University of Edinburgh
School of Mathematics and BioSS
Date: Friday 22nd September, 15:05/16:05 Location: JCMB 6206
Speakers: Luiz Max Carvalho (15:05)
Institute of Evolutionary Biology, University of Edinburgh
Jonathan Keith (16:05)
Monash University
Title: Bayesian estimation of time-trees: a journey through a strange land
Abstract: Phylogenetic trees are planar graphs used to represent the evolutionary history of individuals and/or species. When combined with sophisticated stochastic models, phylogenetic trees can offer insight into population dynamics and migration patterns. Estimation of trees from DNA alignments is a challenging endeavour among other reasons because of the super-exponential growth of the search space as the number of leaves grows. I will present some of the mathematical and statistical challenges involved in tree estimation, with a special focus on some adaptive proposals for Metropolis-Hastings MCMC.
Title: Markov chain Monte Carlo in discrete spaces, with applications in bioinformatics and ecology
Abstract: Efficient sampling of probability distributions over large discrete spaces is a challenging problem that arises in many contexts in bioinformatics and ecology. For example, segmentation of genomes to identify putative functional elements can be cast as a multiple change-point problem involving thousands or even millions of change-points. Another example involves reconstructing the invasion history of an introduced species by embedding a phylogenetic tree in a landscape. A third example involves inferring networks of molecular interactions in cellular systems.
In this talk I describe a generalisation of the Gibbs sampler that allows this well known strategy for sampling probability distributions in R^n to be adapted for sampling discrete spaces. The technique has been successfully applied to each of the problems mentioned above. However, these problems remain highly computationally intensive. I will discuss a number of alternatives for efficient sampling of such spaces, and will be seeking collaborations to develop these and other new approaches.
This seminar is a part of Maxwell Institute seminar series.
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