all previously known Ciesielski-Taylor identities within the latter class. The approach makes use of three fundamental features. Firstly a new transformation which maps a subset of the family of Laplace expo- nents of spectrally negative Le?vy processes into itself. Secondly some classical features of fluctuation theory for spectrally negative Le?vy processes and thirdly some more recent fluctuation identities for positive self-similar Markov processes due to Pierre Patie. (joint work with Pierre Patie, Universite Libre de Bruxelles)
30 MarchChao's Lower Bound Estimator of Population Size with Covariate Information
2011
Dankmar Böhning (University of Reading)
2.15pm - G.205, Alan Turing BuildingAbstractAbstract: Capture-Recapture methods are used frequently to estimate the size of elusive populations. One of the most popular estimators has been suggested by Chao (1987, 1989 Biometrics) is only based upon the frequencies of counts of ones and twos in the frequency distribution of counts of how often a member of the target population has been identified by an indentifying mechanism (trap, register, reviewer). The estimator of Chao is very popular among practitioners since it is easy to understand and use, has good variance with variance estimator in closed form available, and provides a lower bound estimator in the case of population heterogeneity with relatively small bias. Although the estimator is known for some while, no extensions are available to incorporate covariate information (except stratifying the estimator with evident strong limitations). The talk presents recent work on how this estimator can be extended if covariate information is available. In case, the heterogeneity can be described by a Poisson regression model the extended estimator is asymptotically unbiased and in case, the heterogeneity is only partially explained by the Poisson regression model (residual heterogeneity present) the extended estimator provides a lower bound.
6 AprilWavelet variance analysis for gappy time series data
2011
Debashis Mondal (University of Chicago)
2.15pm - G.205, Alan Turing BuildingAbstractTitle: Wavelet variance analysis for gappy time series data
Abstract: Wavelet variances and covariances (sometime also known as wavelet spectra and co-spectra) are a form of analysis of variance that find extensive use in the study of time series arising from atmospheric science, economics, hydrology, oceanography, soil science and other areas of geophysics. Specifically, as precursor to a more formal statistical analysis, wavelet variances and covariances are often applied to time series to explore their structure and behavior, to identify important scales, to assess long memory parameters, to detect inhomogeneity and to estimate time-varying spectral densities. In this talk, we focus on estimation and inference of wavelet variances and covariances when the observed time series is `gappy', i.e., sampled at regular intervals, but certain observations are missing. In particular, we propose a method of estimation that extends the usual estimation procedure for the non-gappy data, investigate statistical properties and discuss large sample theory. We then show how our approach to this problem opens up new avenues in advancing statistical calculations for wavelet-based principal components, clustering and classification of multivariate time series that contain missing values. Finally, we consider an application of our method to NOAA's tropical sea level barometric pressure data.
This is joint work with Don Percival, University of Washington.20 AprilStatistical Challenges In The Pharmaceutical Industry
2011
Chris Harbron (AstraZeneca)
2.15pm - G.205, Alan Turing BuildingAbstractThe pharmaceutical industry is facing many challenges, but the rapid development of new technologies coupled with improved detailed molecular understanding of biology and the mechanisms of disease also makes this an exciting time of great opportunity. One common strand is the reliance on data for decision making. This data can often be expensive to generate and challenging and complex to interpret, making the involvement of statistics and statisticians essential. I will discuss the role and contributions of statisticians with some examples and pose some challenges.
4 MayMissing data: It is better to prepare and prevent than to repair and repent.
2011
Sara Hughes (Head of Statistics, ViiV Healthcare)
4:00pm - G.205, Alan Turing BuildingAbstractConsiderable research has been done in recent years to develop sophisticated statistical methods for handling missing data and dropouts in the analysis of clinical trial data. However, there has not been sufficient emphasis by either statisticians or other clinical trial personnel on proactively setting out at the study initiation stage to assess the impact of missing data and investigate ways in which to reduce dropouts. Doing this has the potential to considerably improve the clarity and quality of study results and also increase efficiency. This talk will present an example from HIV where Statistical & Operational staff collaborated to try and reduce non-treatment-related dropouts. The first step was to perform a pooled analysis of past HIV trials investigating which patient subgroups are more likely to drop out unnecessarily. The second step was to educate study personnel at all levels about the patient types more likely to dropout, and the impact this has on data quality and sample sizes required. The final step was to then work with each group to create a proactive plan regarding focused retention efforts, identifying ways to increase retention relevant to the patients most at risk.
11 MayDiverse beliefs and market selection
2011
L.C.G. Rogers (University of Cambridge)
2.15pm - G.205, Alan Turing BuildingAbstractThe Market Selection Hypothesis is a principle which (informally) proposes that `less knowledgeable' agents are eventually eliminated from the market. This elimination may take the form of starvation (the proportion of output consumed drops to zero), or may take the form of going broke (the proportion of asset held drops to zero), and these are not the same thing. Starvation may result from several causes, diverse beliefs being only one. We firstly identify and exclude these other possible causes, and then prove that starvation is equivalent to inferior belief, under suitable technical conditions. On the other hand, going broke cannot be characterized solely in terms of beliefs, as we show. We next present a remarkable example with two agents with different beliefs, in which one agent starves yet amasses all the capital, and the other goes broke yet consumes all the output. This example also serves to show that although an agent may starve, he may have long-term impact on the prices.
18 MayModelling and pricing of derivatives in electricity markets
2011
Ben Hambly (University of Oxford)
3:30pm - Frank Adams 2, Alan Turing BuildingAbstractElectricity markets show a range of unusual features for financial markets, such as price spiking in the spot price. I will begin with a simple model for price formation in electricity markets and describe some natural models for prices. We will then investigate the pricing of complex derivatives such as swing options, which give the holder the ability to reduce the spike risk from exposure to the spot electricity price.
8 JuneRecent nonuniqueness for some stochastic PDE
2011
Carl Mueller (University of Rochester )
2:15pm - Frank Adams, Alan Turing BuildingAbstractThe uniqueness theories for PDE and stochastic PDE (SPDE) are quite different. Recently there has been substantial progress in clarifying uniqueness questions for SPDE. Proofs use a broad range of techniques, such as superprocesses, backward equations, and others. I will review some of these results and discuss the latest progress.
1st Semester 2010/2011
- 6 OctoberMartingale aspects of financial bubbles
2010
H. Föllmer (Humboldt University of Berlin)
2.15pm - G205, Alan Turing BuildingAbstractAbstract:
We discuss some recent developments in the literature on financial bubbles. This will include the effects of filtration shrinkage (joint work with Philip Protter, Cornell) and the appearance of bubbles in the robust valuation of cash flows (joint work with Beatrice Acciaio, TU Wien, and Irina Penner, HU Berlin).11 October (Monday!)Levy's stochastic area formula for Orstein Uhlenbeck processes and the KdV equation
2010
N. Ikeda (Osaka University)
2.00pm - Frank Adams 2, Alan Turing BuildingAbstractAbstract:
As a special case of H.Matsumoto's results,(J.Funct. Anal. ,129(1995)),I first will show Levy's stochastic area formula for Ornstein Uhlenbeck processes. By using this I will give a representaition in terms of Wiener space of a one-parameter family of 1-soliton solutions to the KdV equation.20 OctoberCharacterisation of stability in solutions of finite dimensional linear and affine stochastic Volterra equations
2010
J. A. D. Appleby (Dublin City University)
4.00pm - G113, Alan Turing BuildingAbstractAbstract:
In this talk we give necessary and sufficient conditions for the almost sure asymptotic stability of the solution of the affine stochastic Volterra equation \[ dX(t)=\int_{[0,t]}\nu(ds)X(t-s)\,dt + \sigma(t)\,dB(t) \] where $\nu$ is a finite matrix-valued measure. These conditions require $\sigma$ to fade to zero sufficiently rapidly as $t\to\infty$, in some sense. We also give a very sharp characterisation of the mean square stability of the zero solution of the linear equation \[ dX(t)= \left(\int_{[0,t]} \mu(ds)\, X(t-s)\right)dt + \sum_{l=1}^{d'} \left(\int_{[0,t]} \eta_l(ds)\, X(t-s)\right)\,dB_l(t). \] In this instance a type of characteristic equation is deduced which captures the mean square integrability of solutions. Our results enable us to determine exact rates of convergence to the equilibrium in each case, and we indicate some other classes of sharp convergence to nontrivial limits. We also sketch how these results can be applied to prove related convergence for stochastic neutral equations, and stochastic differential equations with finite delay. The results develop recent joint work with Markus Riedle and Xuerong Mao which deal with scalar linear equations, or require some monotonicity conditions on the diffusion coefficient in the affine equation. The work relies on recent work on SDEs with Jian Cheng and long memory in finance with Katja Krol, and is supported by Science Foundation Ireland through the grant 07/MI/008 "Edgeworth Centre for Financial Mathematics".10 NovemberModelling bounded health scores with censored skew-normal distributions.
2010
Jane Hutton (University of Warwick)
2.15pm - G.205, Alan Turing BuildingAbstract'Modelling bounded health scores with censored skew-normal distributions'
(joint work with Elena Stanghellini, Univ Perugia)
Abstract:
Health care interventions which use quality of life or health scores often provide data which are skewed and bounded. The scores are typically formed by adding up numerical responses to a number of questions. Different questions might have different weights, but the scores will be bounded, and are often scaled to the range 0 to 100. If improvement in health over time is measured, scores will tend to cluster near the 'healthy' or 'good' boundary as time progresses, leading to a skew distribution. Further, some patients will drop out as time progresses, so the scores reflect a selected population. We fit models based on the skew-normal distribution to data from a randomised controlled trial of treatments for sprained ankles, in which scores were recorded at baseline and at 1, 3 and 9 months after injury. We consider the extent to which skewness in the data can be explained by clustering at the boundary via a comparison between a censored normal and a censored skew-normal model. As this analysis is based on the complete data only, a formula for the bias of the treatment effects due to informative drop-out is given. This allows us to assess under which conditions the conclusions drawn from the complete data might be either reinforced or reversed, when the informative drop-out process is taken into account.12 NovemberSustained Oscillations for Density Dependent Markov Chains
2010
Priscilla Greenwood (Arizona State University)
2.00pm - G.114, Alan Turing BuildingAbstractAbstract:
Abstract: Simulations of models of epidemics, biochemical systems, and other bio-systems show that when deterministic models yield damped oscillations, stochastic counterparts show sustained oscillations at an amplitude well above the expected noise level. A characterization of damped oscillations in terms of the local linear structure of the associated dynamics in two dimensions is well known but in general there remains the problem of identifying the stochastic process which is observed in stochastic simulations. We show that in a limiting sense the stochastic path describes a circular motion modulated by a slowly varying Ornstein Uhlenbeck process. This is joint work with Peter Baxendale at USC.17 NovemberRandom networks with concave preferential attachment
2010
P. Mörters (University of Bath)
2.15pm - G.205, Alan Turing BuildingAbstractAbstract:
We study a dynamical random network model in which at every construction step a new vertex is introduced and attached to every existing vertex independently with a probability proportional to a concave function of its current degree. We use approximation by branching random walks to find necessary amd sufficient criteria for the existence and robustness of a giant component in these networks. The talk is based on joint work with Steffen Dereich (Marburg).24 NovemberOptimum Experimental Designs for Enzyme Kinetic Models
2010
Anthony C. Atkinson (London School of Economics)
2.15pm - G.205, Alan Turing BuildingAbstractOptimum Experimental Designs for Enzyme Kinetic Models
Anthony Atkinson, London School of Economics, London WC2A 2AE
Enzymes are biological catalysts that act on substrates. The speed of reaction as a function of substrate concentration typically follows the nonlinear Michaelis-Menten model. The reactions can be modified by the presence of inhibitors, which can act by several different mechanisms, leading to a variety of models, all also nonlinear.
The paper describes the models and derives optimum experimental designs for model building. When the model is known these include D-optimum designs for all the parameters and Ds-optimum designs for subsets of parameters, appropriate when not all rate constants are of interest. In one special case of an unknown model, a simpler model results when two of the four parameters are equal. Designs are found for testing such equality. More generally, compound T-optimum designs are found for testing which of two models adequately describes the reaction structure. The numerical construction of all designs is checked by use of various forms of Kiefer and Wolfowitz's General Equivalence Theorem. Compound designs will also be explored that have good efficiency both for model building and parameter estimation.24 NovemberProperties of Fractional Schrödinger Operators through Stochastic Methods
2010
József Lörinczi (Loughborough University)
2.15pm - G.108, Alan Turing BuildingAbstractFractional Schrödinger operators are obtained as sums of the fractional Laplacian and a multiplication operator called potential. I will use a functional integral representation for semigroups generated by fractional Schrödinger operators involving symmetric stable processes under this potential. Then I will discuss some analytic and spectral properties of such operators and semigroups such as intrinsic ultracontractivity and spatial decay of the first eigenfunction. Finally, I will address existence, uniqueness and support properties of Gibbs measures on stable processes, and discuss some applications and examples.
1 DecemberLinear combinations of Gamma, (LG) processes and Dirichlet (B-) splines: Applications in finance and insurance
2010
Vladimir Kaishev (City University)
(earlier start!) 1.45pm - G.205, Alan Turing BuildingAbstract15 DecemberSpace-time modelling for blue ling using soap film smoothers
2010
Nicole Augustin (University of Bath)
2.15pm - G.205, Alan Turing BuildingAbstractTitle: Space-time modelling for blue ling using soap film smoothers
Abstract:
Fishery catch data offers a rich potential source of information for stock management, if the data can be modelled in a way that separates out the effects of fishing effort, species behaviour and population abundance on the raw data. Fisheries managers require models for two main purposes. One is simply to obtain estimates of overall stock abundance trends. The second is to look for other indicators of stock vulnerability: in particular `serial depletion' in which areas of high stock abundance are depleted by fishing, with the boats then moving to another high density area; and local depletion in areas with longer exploitation histories. Both purposes require the use of flexible space-time models capable of representing space-time interactions, but in order to investigate the possibility of local and serial depletion some care is needed to avoid possible contamination of the results by boundary artefacts. Here we model catch data from the Blue Ling fishery off the northwest coast of Scotland, using Generalized Additive Mixed Models with a space time interaction represented via a novel tensor product of a soap film smooth of space with a penalized regression spline of time. The distribution of Blue ling has a relatively complicated boundary, substantially determined by sea bed depth. The use of soap film smoothers enables us to avoid imposing artificial correspondences between spatially adjacent areas that are in fact separated by the stock boundary. This in turn avoids compromising our conclusions about the presence or absence of space-time interactions. After model selection, checking and validation there is some evidence for a space time interaction in the data, but in this case no evidence of depletion. However the most robust models for overall prediction have log additive space and time effects and suggest increase in overall Blue Ling abundance in the study area from 2000-2008.2nd Semester 2009/2010
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6 JanuaryVariable Selection for Censored Linear Regression Models: A New Perspective. (seminar cancelled due to bad weather)
2010
Yi Li (Harvard University, USA)
2.15pm - G.207, Alan Turing BuildingAbstractThe Dantzig variable selector has recently emerged as a powerful tool for fitting regularized regression models. A key advantage is that it does not pertain to a particular likelihood or objective function, as opposed to the existing penalized likelihood methods, and hence has the potential for wide applications. To our knowledge, most work has been performed with fully observed response variables. This talk discusses a new class of adaptive Dantzig variable selectors for linear regression models when the response variable is subject to right censoring. This is motivated by a clinical study of detecting predictive genes for myeloma patients' event-free survival, which is subject to right censoring. Under some mild conditions, we establish the theoretical properties of our procedures, including consistency in model selection (i.e. the right subset model will be identified with a probability tending to 1) and the oracle property of the estimation (i.e. the asymptotic distribution of the estimates is the same as that when the true subset model is known a priori). The practical utility of the proposed adaptive Dantzig selectors is verified via extensive simulations. We apply the new method to the aforementioned myeloma clinical trial and identify important predictive genes for patients' event free survival.
17 FebruaryShape invariant modelling pricing kernels and risk inversion
2010
Juhyun Park (Lancaster University)
2.15pm - G.114, Alan Turing BuildingAbstractPricing kernels play a major role in quantifying risk aversion and investors' preferences.Several empirical studies reported that pricing kernels exhibit a common pattern across di erent markets. Mostly visual inspection and occasionally numerically summarise are used to make comparison. With increasing amount of information updated every day, the collection of empirical pricing kernels can be viewed as functional data where the unit of analysis is taken to be continuous functions.
The standard functional data analysis proceeds with functional principal component analysis which decomposes the variability into a few common principal component functions. This approach is not appropriate for pricing kernels, as the main variability of interest is rather nonlinear and the interpretability becomes an issue. We propose to utilise shape invariant models, a special case of semi-parametric self-modelling regression approach. It captures the common features contained in the shape of the functions and at the same time characterises the variability between the pricing kernels based on a few interpretable parameters. The method is demonstrated with the European options and returns values of DAX index.3 MarchThe Best Choice Problem under Ambiguity
2010
Tatjana Chudjakow (University Bielefeld)
2.15pm - G.114, Alan Turing BuildingAbstractWe model and solve Best Choice Problems in the multiple prior framework: A decision maker aims to choose the best among a fixed number of applicants that appear sequentially in a random order. However, she is uncertain about the right probability model, i.e. the decision maker faces ambiguity about the probability that a candidate – a relatively top applicant — is actually best among all applicants. We show that our model covers the classical secretary problem, but also other interesting classes of problems. We provide a closed form solution of the problem for time-consistent priors using minimax backward induction. As in the classical case the derived stopping strategy is simple. Ambiguity can lead to substantial differences to the classical threshold rule.
3 MarchOn solving optimal stopping problems for Lévy processes in finite horizon
2010
Elena Boguslavskaya (London School of Economics)
3.15pm - G.114, Alan Turing BuildingAbstractWe present a way to solve optimal stopping problems with finite (or infinite) horizon for a Lévy process. We pay special attention to the case when the gain function is analytic and monotone. The main tool in our method is to construct the appropriate Appell function, and, consequently, find the optimal stopping boundary. Finally, we illustrate our method by several examples.
10 MarchSome recent developments in the theory of random times and enlargements of filtrations
2010
Ashkan Nikeghbali (University Zürich)
2.15pm - G.114, Alan Turing BuildingAbstract10 MarchGaussian fluctuations for Plancherel partitions
2010
Leonid V. Bogachev (University of Leeds)
3.15pm - G.114, Alan Turing BuildingAbstractThe limit shape of Young diagrams under the Plancherel measure was found by Vershik & Kerov (1977) and Logan & Shepp (1977). We obtain a central limit theorem for fluctuations of Young diagrams in the bulk of the partition 'spectrum'. More specifically, under a suitable (logarithmic) normalization, the corresponding random process converges (in the FDD sense) to a Gaussian process with independent values. We also discuss a link with an earlier result by Kerov (1993) on the convergence to a generalized Gaussian process. The proof is based on poissonization of the Plancherel measure and an application of a general central limit theorem for determinantal point processes. (Joint work with Zhonggen Su.)
17 MarchVon Neumann-Gale Dynamical Systems and their Applications in Finance
2010
Igor Evstigneev (University of Manchester)
2.15pm - G.114, Alan Turing BuildingAbstractVon Neumann-Gale dynamical systems are defined in terms of multivalued operators possessing certain properties of convexity and homogeneity. These operators assign to each element of a given cone a convex subset of the cone describing possible one-step transitions from one state of the system to another. The classical, deterministic theory of such dynamics was originally aimed at the modelling of economic growth (von Neumann 1937 and Gale 1956). First attempts to build a stochastic generalization of this theory were undertaken in the 1970s by Dynkin, Radner and their research groups. However, the initial attack on the problem left many questions unanswered. Substantial progress was made only in the late 1990s, and final solutions to the main open problems were obtained only in the last two or three years. Recently it has been observed that stochastic analogues of von Neumann-Gale systems provide a natural and convenient framework for financial modelling (asset pricing and hedging under transaction costs, capital growth theory). This observation gave a new momentum to studies in the field and posed new interesting questions. The talk will give an introduction into the theory, review recent progress and discuss applications.
24 MarchBand-limited Stochastic Processes In Discrete And Continuous Time
2010
D.S.G. Pollock (University of Leicester)
2.15pm - G.114, Alan Turing BuildingAbstractBAND-LIMITED STOCHASTIC PROCESSES IN DISCRETE AND CONTINUOUS TIME
By D.S.G. POLLOCK
University of Leicester
Email: stephen_pollock@sigmapi.u-net.com
In the theory of stochastic differential equations, it is commonly assumed that the forcing function is a Wiener process. Such a process has an infinite bandwidth in the frequency domain. In practice, however, all stochastic processes have a limited bandwidth. A theory of band-limited linear stochastic processes is described that reflects this reality, and it is shown how the corresponding ARMA models can be estimated. By ignoring the limitation on the frequencies of the forcing function, in the process of fitting a conventional ARMA model, one is liable to derive estimates that are severely biased. If the maximum frequency in the sampled data is less than the Nyquist value, then the underlying continuous function can be reconstituted by sinc function or Fourier interpolation. The estimation biases can be avoided by resampling the continuous process at a rate corresponding to the maximum frequency of the forcing function. Then, there is a direct correspondence between the parameters of the band-limited ARMA model and those of an equivalent continuous-time process.21 AprilMetric measure spaces and the transition function of a Levy process
2010
Niels Jacob (Swansea University)
2.15pm - G.114, Alan Turing BuildingAbstract21 AprilAn application of the Kusuoka-Lyons-Victoir cubature method to the numerical solution of the backward SDEs
2010
Dan Crisan (Imperial College London)
3.15pm - G.114, Alan Turing BuildingAbstractWe propose a new method for the numerical solution of backward stochastic differential equations (BSDEs) with Markovian terminal condition. The key property used here is that the solution of a BSDE can be written as an integral of a certain functional against the law of the underlying diffusion. The algorithm combines the Bouchard-Touzi-Zhang discretization of BSDEs with the Kusuoka-Lyons-Victoir cubature method. The main results concerning the propagation of the error are reported and a numerical example is included. This is joint work with Konstantinos Manolarakis.
28 AprilSmoothing based Lack-of-Fit (or Goodness-of-Fit) Tests
2010
Prakash Patil (University of Birmingham)
2.15pm - G.114, Alan Turing BuildingAbstractAbstract:
To construct a nonparametric (smoothing-based) test of lack-of-fit, one measures one way or other, the discrepancy between a smooth estimator of the unknown curve and the hypothesised curve. Although there are many possible choices for measuring this discrepancy, for being technically most easy to deal with, the lack-of-fit tests based on the ISE seem to have received the most(?) attention. But since a test based on the ISE requires the estimation of the unknown curve, its ability to distinguish between the null model and the departures from the null model is linked to the smoothing parameter that one chooses to estimate the curve. Whereas, if one takes a local view and then constructs a test, one can show that the test has better power properties. And although the performance of the test is still linked to the smoothing parameter, the choice of smoothing parameter will now be dictated by the `testing' aspect of the problem rather than be driven by the estimation of the unknown curve. In this talk, we will mainly use regression quantile curves to illustrate the above points but will show that this procedure could be used for density and hazard rate curves.5 MaySome thought on Parameter-dependent Optimal Designs
2010
J N S Matthews (Newcastle University)
(later start) 4pm - G.207, Alan Turing
AbstractAbstract will appear here
12 MayLinear SPDEs: Anticipation and Dynamics
2010
Salah-Eldin A. Mohammed (Southern Illinois University, Carbondale, Illinois)
2.15pm - G.114, Alan Turing BuildingAbstractWe use ideas from stochastic dynamics to study anticipating properties of linear stochastic partial differential equations, their long-time asymptotics and their invariant subspaces.
19 MayModel Selection of Correlation Structure for Clustered Data
2010
Annie Qu (University of Illinois at Urbana-Champaign)
2.15pm - G.114, Alan Turing BuildingAbstractAbstract:
Model selection of correlation structure is a challenging problem because it involves a higher order of moments than model selection of covariates only. However, the correct specification of the correlation structure plays an important role in improving estimation efficiency for clustered data. Our strategy is to approximate the empirical estimator of the correlation matrix as closely as possible using a pool of basis matrices candidates, and penalize models involving too many basis matrices. The proposed method has the advantages of not requiring the likelihood function and of being computationally efficient. In addition, it can identify complex correlation structures through the group-wise selection strategy from a large number of basis matrices, and is applicable for both continuous and discrete response data. In theory, we show that the proposed method enjoys the oracle property of selecting the true correlation structure consistently and estimating the correlation parameters with the same asymptotic normal distribution as if the true structure is known. Our simulation studies and data example show that the proposed method works effectively to select the true structure. This is joint work with Jianhui Zhou of University of Virginia.19 MayA Darboux-Wiener type lemma and random walk self-intersections
2010
George Deligiannidis (University of Leicester)
2.15pm - University Place 5.207AbstractWe state and prove a Darboux-Wiener type complex Tauberian lemma which removes the monotonicity restrictions of the classical Tauberian theorem. The lemma is then applied to obtain an exact asymptotic for the variance of the self-intersections of a recurrent, integer-valued random walk attracted to the symmetric Cauchy law.
19 MayOn Ruin Probabilities in Models with Constant Interest Rate
2010
Alexander Novikov (University of Technology Sydney)
3.15pm - University Place 5.207AbstractWe find an explicit formula for the finite-time ruin probability in a discrete-time collective ruin model with constant interest rate when a size of claims has a hyperexponential distribution. We find also a theoretical bound for accuracy of approximations of the finite-time ruin probabilities in terms of a distance between a distribution of claims and its approximation. Results of numerical comparisons with asymptotic formulas and simulations are presented. Similar results are obtained for the continuous-time collective ruin model with constant interest rate, Poisson arrivals for claims having a hyperexponential distribution for individual claims.
26 MayAdapting to design sparsity in univariate and bivariate local linear regression
2010
Ming-Yen Cheng (UCL)
2:15pm - 3.209 University placeAbstractAbstract: Local linear regression enjoys many nice theoretical properties such as automatic boundary correction and linear minimax optimality, and has become very popular in applications. In finite sample cases, however, the local least squares problem in local linear estimation becomes ill-posed when the design is sparse and, as a result, the local linear estimator either does not exist or exhibits drastic roughness in the sparse design regions. Many methods have been proposed to address this serious problem in the univariate case, however, they all require extra tuning parameters. We propose a new method to tackle this problem in both the univariate and the bivariate cases. The method is computationally simple and does not involve any extra tuning parameters. The finite sample variance of the modified local linear estimator is bounded above. We further show that it has the same asymptotic mean squared error as the original local linear estimator. Numerical studies demonstrate that it has very good finite sample performance.
2 JuneOn the non linear stochastic Schrodinger equation
2010
Annie Millet (Université Paris 1)
2.15pm - University Place 5.207AbstractWe consider a non linear Schrödinger equation on a compact manifold of dimension d subject to some multiplicative random perturbation. Using some stochastic Strichartz inequality, we prove the existence and uniqueness of a maximal solution in H^1 under some "general" conditions on the diffusion coefficient. Under stronger conditions we deduce the existence of a global solution. This is a joint work with Z. Brzezniak.
10 JuneOn the Ito-Wentzell formula for distribution-valued processes and related topics
2010
Nicolai V. Krylov (University of Minnesota)
2.15pm - University Place 3.214AbstractWe prove the Ito-Wentzell formula for processes with values in the space of generalized functions by using the stochastic Fubini theorem and the Ito-Wentzell formula for real-valued processes, appropriate versions of which are also proved.
1st Semester 2009/2010
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9 SeptemberIntegral stochastic orderings and associated random variables
2009
Jørgen Hoffmann-Jørgensen (University of Aarhus)
2:00pm - Frank Adams 2 (room 1.212), Alan Turing BuildingAbstract30 SeptemberThe stochastic heat equation in high dimensions: existence and Gaussian estimates for the density.
2009
Lluís Quer i Sardanyons (Universitat Autònoma de Barcelona)
2:15pm - G.207, Alan Turing BuildingAbstractWe consider a stochastic heat equation in any space dimension and with a Gaussian random perturbation which is white in time and has some general spatially homogeneous correlation. First, we establish optimal conditions on the spectral measure associated to the noise ensuring that the law of the solution is absolutely continuous with respect to the Lebesgue measure. Secondly, in the case where the diffusion coefficient is constant, we aim to prove that the probability density admits lower and upper bounds of Gaussian type. The main ingredients in the proofs are based on a extension of Walsh's stochastic integral, which turns out to be equivalent to Dalang's one, and Malliavin calculus techniques. Indeed, we apply recently-obtained results of Nourdin and Viens, where they provide a general criterium for a smooth random variable in the Wiener space to posses a density admitting lower and upper Gaussian bounds.
7 OctoberFunctional Principal Component Analyses of Biomedical Images as Outcome Measures.
2009
Nick Fieller (University of Sheffield)
2.15pm - G.207, Alan Turing BuildingAbstractFunctional Principal Component Analyses of Biomedical Images as Outcome Measures
Nick Fieller
Department of Probability & Statistics, University of Sheffield
Medical imaging provides a non-destructive method of direct investigation of effects of treatments on target tissues. This allows tissue to be examined on several occasions during the course of treatment, thus avoiding inter-individual variability. This presentation investigates methodology for assessing the statistical differences between images and hence the effectiveness (or otherwise) of the treatment. The first study described here involved collection of three-dimensional images by MRI before and after treatment on individuals receiving one of a range of doses. Data extracted from the images were the separate voxel values of parameters of interest. Statistical analysis focuses on the univariate and bivariate frequency distributions of these voxel values. The main analysis is based upon functional principal component analysis of the kernel density estimates obtained from each distribution. Statistical assessment of the effects of treatment is based upon a randomization test involving the differences in PC scores between images before and after treatment. Other examples include studies of lung function and in vivo does-response studies of the effect of insulin binding agonists on cell activity where the techniques are compared with parametric log-hyperbolic modelling. The talk outlines the various stages in the development of the analysis as well as some avenues which did not prove productive in these particular studies15 OctoberEquality of BLUEs or BLUPs under two linear models
2009
Simo Puntanen (University of Tampere, Finland)
2.00pm - G.107, Alan Turing Building
(note: it is a Thursday and the start is on the hour)AbstractEquality of BLUEs or BLUPs under two linear models
Simo Puntanen
Department of Mathematics and Statistics,
FI-33014 University of Tampere, Finland
email: simo.puntanen@uta.fi
Abstract In this talk we consider mixed linear models, possibly with singular covariance matrices, by supplementing a particular fixed effects model with appropriate stochastic restrictions. We show that all representations of the best linear unbiased estimator (BLUE) and best linear unbiased predictor (BLUP) can be obtained through the augmented model including stochastic restrictions. Using this approach, we consider two mixed linear models, $M_1$ and $M_2$, say, which have different covariance matrices. We give necessary and sufficient conditions that the BLUP and/or BLUE under the model $M_1$ continue to be BLUP and/or BLUE also under the model $M_2$.
This is joint work with
Stephen J. Haslett
Massey University, Palmerston North, New Zealand21 OctoberModelling the association between patient characteristics and the change over time in a disease measure using observational cohort data
2009
Andrew Copas (University College London)
4:00pm - G.207, Alan Turing BuildingAbstractModelling the association between patient characteristics and the change over time in a disease measure using observational cohort data
L. Harrison, D. T. Dunn, H. Green and A. J. Copas
Hub for Trials Methodology Research, MRC Clinical Trials Unit, London
In observational cohort studies we may wish to examine the associations between the fixed patient characteristics and the longitudinal changes from baseline in a repeated outcome measure. Many biological and other outcome measures are known to be subject to measurement error and biological variation. In an initial analysis we may fit a regression model to all outcome measurements, accounting for all the identified sources of variability, and see how the characteristics are linked to the change for typical patients. However, the characteristics may also be linked to different distributions of the underlying outcome value at baseline, which itself may be correlated with the change over time. Therefore, if we wish to examine the change over time for patients of different characteristics but with the same underlying baseline value then the initial approach is confounded by the baseline values. Furthermore, if we attempt to remove this confounding by including the observed baseline measure as a covariate in a model for later measurements, then this may provide an approximate solution but is likely to introduce some bias. We propose a method based on first following the initial approach but then, applying a correction to the parameter estimates. This allows the predicted trajectories to be plotted and valid significance tests of association with characteristics. Our approach is compared with other methods and illustrated through a simulation study and an analysis of the association between HIV-1 subtype and immunological response after starting antiretroviral therapy.28 OctoberLog-Harnack inequality and applications
2009
Fengyu Wang (Swansea University/Beijing Normal University)
2:15pm - Frank Adams 2 (room 1.212), Alan Turing BuildingAbstractBy using the $L^2$-gradient estimate of diffusion semigroups with non-constant diffusion coefficients, the parabolic log-Harnack inequality is established. As applications, the strong Feller property and the entropy inequality for heat kernels is proved for a class of SPDEs with multiplicated noises.
4 NovemberEuropean, Asian and American options with discrete dividend payments
2009
Sam Howison (University of Oxford)
2:15 pm - University Place 1.218AbstractThis talk looks at a rather old-fashioned problem, option pricing in a Black-Scholes world, and specifically at the differences that occur between models in which dividends are paid, or averages are sampled, in a continous-time way, and those in which the payment or sampling is discrete. Some intricate phenomena appear, and they will be explored using asymptotic methods and in particular the method of multiple scales.
11 NovemberDISTRIBUTIONOLOGY
2009
Chris Jones (Open University)
2.15pm - G.205, Alan Turing BuildingAbstractDISTRIBUTIONOLOGY
The silly title is my shorthand way of saying that the talk will be about the study of parametric families of distributions and the fitting of them to data. I will concentrate on four-parameter distributions for univariate continuous data taking values on the whole real line. The four parameters consist of the usual location and scale parameters plus two shape parameters which between them allow for skewness and variation in tailweight. The first, and longer, part of the talk will be about "sinh-arcsinh distributions" (Jones & Pewsey, forthcoming) which allow both lighter and heavier tails than their generating distribution. In addition to looking at various properties of these distributions, I note that tests of normality (and symmetry) based on them are powerful quite generally in both heavy- and light-tailed situations. The second part of the talk will concern issues of parameter orthogonality. It turns out that "two-piece distributions", of much longer history, can be made to have helpful properties in this regard.18 NovemberRobust clustering using exponential power mixture models
2009
Jian Zhang (York University)
2.15pm - G.205, Alan Turing BuildingAbstractRobust Clustering Using Exponential Power Mixtures
Jian Zhang
Clustering is a widely used technology in extracting useful information from gene expression data, where unknown correlation structures in genes are believed to persist even after normalisation. Such correlation structures pose a great challenge to the conventional clustering methods, such as the Gaussian mixture model (GM), k-means (KM), and partitioning around medoids (PAM), as they are not robust against general dependence within data. Here we use the exponential power mixture model to increase the robustness of clustering against general dependence and non-Gaussian components in the data. An expectation-conditional-maximisation algorithm is developed to calculate the maximum likelihood estimators of the unknown parameters in these mixtures. The Bayesian Information Criterion (BIC) is then employed to determine the numbers of components of the mixture. The maximum likelihood estimators are shown to be consistent under sparse dependence. Our numerical results indicate that the proposed procedure outperforms GM, KM, and PAM when there are strong correlations or non-Gaussian components in the data.24 NovemberA multi-dimensional generalisation of a theorem of Matsumoto and Yor
2009
Neil O'Connell (University of Warwick)
1.00pm - G.113, Alan Turing Building (note: it is a Tuesday)AbstractMatsumoto and Yor (1999) proved that, if $X$ is a Brownian motion with drift, then $\int_0^t \exp(2X(s)-X(t)) ds$ is a diffusion process in its own flitration, with is strictly smaller than the filtration of $X$. This can be regarded as an exponential analogue of Pitman's celebrated $2M-X$ theorem, which states that, if $M(t)=\max_{0\le s\le t} X(s)$, then $2M-X$ is a three- dimensional Bessel process with parameter $|\mu|$, where $\mu$ is the drift of $X$. In fact, Pitman's theorem can be recovered from the theorem of Matsumoto and Yor by Brownian scaling and the method of Laplace. In recent years, various multi-dimensional generalisations of Pitman's theorem have been obtained in which Dyson's non-colliding Brownian motions play the role of the three-dimensional Bessel process. I will describe a multi- dimensional generalisation of the theorem of Matsumoto and Yor. In this setting, the analogue of Dyson's non-colliding Brownian motions is a multi- dimensional diffusion which is closely related to a quantum integrable system known as the quantum Toda lattice.
2 DecemberM-estimation in the conditional heteroscedastic models.
2009
Kanchan Mukherjee (Lancaster University)
2.15pm - G.207, Alan Turing BuildingAbstractIn this talk we discuss properties of a class of M-estimators in the conditional heteroscedastic models. The class of estimators includes least absolute deviation and Huber's estimator as well as the well-known quasi maximum likelihood estimator. For some estimators, the asymptotic normality results are obtained only under the existence of fractional unconditional moment assumption on the error distribution and some mild smoothness and moment assumptions on the score function. Application to the analysis of financial data sets will be described.
9 DecemberTaylor expansions and numerical approximations of stochastic PDEs
2009
Peter Kloeden (J.W. Goethe-University Frankfurt)
4.00pm - G.114, Alan Turing BuildingAbstractt.b.a.
16 DecemberMaximum likelihood estimation of a multidimensional log-concave density.
2009
Richard Samworth (Cambridge University)
2.15pm - G.205, Alan Turing BuildingAbstractTitle: Maximum likelihood estimation of a multidimensional log-concave density
Abstract
We show that if $X_1,...,X_n$ are a random sample from a density $f$ in $\mathbb{R}^d$, then with probability one there exists a unique log-concave maximum likelihood estimator $\hat{f}_n$ of $f$. The use of this estimator is attractive because, unlike kernel density estimation, the estimator is fully automatic, with no smoothing parameters to choose. We exhibit an iterative algorithm for computing the estimator and show how the method can be combined with the EM algorithm to fit finite mixtures of log-concave densities. Applications to classifcation, clustering and functional estimation problems will be discussed, and the talk will be illustrated with pictures from the R package LogConcDEAD. Finally, I will present some recent results on the theoretical performance of the estimator.
Co-authors: Madeleine Cule (University of Cambridge), Robert Gramacy (University of Cambridge) and Michael Stewart (University of Sydney).2nd Semester 2008/2009
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4 FebruarySpace-Time modeling of coupled variables.
2009
Luigi Ippoliti (University G. d'Annunzio)
2.15pm - G.207, Alan Turing BuildingAbstractWe'll present preliminary results on a dynamic model for spatio-temporal coupled variables. The model is discussed in a state-space framework which results useful to provide full probabilistic inference for the model parameters, interpolation and forecast of the variables of interest. The role of the measurement matrix in spatial interpolation is also considered and both the use of deterministic and stochastic spatial patterns will be discussed. This is a joint work with D. Gamerman, P. Valentini and L. Fontanella.
4 February (as above!)Supervised classification of Infrared Imaging Signals.
2009
Simone Di Zio (University G. d'Annunzio)
3.15pm - G.207, Alan Turing BuildingAbstractIn this talk we'll consider the problem of analysing data related to the Raynaud's syndrome. Raynaud's phenomenon (RP) is defined as an episodic vasoconstriction, in response to cold or emotional stress of fingers' small arteries. The syndrome can present two different levels distinguishing Primary RP (PRP) and Scleroderma (SSC) patients, and the main goal is to discriminate PRP from SSC. By analysing Infrared Imaging signals we shall discuss the problem of extracting discriminating variables, also using functional data analysis techniques.
11 FebruaryErgodic Hamilton-Jacobi-Bellman Equation in Infinite Dimensions
2009
Bohdan Maslowski (Academy of Sciences of Czech Republic)
2.15pm - G.207, Alan Turing BuildingAbstractRecent results obtained jointly with Ben Goldys on stochastic ergodic control of SPDEs will be outlined. The optimal cost and optimal ergodic control may be found in a feedback form by means of the solution to an appropriate stationary HJB equation in a Banach space, the existence and uniqueness of which has been proved. The results are applicable to controlled stochastic reaction-diffusion equations.
18 FebruaryL-splines within the mixed model framework
2009
Sue Welham (Rothamsted Research)
2.15pm - G.207, Alan Turing BuildingAbstractL-splines within the mixed model framework
Sue Welham, Rothamsted Research
It is now well-known that the cubic smoothing spline can be fitted within the linear mixed model framework using REML estimation of the smoothing parameter. This method is becoming increasingly popular in practical data analysis as it provides the ability to model nonlinear functions whilst allowing for appropriate, possibly complex, covariance structures, and can be fitted using standard mixed model software. The wider class of L-splines can similarly be fitted within the mixed model framework. This talk will describe the class of L-splines, show how they can be fitted as linear mixed models and will discuss whether there is any real advantage in using these functions rather than the simpler cubic smoothing spline model.4 MarchStationary time series and long memory
2009
Nicholas Bingham (Imperial College London)
2.15pm - G.207, Alan Turing BuildingAbstractIn the classical theory of stationary time series and prediction theory in discrete time, the structure is described either by a spectral measure on the unit circle, or alternatively by the autocorrelation function. An alternative description is known, in terms of the partial autocorrelation function or PACF. This has various advantages, for example it gives an unrestricted parametrization. This fact was known long ago in the theory of orthogonal polynomials on the unit circle (OPUC), where it is the content of Verblunsky's theorem. Baxter's theorem gives a necessary and sufficient condition for the PACF sequence to be summable (absolutely convergent). This and related matters have been explored in a series of recent papers by Inoue and Kasahara (separately and together). The two leading candidates for a definition of long-range dependence (LRD) are considered in this light. We propose a new definition: LRD = PACF non-summable.
4 MarchScientific and statisitical computing in the cloud, towards a federative and collaborative platform for research and education
2009
Karim Chine (Cloud Era Ltd, Cambridge UK; visting fellow at NCeSS)
4:00pm - G.207, Alan Turing BuildingAbstractWe propose to build on top of R, the highly popular statistical environment, an open platform for computing and data analysis. Using a rich workbench within the browser, the statistician can now work with an R server running at any location as if it was local to his machine. The platform hides the complexity of High Performance Computing or cloud computing Infrastructures and the computational resource is abstracted with a simple URL. The new platform widens the scope of the computational research resources that can be easily shared. Besides the interoperable software components, the R packages, the statistician can share functions and algorithms as Web Services or as nodes for workflow workbenches. Plugins/Views for the workbench can be created with a drag & drop editor, published and reused. An R server can also be shared: Statistician and collaborators can connect their workbenches to the same R and analyze shared data collaboratively via a set of broadcasted and high interaction views. The collaborative views include a highly programmable spreadsheet fully integrated with R functions and data. The new platform makes distributed computing accessible to a larger number of statisticians. Easy-to-use functions enable the control from within an R session of several R servers running at any location as additional workers or as clusters to solve embarrassingly parallel problems. The seminar will give an overview of the new platform. Biocep's deployment on Amazon Elastic Compute Cloud (EC2) will be demonstrated.
project web site : www.biocep.net
virtual R workbench : www.biocep.net/rworkbench.jnlp11 MarchExploring Change Point Distributions through HMMs.
2009
John Ashton (Warwick University )
2.15pm - G.207, Alan Turing BuildingAbstractFinite state Hidden Markov Models (HMMs) provide a way to model sequences and time series subject to sudden structural breaks or change points. Exact change point distributions in general finite state HMMs, including Markov switching models, will be found by exploiting the duality between the location distributions and the waiting time distributions of runs in the state sequence of an HMM. These distributions can help quantify uncertainty in change point locations and other features of interest in the data series. The methodology has wide application and examples will be used to motivate the methodology. These applications include finding the uncertainty in gene locations in bioinfomatics, assessing the uncertainty in recession starts and ends in econometrics and determining emotional changes during psychological experiments performed using fMRI.
Joint work with Michael Jyh-Ying Peng and Donald Martin11 MarchStrong Feller property for equations with Levy noise.
2009
Jerzy Zabczyk (Polish Academy of Sciences)
2.15pm - G.113 (note the change), Alan Turing BuildingAbstractIn the first part of the talk we investigate the strong Feller property for Ornstein-Uhlenbeck processes with Levy noise both in finite and infinite dimensional Hilbert spaces. The second part is devoted to some extensions to non-linear equations with additive perturbations.
Presented results are based on a joint research with Enrico Priola.18 MarchJOURNAL QUALITY AND RESEARCH RATINGS: A Statistical Audit of the Results of the 2001 RAE via Maximum Likelihood
2009
Michael Cain (University of Wales)
2.15pm - G.207, Alan Turing BuildingAbstract25 March (as above!)The optimal design of choice experiments
2009
Peter Goos (University of Antwerpen)
3.30pm - G.207, Alan Turing BuildingAbstractStated preference data are commonly collected by means of conjoint choice experiments or discrete choice experiments in marketing, health economics or environmental economics. The optimal design of these experiments is a challenging research area because of the nonlinearity of the statistical models used to analyze the data. These models include the conditional logit model, the mixed logit model and the nested logit model. In this talk, I will discuss recent advances in the optimal design for such models as well as some of the challenging computational aspects of the optimal design search.
25 MarchAsymptotics of killed Markov processes, with applications to the biodemography of ageing
2009
David Steinsalz (University of Oxford)
2.15pm - G.207, Alan Turing BuildingAbstractThe convergence of Markov processes to stationary distributions is a basic topic of introductory courses in stochastic processes, and the theory has been thoroughly developed. What happens when we add killing to the process? The process as such will not converge in distribution, but the survivors may; that is, the distribution of the process, conditioned on survival up to time t, converges to a "quasistationary distribution" as t goes to infinity.
This talk presents recent work with Steve Evans, proving an analogue of the transience-recurrence dichotomy for killed one-dimensional diffusions. Under fairly general conditions, a killed one-dimensional diffusion conditioned to have survived up to time t either escapes to infinity almost surely (meaning that the probability of finding it in any bounded set goes to 0) or it converges to the quasistationary distribution, whose density is given by the top eigenfunction of the adjoint generator.
These theorems arose in solving part of a longstanding problem in biological theories of ageing, and then turned out to play a key role in a very different problem in population biology, the effect of unequal damage inheritance on population growth rates.22 AprilSingular control with partial information of jump diffusions
2009
Bernt Øksendal (University of Oslo)
2.15pm - G.207, Alan Turing BuildingAbstractSingular control theory is a topic with many applications, e.g. to optimal harvesting in biology or to optimal trading with transaction costs in finance. The classical approach to singular stochastic control problems of jump diffusions is based on variational inequalities. This is a powerful method, but it assumes that the system is Markovian and that the controller has access to the full information generated by the underlying driving processes (Brownian motion and Poisson random measures). However, in many real life situations this is not the case. For example, in applications to finance the trader may only have access to a delayed information flow. This brings us outside the Markovian setting, and variational inequalities can no longer be used.
To handle such cases we use Malliavin calculus for Lévy processes. We obtain conditions for optimality of the singular control in this general setting. The conditions may be regarded as general path dependent versions of the classical variational inequalities. The results are illustrated by examples.
The talk is based on joint work in progress with Agnès Sulem, INRIA, Paris.29 AprilOn the behaviour in the space parameter of solutions of the stochastic heat equation
2009
Sigurd Assing (University of Warwick)
2.15pm - G.207, Alan Turing BuildingAbstractThe stochstic heat equation defines a two-parameter random field which follows Levy's Markov property. We reconsider the proof of this result but apply a new technique based on enlargement of filtrations revealing a new structure of the random field in the space parameter.
13 MayMultivariate utility maximization with proportional transaction costs
2009
Mark P. Owen (Heriot-Watt University)
2.15pm - G.207, Alan Turing BuildingAbstractMy talk will be about optimal investment in Kabanov's model of currency exchange with transaction costs. The model is general enough to allow a random, discontinuous bid-offer spread. The investor wishes to maximize their "direct" utility of consumption, which is measured in terms of consumption assets linked to some (but not necessarily all) of the traded currencies. The analysis will centre on two conditions under which the existence of a dual minimiser leads to the existence of an optimal terminal wealth. The first condition is a well known, but rather unintuitive, condition on the utility function. The second weaker, and more natural condition is that of "asymptotic satiability" of the value function. We show that the portfolio optimization problem can be reformulated in terms of maximization of a terminal liquidation utility function, and that both problems have a common optimizer. This is joint work with Luciano Campi.
8 June (Monday!)Two-Way ANOVA with Random Cell Sizes.
2009
Peter Moschopoulos (The University of Texas at El Paso)
2.15pm - Horace Lamb Room (1.204), Alan Turing BuildingAbstractWe consider inference for row effects in the presence of possible interactions in a two-way fixed effects model when the numbers of observations are themselves random variables following the multinomial distribution with unknown probabilities. This situation occurs commonly in survey-type studies where the observations are categorized into the cells of an ANOVA table after the sample is drawn. The paper focuses on testing the hypothesis of equality of row means. With the cell probabilities assumed unknown, there is no obvious sum of squares and F-ratio computed by the widely available statistical packages for testing this hypothesis. Under the multinomial assumption, we find the asymptotic joint distribution of the sample row means. The result is then used to construct a sensible asymptotic test of the equality of the corresponding row means and asymptotic simultaneous confidence intervals for contrasts. The talk is based on joint work with Steve Arnold (under review).
References
Moschopoulos, P.G., and Davidson, M.I. (1985), "Hypothesis Testing in ANOVA under Multinomial Sampling", Sankhyã, Ser. B Vol. 47, Pt. 3, pp. 301-309.1st Semester 2008/2009
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15 September (Monday!)Accounting for Covariance in Nonparametric and Semiparametric Modeling of Longitudinal Observations.
2008
Naisyin Wang (Texas A&M University, USA)
2.15pm - Frank Adams (room 1.212), Alan Turing BuildingAbstractThe analysis of hierarchical biomedical data sometimes requires more modeling flexibility than that can be provided by standard parametric approaches. It is commonly believed that the effect of ignoring covariance structure is mainly on the lost of efficiency. In this talk, I will discuss some recently developed nonparametric or semiparametric models for longitudinal observations. I will use numerical outcomes and examples to illustrate some potential concerns when one ignores the correlations in longitudinal measurements. The less known fact is the serious biases that could be induced by ignoring correlations in the longitudinal covariate observations. The modeling consideration of the use of functional principle component analysis in a recently developed nonparametric latent-feature regression model will also be discussed.
1 OctoberDesigning for and Fitting Latent Variable Models for Paired Comparisons Studies
2008
Ben Torsney (University of Glasgow)
2.15pm - Frank Adams (room 1.212), Alan Turing BuildingAbstractWhen there is control of explanatory variables, say x, in a regression model at which of their permitted values should observations be taken and in what proportion? This defines the approximate optimal design problem, the theory of which, will be briefly reviewed, with a particular focus on generalised linear models (glm's) and algorithms for determining optimal design weights. In the case of non-linear models optimal designs are parameter dependent (locally optimal), but in the case of glm's a canonical approach of Ford et al. (JRSSB, 1992) can, through a parameter dependent transformation, convert the design problem to that for a weighted linear model. Models such as Bradley Terry or Thurstone models for data arising from paired comparisons experiments also generate weighted linear design problems. In a simple version of these a subject has to indicate which of two 'treatments' Ti, Tj is preferred. We observe Oij, the frequency with which Ti is preferred to Tj. Under the above models P(Ti is preferred to Tj) = F(li - lj), where F(.) is a distribution function and (li) is a treatment index. For identifiability purposes pi = ln(li) can be treated as a positive weight. Thus theorems and algorithms from the optimal design arena carry over to the maximum likelihood estimation of these parameters as well as to determining locally optimal designs. We will explore this fusion of topics, Time permitting the parallel can be taken beyond simple paired comparisons experiments to models for orderings or rankings and to models under which treatments are defined by a design vector of characteristics x.
8 OctoberMarket completion using options
2008
Mark H. A. Davis (Imperial College London)
2.15pm - Frank Adams (room 1.212), Alan Turing BuildingAbstractMathematical models for financial asset prices which include, for example, stochastic volatility or jumps are incomplete in that derivative securities are generally not replicable by trading in the underlying asset. In earlier work [Proc. R. Soc. London 2004], the first author provided a geometric condition under which trading in the underlying asset and a finite number of vanilla options completes the market. We complement this result in several ways. First, we show that the geometric condition is not necessary and a weaker, necessary and sufficient, condition is presented. This condition simplifies to matrix non-degeneracy in a single point when the pricing functions are real analytic functions. In particular, any stochastic volatility model is then completed with an arbitrary European type option. Further, we show that adding path-dependent options such as a variance swap to the set of primary assets, instead of plain vanilla options, also completes the market.
15 OctoberSome ideas on statistical arbitrage for online implementation
2008
Kostas Triantafyllopoulos (Sheffield University)
2.15pm - Frank Adams (room 1.212), Alan Turing BuildingAbstractIn this talk I will discuss two frameworks of practical implementation of statistical arbitrage. In the first part I will look at arbitrage opportunities based on relative misspricing of two assets that in the long term exploit mean reversion. A Bayesian time series model is employed to model the dynamics of spreads between the two prices and an online estimation approach is adopted so that we can monitor mean reversion in real time. I will consider simulated data as well as real data consisting of equity data and some of the, relatively new exchange traded funds. In the second part I will discuss a new market neutral arbitrage strategy, which is similar to index arbitrage. I consider the S&P 500 Price index and the objective is to identify constituents of the index (future contracts) that are most correlated with the index itself. Using an online version of PCA we detail 2 trading strategies that allow us to realize arbitrage opportunities. Some relevant ideas on data mining in finance will be briefly discussed.
27 October (Monday!!!)SPDEs driven by Levy noise: new results
2008
Erika Hausenblas (University of Salzburg)
2.00pm - Frank Adams 2 (room 1.212), Alan Turing BuildingAbstractI will start with Levy processes and the notation of Poisson random measures. The next point will be stochastic integration in Banach spaces with respect to Levy processes. Finally, I will present some new results about existence to solutions of SPDEs.
29 OctoberPortfolio optimization for a large trader
2008
Thorsten Rheinländer (London School of Economics)
2.15pm - Frank Adams (room 1.212), Alan Turing BuildingAbstractOne of the classic but unrealistic assumptions of many studies in mathematical finance is that all traders are assumed to be 'small', i.e. are just acting as price takers. This has been relaxed in several studies allowing for a situation where there is in addition to a pool of small traders also one 'large' investor around who faces different prices for her transactions depending on the trade size. We will discuss issues like arbitrage opportunities and stealth trading, and in particular focus on optimization of expected utility from terminal wealth. It turns out that the large trader can destabilize the market, depending on the strength of her impact on the price process.
12 NovemberNavier's boundary-value problem of Stochastic Navier-Stokes equations
2008
Zhongmin Qian (University of Oxford)
2.15pm - Frank Adams (room 1.212), Alan Turing BuildingAbstractt.b.a.
19 NovemberBiological Kinetics: Design of Experiments and Data Analysis
2008
Steven Gilmour (Queen Mary, University of London)
2.15pm - Frank Adams (room 1.212), Alan Turing BuildingAbstractIn drug development and other areas of biotechnology, as well as in theoretical studies in biochemistry, it is important to characterise the steady-state kinetics of enzymes. Biochemical theory leads to nonlinear models relating the enzyme reaction rate to the substrate concentration. Various methods have been used to estimate the parameters of the Michaelis-Menten model, but for higher order models, the most general and successful method seems to be the transform-both-sides methodology of Ruppert and Carroll. A new, more stable method of fitting these models in the context of replicated experiments, will be described and shown to have good properties. The choice of substrate concentrations at which to experiment is a problem of optimal design of experiments. A method for obtaining Bayesian exact designs will be described, which makes a novel use of some computational shortcuts, which allow us to handle complex models. The stability of these designs under different prior assumptions will be explored.
26 NovemberCylindrical Levy Processes
2008
Dave Applebaum (The University of Sheffield)
2.15pm - room G.108 (room changed!!!), Alan Turing BuildingAbstractCylindrical probability measures are finitely additive measures on Banach spaces that have sigma-additive projections to Euclidean spaces of all dimensions. They are naturally associated to notions of weak random variable and hence weak processes which may be good candidates to be the driving noise in stochastic evolution equations. In this talk I'll focus on cylindrical Levy processes. These have (weak) Levy-Ito decompositions and an associated Levy-Khintchine formula. If the process is weakly square integrable, its covariance operator can be used to construct a reproducing kernel Hilbert space in which the process has a decomposition as an infinite series built from a sequence of uncorrelated bona fide one-dimensional Levy processes. This series is used to define cylindrical stochastic integrals from which you can develop cylindrical Ornstein-Uhlenbeck processes. (Based on joint work with Markus Riedle)
3 DecemberInterpretable discrimination and classification (cancelled)
2008
Nikolay Trendafilov (Open University)
2.15pm - Frank Adams (room 1.212), Alan Turing BuildingAbstractAbstract: Discriminant analysis (DA) is a descriptive multivariate technique for analyzing grouped data. Recently DA has also been viewed as a promising dimensionality reduction technique. The best known variety of DA is linear discriminant analysis (LDA), whose central goal is to describe the differences between the groups in terms of discriminant functions defined as linear combinations of the original variables. The interpretation of the discriminant functions is based on the coefficients of the original variables in the linear combinations. The problem is that the interpretation can be clear and obvious if there are only few large coefficients and the rest are all close to or exactly zero. Two approaches for obtaining interpretable discriminant functions will be considered. The first one is based on the LDA modified so that the discriminant functions satisfy the additional LASSO constraint. The LASSO inequality constraint requires that the sum of the absolute values of the coefficients of a unit length vector be less than some pre-specified threshold. The idea is very simple: as the threshold decreases, an increasing number of coefficients are driven to zero, or close to it. These DALASS discriminant functions have loadings vectors with the largest entries corresponding to the variables that dominate the discrimination. The second approach seeks approximate discriminant functions whose loadings vectors can be classified one of the following three ways: homogeneous, contrast or sparse. The resulting approximate discriminant functions should therefore be much easier to interpret than their exact counterparts as they require low computational cost, are easy to interpret because most of the loadings are 0s, and approximate the original discriminant functions.
8 December (Monday!!!)Hitting probabilities for stochastic waves
2008
Marta Sanz-Sole (University of Barcelona)
2.00pm - Simon 4.47 (NOT Alan Turing!)AbstractFor $\mathbb{R}^d$-valued stochastic processes $\{v(x), x\in \mathbb{R}^m\}$, we shall discuss conditions providing lower and upper bounds for the hitting probabilities $P\{v(I)\cap A\ne\emptyset\}$ in terms of the capacity and the Hausdorff measure of $A$, respectively. Applications to the stochastic wave equation with additive correlated noise will be given. The results are part of ongoing work with R. Dalang.
8 December (Monday!!!)Self-organized criticality and SPDEs
2008
Michael Röckner (University of Bielefeld)
3.00pm - Simon 4.47 (NOT Alan Turing!)Abstractnot available
17 DecemberNonparametric methods for biological and psychometric data
2008
Kamila Zychaluk (University of Liverpool)
2.15pm - Frank Adams (room 1.212), Alan Turing BuildingAbstractBiological experiments often involve data with non-Gaussian distributions that belong to the exponential family. Such data are customarily modelled by generalised linear models. Examples include psychometric experiments, and responses from nerve fibres. But the results of analysis based on generalised linear models can strongly depend on the chosen link function. In practice the correct link is rarely known, and a poorly motivated link can lead to biased results and misleading inferences. This problem is avoided if a nonparametric method, such as local linear fitting, is used instead. The local method still requires the link function to ensure that the estimated response does not take impossible values (e.g. negative mean for Poisson distribution), but the results are much less dependent on the form of the link function. Thus the analysis is less dependent on arbitrary model choices. The local method has its own problems, such as the choice of the smoothing parameter, or the choice of the kernel. The first of these issues is most important in practice, and thus will be discussed in more detail. Other problems related to local smoothing and suggestions for further development will be discussed.
2nd Semester 2007/2008
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30 JanuaryLocal time and the pricing of time-dependent barrier options.
2008
Aleksandar Mijatovic
2.15pm - G.108, Alan Turing BuildingAbstractA time-dependent barrier option is a derivative security which delivers the terminal value of the payoff at expiry T if neither of the continuous time-dependent barriers b, B: [0,T] -> R (satisfying b(t) < B(t) for all t) have been hit during the time interval [0,T]. In this talk we describe a decomposition of the time-dependent barrier option price into the corresponding European option price minus the barrier premium for a wide class of linear diffusions, possibly discontinuous payoff functions and twice differentiable barrier functions b, B. We show that the barrier premium can be expressed as an integral of the option's delta at the barriers and that the pair of functions describing the deltas at the barriers solves a system of Volterra integral equations of the first kind.
6 FebruaryLaw of the exponential functional of a family of one-sided Lévy processes.
2008
Pierre Patie (University of Bern)
2.15pm - G.108, Alan Turing BuildingAbstractJ. Bertoin and M. Yor determine the law of the exponential functional of a spectrally positive Lévy process with a negative mean through their negative entire moments. In this talk, we start by computing, in terms of new power series, the Laplace transform of such a functional associated to a spectrally negative Lévy process satisfying Rivero's condition. Then, specifying on a new family of one-sided Lévy processes, we provide an expression for the density of their corresponding exponential functionals in terms of the Wright hypergeometric functions. This is achieved by connecting such laws with the entrance laws of the family of self-similar continuous state branching processes with immigration. We end up by establishing some interesting analytical properties enjoyed by the Wright hypergeometric functions.
13 FebruaryNonparametric Copula, Conditional Distribution and Quantile Regression
2008
Keming Yu (Brunel University)
2.15pm - G.108, Alan Turing BuildingAbstractDevelopment of new methodologies for high-dimensional data analysis has exploded over the last decade in an effort to mine interesting information from the data. Sklar theorem based Copula can help to describe the dependence between high-dimensional random variables via marginal distributions. We study nonparametric copula based conditional distribution estimation and quantile regression by local quadratic fitting. We show that a d-dimensional nonparametric multivariate analysis can be carried out via d(d+1)/2 times of local univariate mean regression.
20 FebruaryStatistics with a human face.
2008
Adrian Bowman (Department of Statistics, University of Glasgow)
4pm - G.108, Alan Turing Building (note: later start)AbstractStereo-photogrammetry provides high-resolution data defining the shape of three-dimensional objects. One example of its application is in a collaborative study of the growth of children's faces. The clinical aims of the study are to describe the facial shape and growth of healthy children and to contrast this with the shape and growth of children who have been born with a cleft lip and/or palate and who have subsequently undergone surgical repair. Information can be extracted in a variety of forms. Methods of analysing landmark shape data are well developed but landmarks alone clearly do not adequately represent the very much richer information present in each digitised face. Facial curves with clear anatomical meaning have also been extracted. In order to exploit the full extent of the information present in the images, standardised meshes, whose nodes correspond across individuals, have also been fitted. Some of the issues involved in analysing data of these types will be discussed and illustrated on the facial growth study. These include graphical exploration, the measurement of asymmetry and longitudinal modelling.
27 FebruaryCancelled !!!
2008
John Appleby (Dublin City University)
2.15pm - G.108, Alan Turing BuildingAbstractNone
27 FebruarySome recent result on scale functions of spectrally negative Lévy processes
2008
Victor Rivero (Center for Mathematical Research, Guanajuato, Mexico)
2.15pm - G.108, Alan Turing Building (note: new start)AbstractThe objective of this talk is to provide methods for constructing new families of scale functions for spectrally negative Lévy processes which are completely explicit. This is the result of an observation in a recent paper by Hubalek and Kyprianou which permits feeding the theory of Bernstein functions directly into the Wiener-Hopf factorization for spectrally negative Lévy processes. Moreover, we will explain how the theory of Volterra equations allows to prove that whenever the Lévy measure of a spectrally negative Lévy process has a non-increasing density which is log convex then for $q > 0$ the scale function $W^(q)$ is convex on some half line $(a^*,\infty)$ where $a^*$ is the largest value at which $W^{(q)'}$ attains its global minimum. if time allows we will expose the application of these results to de Finetti’s classical actuarial control problem.
5 MarchOptimum experimental design for non-linear models.
2008
Barbara Bogacka (Queen Mary College)
2.15pm - G.108, Alan Turing BuildingAbstractIn this talk I will present a short introduction to the theory of optimum experimental design for non-linear models followed by examples of such designs in some early drug development studies. In particular, I will discuss the role of model parameter sensitivities and of the Equivalence Theorem in finding optimum designs for such models.
12 MarchLocal probabilities for random walks conditioned to stay positive
2008
Vitali Wachtel (Technical University Munich)
2.15pm - G.108, Alan Turing BuildingAbstractLet $S_{0}=0,\{S_{n},\,n\geq 1\}$ be a random walk generated by a sequence of i.i.d. random variables $X_{1},X_{2},...$ and let $\tau^{-}=\min \{n\geq 1:S_{n}\leq 0\}$ and $\tau ^{+}=\min \{n\geq 1:S_{n}>0\}$. Assuming that the distribution of $X_{1}$ belongs to the domain of attraction of an $\alpha$-stable law we study the asymptotic behavior, as $n\rightarrow\infty$, of the local probabilities $\mathbf{P}(\tau^{\pm}=n)$ and prove the Gnedenko and Stone type conditional local limit theorems for the probabilities $\mathbf{P}(S_{n}\i \lbrack x,x+\Delta )|\tau ^{-}>n)$ with fixed $\Delta $ and $x=x(n)\in (0,\infty )$.
27 MarchHierarchically penalized Cox regression for censored data with grouped variables and its oracle property.
2008
Bin Nan (University of Michigan)
3.15pm - G.108, Alan Turing BuildingAbstractIn many biological and other scientific applications, prediction variables are often naturally grouped. For example, in biological applications, assayed genes or proteins are grouped by biological roles or biological pathways. When studying the dependence of survival outcome on these grouped prediction variables, it is desirable to select variables at both the group level and the within-group level. In this article, we develop a new method to address the group variable selection problem in the Cox proportional hazards model. Our method not only effectively removes unimportant groups, but also maintains the flexibility of selecting variables within the identified groups. We also show that the new method offers the potential for achieving the asymptotic oracle property.
9 AprilMaximization by Parts in Likelihood Inference.
2008
Peter Song (University of Waterloo, Canada)
2.15pm - G.108, Alan Turing BuildingAbstractIn this talk I will present a new algorithm for solving a score equation for the maximum likelihood estimate in certain problems of practical interest. The method circumvents the need to compute second order derivatives of the full likelihood function. It exploits the structure of certain models that yield a natural decomposition of a very complicated likelihood function. In this decomposition, the first part is a log likelihood from a simply analyzed model and the second part is used to update estimates from the first. Convergence properties of this iterative (fixed point) algorithm are examined and asymptotics are derived for estimators obtained by using only a finite number of iterations. I will illustrate several examples in the presentation, including multivariate Gaussian copula models, nonnormal random effects models, generalized linear mixed models, and state space models. Properties of the algorithm and of estimators are discussed in detail via simulation studies on a bivariate copula model and a nonnormal linear random effects model.
16 AprilA Support Theorem and a Large Deviation Principle for Kunita Stochastic Flows via Rough Paths
2008
Steffen Dereich (University of Bath, Technical University of Berlin)
2.15pm - G.108, Alan Turing BuildingAbstractIn the past the theory of rough paths has proven to be an elegant tool for deriving support theorems and large deviation principles for solutions to Stratonovich SDE's. The aim of this talk is to elucidate this approach and to present new results for SDE's driven by general Banach space-valued Wiener processes. These results lead naturally to a support theorem and a LDP for stochastic flows induced by Kunita SDE's. I identify its rate function and show how rate minimizing functions look like for a particular class of events.
18 AprilAdvances in Statistical Computing For Linear Time Series.
2008
Ian McLeod (The University of Western Ontario)
2:15pm - 2.216, Alan Turing Building
(Note: 18 April is on Friday)AbstractAdvances in Statistical Computing For Linear Time Series.pdf
Ian McLeod's talk is available as pdf file: AIM.pdf23 AprilThe allele frequency spectrum associated with the Bolthausen-Sznitman coalescent
2008
Christina Goldschmidt (University of Oxford)
2.15pm - G.108, Alan Turing BuildingAbstractI will take as my starting point a problem which is classical in population genetics: we wish to understand the distribution of numbers of individuals in a population who carry different alleles of a certain gene. We imagine a sample of size n from a population in which individuals are subject to neutral mutation at a certain constant rate. Every mutation gives rise to a completely new type. The genealogy of the sample is modelled by a coalescent process and we imagine the mutations as a Poisson process of marks along the coalescent tree. The allelic partition is obtained by tracing back to the most recent mutation for each individual and grouping together individuals whose most recent mutations are the same. The number of blocks of each of the different possible sizes in this partition is called the allele frequency spectrum. Recently, there has been much interest in this problem when the underlying coalescent process is a so-called Lambda-coalescent (even when this is not a biologically ``reasonable'' model) because the allelic partition is a nice example of an exchangeable random partition. In this talk, I will describe the asymptotics (as n tends to infinity) of the allele frequency spectrum when the coalescent process is a particular Lambda-coalescent which was introduced by Bolthausen and Sznitman. It turns out that the frequency spectrum scales in a rather unusual way, and that we need somewhat unusual tools in order to tackle it.
This is joint work with Anne-Laure Basdevant (Toulouse III).7 MayModelling transmission of antibiotic-resistant pathogens in hospital settings
2008
Philip O'Neill (University of Nottingham)
2.15pm - G.108, Alan Turing BuildingAbstractStochastic models and Bayesian inference are used to address questions regarding control measures for antibiotic-resistant pathogens such as MRSA. The data come from various recent intervention studies. This is joint work with Ben Cooper (Health Protection Agency) and Theodore Kypraios (Nottingham).
14 MayNone
2008
Frank G. Ball (University of Nottingham)
2.15pm - G.108, Alan Turing BuildingAbstractAbstract here
19 MayJoint modeling of longitudinal and competing risks survival data
2008
Gang Li (University of California at Los Angeles)
2.15pm - G.108, Alan Turing BuildingAbstractJoint modeling of longitudinal measurements and survival data has received much attention in recent years. However, previous work has primarily focused on a single failure time with independent censoring. In this talk I will review some recent developments in joint modeling of longitudinal data and competing risks survival data. A joint model enables one to make joint inference on both outcomes which is often desired in analysis of clinical trials. By modeling the event time jointly, the analysis of longitudinal measurements is adjusted for non-ignorable missing data due to informative dropout that cannot always be handled appropriately by the standard linear mixed effects models alone. In addition, joint models utilize information from both outcomes, and thus can be more efficient. Our models allow for more than one type of failures and provide a simple means to handle dependent censoring. New methods for dealing with outliers and heterogeneous random effects will also be discussed. The developed methods will be illustrated using data from a clinical trial for scleroderma lung disease
21 MayDoubly Robust Generalised Estimating Equations for Longitudinal Data
2008
Shaun Seaman (University College London)
2.15pm - G.108, Alan Turing BuildingAbstract(joint work with:
Andrew Copas
MRC Clinical Trial Unit and University College London)
A popular method for analysing repeated-measures data are generalised estimating equations (GEE). When response data are missing at random (MAR), two modifications of GEE use inverse-probability weighting and imputation. The weighted GEE method involves weighting observations by their inverse probability of being observed, according to some assumed missingness model. Imputation methods involve filling in missing observations with values predicted by an assumed imputation model. Weighted GEE are consistent when the data are MAR and the dropout model is correctly specified. Imputation methods are consistent when the data are MAR and the imputation model is correctly specified.
Recently, doubly robust methods have been developed. These involve both a model for probability of missingness and an imputation model for the expectation of each missing observation, and are consistent when either is correct. In this talk, I shall describe doubly robust GEE, and illustrate their use on simulated data and data from the INITIO randomised clinical trial of HIV therapy.17 JuneOn the uniqueness of invariant measures for stochastic delay equations.
2008
Michael Scheutzow (Technical University Berlin)
2.15pm - Frank Adams 2, Alan Turing BuildingAbstractNone
18 JuneSealed Ceiling Bids and Mathematical Programming.
2008
Alex Belenky (MIT)
2.15pm - G.108, Alan Turing BuildingAbstractNone
23 JulyRecent results on the Minimax quickest detection problems.
2008
Albert N. Shiryaev
11.00pm and 2.00pm - G.209, Alan Turing BuildingAbstractNone
1st Semester 2007/2008
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3 OctoberSurvival Extrapolation
2007
N. Demiris (MRC, University of Cambridge)
2.15pm - G.108, Alan Turing BuildingAbstractNone
10 OctoberStrong solutions to stochastic wave equations in Riemannian manifolds
2007
Z. Brzenaik (University of York)
2.15pm - G.108, Alan Turing BuildingAbstract29 OctoberFrom discrete Markov jump systems to two species competitive stochastic Lotka-Volterra equations
2007
Y. Wang (Nankai University, China)
2.15pm - Frank Adams 1, Alan Turing BuildingAbstractIn this talk, we propose a pair of interacting stochastic partial differential equations (abbr. SPDEs) with space-time branching noises, which corresponds to a model of two species competitive stochastic Lotka-Volterra system. We establish the weak solution of the pair of SPDEs through a heuristic approximation from a sequence of pure jump birth-death Markov processes with branching components.
7 NovemberComparison results for Stochastic volatiltiy models
2007
D. Hobson (University of Warwick)
2.15pm - G.108, Alan Turing BuildingAbstractNone
14 NovemberA Delayed Option-Pricing Formula
2007
S. Mohammed (Southern Illinois University)
2.15pm - G.108, Alan Turing BuildingAbstractIn this talk we develop a formula for pricing European options when the underlying stock price follows a non-linear stochastic differential equation with memory. We expect the model for the stock dynamics to be sufficiently flexible to fit real market data, yet simple enough to allow for a closed-form representation of the option price (for long delays) as well as a hedging strategy. Furthermore, the model maintains the completeness of the market. The analysis is based on the construction of an equivalent martingale measure (no arbitrage) using a successive backward conditioning argument.
The results are joint work with M. Arriojas, Y. Hu and G. Pap.21 NovemberStatistical Inference for time-varying ARCH processes
2007
S. Subba Rao (Texas A&M University)
2.15pm - G.108, Alan Turing BuildingAbstractWe consider a class of time-varying ARCH (tvARCH) processes and study some of its probabilistic properties. We consider various methods for estimating the parameters of the tvARCH process. Finally we fit the tvARCH process to some real data examples.
28 NovemberOptimal Skorokhod Embeddings: extremal range probabilities
2007
A. Cox (University of Bath)
2.15pm - G.108, Alan Turing BuildingAbstractThe Skorokhod embedding problem is to find a stopping time of a Brownian motion such that the stopped process has a specified distribution. Many solutions are known, including the solution of Azéma and Yor, which additionally maximises the probability of the maximium being greater than a given level among all Skorokhod embeddings of a given distribution. Motivated by applications to finance, we construct embeddings which maximise and minimise the probability of both passing above a given level, and passing below a given level. (Joint work with Jan Oblój, Imperial College.)
10 DecemberValuing Executive Stock Options: Performance Hurdles, Early Exercise and Stochastic Volatility
2007
A. Szimayer
2.15pm - Frank Adams 1, Alan Turing BuildingAbstractShare-based Payment, IFRS 2, issued by the International Accounting Standards Board and adopted in Australia as AASB 2, and its US GAAP equivalent, FAS 123R, require the fair value of ESOs as measured at their grant date to be reported as an expense in the employer´s financial statements. But ESOs can be complex instruments. We provide a framework and develop a model for accurately valuing ESOs from the employer´s viewpoint. In particular, we focus on performance hurdles, the effect of expected early exercise, and the uncertain volatility arising from the typically long life span of ESOs. We use the model to explore two case studies, observing that performance hurdles and early exercise can cause ESO values to be much less than the traditional Black-Scholes option values and that the ESO values decrease further once stochastic volatility is included. Clearly these observations have serious implications for bias in accounting standards, and for experimental bias in capital-markets based accounting studies of ESOs. We then extend our analysis to consider its implications for pay-for-performance sensitivity and the design of effective share-based incentive schemes. Our results imply that the push by financial institutions to have investees introduce performance-based vesting criteria can require a greater proportion of total compensation to be in the form of a fixed salary, if pre-existing incentive levels are to be preserved.
Key words: Executive stock options; Performance hurdles; Early exercise; Stochastic Volatility12 DecemberStatistically efficient designs in observational research: beyond the random sample.
2007
R. McNamee (Biostatistics, University of Manchester)
2.15pm - G.108, Alan Turing BuildingAbstractEfficient design of experiments is a well-known area of statistical expertise but the efficient design of observational, ie non-experimental, studies has received less attention. The first part of the talk will focus on statistically efficiency in the context of studies where the objective is to estimate an odds ratio eg as a measure of association between exposure and disease. Starting first with simple designs, it will develop the idea of 2-phase study designs. The approach to finding optimal designs is described and resulting formulae shown. If time permits, optimal 2-phase designs for estimation of regression coefficients will also be discussed.
2nd Semester 2006/2007
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31 Jan