Event Details

Statistics Research Seminar showcasing research from across the statistics section

Speaker: Simon Lunagomez

Title: Modeling Network Populations via Graph Distances

Abstract:

We introduce a new class of models for multiple networks. The core idea is to parametrize a distribution in the space of labelled graphs in terms of the Frechet mean (which is itself a network) and a parameter that controls the concentration of this distribution with respect to the mean.The Frechet mean in turn depends on a pre-specified metric, and we further define concentration for this new class of models in terms of entropy, varying from a point mass concentrated on the Frechet mean network to a uniform distribution over networks on the same vertex set. We provide a hierarchical Bayesian approach for exploiting this construction, along with straightforward strategies for sampling from the resultant posterior distribution. We demonstrate the efficacy of our approach via simulation studies and a data analysis example drawn from systems biology. We conclude with a discussion of a data set from ecology that is motivating extensions of this work.This is joint work with Sofia Olhede and Patrick Wolfe

Speaker: Chris Sherlock

Title: Fast exact inference for Markov jump processes using the rate matrix.

Abstract:

We consider the problem of inference for discretely observed Markov jump processes with an infinite statespace, such as occur in biological and environmental systems. When the statespace is finite, inference for the resulting continuous-time Markov chain using its rate matrix, Q, is straightforwards, but in the case of an infinite state space the method of choice is particle MCMC. We provide a new method, the minimal extended statespace algorithm (MESA) for exact Bayesian inference that uses finite-dimensional rate matrices even though the statespace is infinite. In contrast to particle MCMC, MESA is most efficient when there is no observation noise, and becomes less efficient as the observation noise increases. This is work in progress, so partial results will be presented.