Probability and Statistics Research Seminars

2nd Semester 2012/2013

• 30 January
  2013
  Analysis of shape functional data with application to cleft lip surgery
  Julian Faraway (University of Bath)
  
  2.15pm, Frank Adams 2
  Abstract

  Facial motion can be recorded using the 3D movement of landmarks on the face. Cleft lip/palate surgery can cause changes to the function of the face which must be assessed. Methods for the analysis of shape change are discussed and used to investigate the distribution of facial motion.

• 6 February
  2013
  Blood, sweat and urine
  Richard Cotton (Live Analytics)
  
  2.15pm, G.207
  Abstract

  Richie Cotton is a data scientist who spent six years working at the Health and Safety Laboratory. In this talk he recounts his job swap with a chemist and tells you what he learnt from the experience. The talk includes:
  - Why laziness is a virtue.
  - Why you should never let a chemist design a database.
  - How to write code that fails.
  - The secrets of inverse-brogramming.
  - How to cure spreadsheet addiction.

• 5 March
  2013
  Dimension reduction in semiparametric multivariate analysis using Fisher's information matrix
  Bruce Lindsay (Penn State University)
  
  1.30pm, Frank Adams 1
  Abstract

  We will show that the Fisher's information matrix can be turned into a powerful tool for the analysis of multivariate data. To date we have shown that the eigenanalysis of this matrix, and other matrices derived from it, can be employed for dimension reduction in many standard multivariate analyses. Examples include projection pursuit, independent components analysis, graphical model fitting, covariate dimension reduction, and population discrimination.

• 13 March
  2013
  Positivity of integrated random walks and other random sequences
  Vladislav Vysotsky (Arizona State University)
  
  2.15pm, Frank Adams 2
  Abstract

  Consider a sequence of oscillating random variables. What is the chance that it stays positive for a long time? We obtain the sharp asymptotic for integrated random walks of a certain type. The problem is deeply related with certain models of mathematical physics. In general, persistance probabilities are well understood only for very few types of random sequences. We give an overview of the field and in addition, discuss our results on persistence of iterated random walks.

• 20 March
  2013
  Revisiting Measuring/Testing Asymmetry/Symmetry of a continuous Probability Density Function
  Prakash Patil (University of Birmingham)
  
  2:15pm, Frank Adams 2
  Abstract

  It is a common practice to make assertions about the symmetry or asymmetry of a probability density function (p.d.f.) based on the coefficients of skewness. Since most of the coefficients of skewness are designed to be zero for a symmetric density, they do, overall, provide an indication of symmetry. However, skewness is primarily influenced by the tail behavior of a density function, and the skewness coefficients are designed to capture this behavior. Therefore, they do not calibrate asymmetry in the density curves. To measure asymmetry in the density curves, we first give two new conditions for a continuous p.d.f. to be symmetric; of the two new conditions, one is only a necessary condition, while the other is necessary and sufficient. These conditions are then used to produce weak and strong asymmetry measures of a continuous p.d.f. on the scale of -1 to 1. We show through examples that both measures do an admirable job of capturing the visual impression of asymmetry of a continuous p.d.f. and briefly discuss the estimation of these coefficients from a sample.
  We then explore the use of the weak measure to test the symmetry of a population based on a sample from it. First we observed that for a given asymmetric population a test based on the weak measure has better power compared to the existing tests. Secondly, and probably more importantly, unlike existing tests, the power of the proposed test increases as the size of asymmetry increases. This is then confirmed mathematically by showing that the test has a positive power against any alternative population with its weak asymmetry coefficient converging to zero at the rate of n^{-1/2}.

• 21 March
  2013
  New estimating equation approaches with application in lifetime data analysis
  Keming Yu (Brunel University)
  
  2.15pm, Frank Adams 1
  Abstract

  Estimating equation approaches have been widely used in statistics inference. Important examples of estimating equations are the likelihood equations. Since its introduction by Sir R. A. Fisher a century ago, maximum likelihood estimation (MLE) is still the most popular estimation method used for fitting probability distribution to data, including fitting lifetime distributions with censored data. However, MLE may produce substantial bias and even fail to obtain valid confidence intervals when data size is not large enough or there is censoring data. In this paper, based on nonlinear combinations of order statistics, we propose new estimation equation approaches for a class of probability distributions, which are particularly effective for skewed distributions with small sample sizes and censored data. We even extend the method to parameter estimation under regression-type of simple step-stress model in accelerated life testing.

• 10 April
  2013
  Simultaneous confidence bands for regression analysis
  Wei Liu (Southampton University)
  
  2.15pm, Frank Adams 2
  Abstract

  This talk will provide an overview of the methodology of simultaneous confidence bands for parametric regression analysis. We will look at how simultaneous confidence bands can be used in regression analysis to make sensible and informative inference, the key in the construction of simultaneous confidence bands, the two optimality criteria for comparison of simultaneous confidence bands, and some unsolved problems. The talk should be accessible to anyone who has done linear regression models.

• 17 April
  2013
  Convex hulls of planar random walks with drift
  Andrew Wade (University of Durham)
  
  2.15pm, Frank Adams 2
  Abstract

  On each of n unsteady steps, a drunken gardener drops a seed. Once the flowers have bloomed, what is the minimum length of fencing required to enclose the garden? Denote by L(n) the perimeter length of the convex hull of an n-step planar random walk whose increments have finite second moment and non-zero mean. Snyder and Steele showed that L(n)/n converges almost surely to a deterministic limit, and proved an upper bound on the variance Var[L(n)] = O(n). I will describe recent work with Chang Xu (Strathclyde) in which we show that Var[L(n)]/n converges, and give a simple expression for the limit, which is non-zero for walks outside a certain degenerate class. This answers a question of Snyder and Steele. Furthermore, we prove a central limit theorem for L(n) in the non-degenerate case.

• 15 May
  2013
  Random matrices, stochastic growth and the KPZ equation
  Jon Warren (University of Warwick)
  
  2.15pm, Frank Adams 2
• 22 May
  2013 (Cancelled)
  Characterizing Stopping Times Obtained from Randomized Stopping
  David Siska (University of Liverpool)
  
  2.15pm, Frank Adams 2
Abstract

It is known that optimal stopping problems can be transformed into optimal control problems using the method of randomized stopping. A general result on the method of randomized stopping will be proved and the way of characterizing the stopping times from the control process will be provided under additional assumptions.

• 29 May
  2013
  Preferential attachment networks with clustering
  Peter Mörters (University of Bath)
  
  2.15pm, Frank Adams 2

1st Semester 2012/2013

• 26 September
  2012
  Effective Hypoelliptic Diffusions on the Hopf fibration
  Xue-Mei Hairer (University of Warwick)
  
  2:15-3:15pm, Frank Adams 2
• 10 October
  2012
  Bootstrap Sequential Determination of the Co-integration Rank in VAR Models
  Robert Taylor (University of Nottingham)
  
  2:15pm, Frank Adams 2
• 17 October
  2012
  Central limit theorem for an additive functional of the fractional Brownian motions
  Yaozhong Hu (University of Kansas)
  
  4-5pm, Frank Adams 1
• 24 October
  2012
  Explained variation in survival and event history
  Robin Henderson (University of Newcastle)
  
  2:00pm (Note time change), Frank Adams 2
  Abstract

  Abdelbaset Ali Mohmed Al Megrahi, the so-called Lockerbie bomber, was freed from prison in August 2009 on compassionate grounds, since he was stated to be in the final stages of terminal prostate cancer and expected to die within three months. He died in May 2012. Should we be surprised that he lived so long? This talk revisits the related issues of prediction and explained variation for survival and more general event history data. There is no shortage of proposed measures of prognostic value for statistical models, but none have been uniformly accepted and those in use in major computer packages may not be the most statistically meaningful. In this talk I review the issues and describe and illustrate use of a rank-based measure, developed in collaboration with Janez Stare and Maja Pohar, which is applicable and interpretable in discrete or continuous time, with tied data or otherwise, with time-varying, time-fixed or dynamic covariates, with time-varying or time-constant effects, with single or multiple event times, with parametric or semi-parametric models, and under general independent censoring/observation.

• 24 October
  2012
  Optimal transport from Lebesgue to Poisson
  Karl-Theodor Sturm (University of Bonn)
  
  3-4pm, Frank Adams 2
• 31 October
  2012
  Bayesian quickest change-point detection problems
  Pavel Gapeev (London School of Economics)
  
  2.15-3.15pm, Frank Adams 2
• 7 November
  2012
  Regression for circular data
  Charles C. Taylor (University of Leeds)
  
  2.15pm, Frank Adams 2
  Abstract

  We consider data of the form (x_i,y_i) in which either x and/or y is measured as an angle and we seek to model a relationship in which y can be predicted from x. Starting with a review of existing parametric models, we put these into a common framework and discuss problems with estimation. Various nonparametric models, which make use of circular kernels, are described, as well as their asymptotic behaviour and approaches to bandwidth selection.

• 14 November
  2012
  Multilevel Wiener-Hopf Monte Carlo and Euler-Poisson schemes for Lévy processes
  Albert Ferreiro-Castilla (University of Bath)
  
  3-4pm, Frank Adams 1
• 21 November
  2012
  Design-free estimation of large variance matrices
  Karim M. Abadir (Imperial College London)
  
  2.15pm, Frank Adams 2
  Abstract

  This paper introduces a new method for estimating variance matrices. Starting from the orthogonal decomposition of the sample variance matrix, we exploit the fact that orthogonal matrices are never ill-conditioned and therefore focus on improving the estimation of the eigenvalues. We estimate the eigenvectors from just a fraction of the data, then use them to transform the data into approximately orthogonal series that deliver a well-conditioned estimator (by construction), even when there are fewer observations than dimensions. We also show that our estimator has lower error norms than the traditional one. Our estimator is design-free: we make no assumptions on the distribution of the random sample or on any parametric structure the variance matrix may have. Simulations confirm our theoretical results and they also show that our simple estimator does very well in comparison with other existing methods, especially when the data are generated from fat-tailed densities.

• 28 November
  2012
  The Estimation of Misspecified Long Memory Models
  Peter M Robinson (London School of Economics)
  
  2.15pm, G.113
  Abstract

  We consider time series that, possibly after integer differencing or integrat- ing or other detrending, are covariance stationary with spectral density that is regularly varying near zero frequency, and unspecified elsewhere. This semi- parametric framework includes series with short, long and negative memory. We establish consistency of the popular log-periodogram memory estimate that, conventionally but wrongly, assumes the spectral density obeys a pure power law. The local-to zero misspecification leads, however, to increased bias, which is liable to prevent the usual central limit theorem from holding. The order of the bias is calculated for several slowly-varying factors, and some discussion of mean squared error and bandwidth choice is included.

• 12 December
  2012
  Large deviation behaviour of supercritical branching processes
  Vitali Wachtel (LM-Universität München)
  
  2.15pm, Frank Adam 2
  Abstract

  Let Z_n be a Galton-Watson process with m:=EZ_1>1. In the talk we describe different strategies which lead to lower or upper deviations of Z_n, that is, Z_nk_n with k_n>>m^n.

Further information

For further information contact

Dr. Christiana Charalambous (Statistics) or

Dr Ronnie Loeffen (Probability)