Probability and Statistics Research Seminars

2nd Semester 2011/2012

• 15 February
  2012
  Nature Penalised regression on a graph
  Arne Kovac (University of Bristol)
  
  2:15pm, Frank Adams 2
  Abstract

  We consider the problem of nonparametric regression where the aim is to approximate noisy observations by simple functions with few local extreme values. In particular we generalise Total Variation denoising from the common situation of regression in one dimension to the problem of regression on graphs. Here the observations lie on the knots of a graph and instead of covariates there is a graphical structure which determines which observations are close to each other. Our new generalised version of TV denoising penalises the distance between the data and the fit on the knots as well as the total variation along the edges of the graph. We consider in particular algorithmical problems and develop a new fast algorithm for regression on a graph.

• 7 March
  2012
  Random walks in cones
  Denis Denisov (University of Cardiff)
  
  2:15pm, Frank Adams 2
  Abstract

  TBA

• 7 March
  2012
  A Bayesian bidirectional Hidden Markov model for ChIP sequencing data.
  Veronica Vinciotti (Brunel University)
  
  3:15pm, Frank Adams 2
  Abstract

  An important biological question is the one of detecting the regions in the genome bound by histones or transcription factors, as these give insight into the mechanism of gene regulation. ChIP sequencing (ChIP-seq) is a biological method to detect these, by generating sequence reads at the positions bound by a transcription factor. In the absence of binding, reads would be expected to be scattered across the genome, following some non-specific binding pattern which generates a background signal across the genome. Statistically, the observed count data, summarised into bins across the genome, are assumed to come either from a background or a signal distribution. Given these data, the interest is in inferring the state of the latent binary variable, which can be either "Enriched" or "Not Enriched". It is realistic in this application to assume a Markov property, whereby the probability of a region being enriched depends on the two neighbouring ones. In this talk, we present a bidirectional Hidden Markov model that can capture all these assumptions. The parameters of the model are estimated in a Bayesian framework, using either a Poisson or a Negative Binomial distribution for the counts. The performance of the method is shown on a comparative simulation study and on ChIP-seq data for two transcription factors.

• 14 March
  2012
  TBA
  Nick Longford (Universitat Pompeu Fabra (UPF), Barcelona)
  
  2:15pm, Frank Adams 2
  Abstract

  TBA

• 21 March
  2012
  Hastings-Levitov aggregation in the small particle limit
  James Norris (University of Cambridge)
  
  2:15pm, Frank Adams 2
  Abstract

  TBA

Further information

For further information contact

Dr. Christiana Charalambous (statistics) or

Prof Tusheng Zhang (probability)