Statistical inference for exponential random graph models

This talk will provide an introduction to exponential random graph models. These models have a long history, and represent a very flexible way to model network data. However, the underlying likelihood function is typically very complicated to evaluate and requires approximations of various kinds. Very often, the corresponding parameter estimates yield a poor fit of the model to the data. I will present two approaches, one Bayesian, the other likelihood-based, which overcome these issues to a certain extent.

Epidemics on random networks incorporating household structure

There has been a growing interest in models for epidemics among structured populations, which incorporate realistic departures from homogeneous mixing whilst maintaining mathematical tractability. Two classes of structured population epidemic models that have attracted considerable recent attention are network models (in which there is a random graph describing possible infectious contacts) and household models (in which the population is partitioned into households with different contact rates for within- and between-household infection). In this talk I describe and analyse a model for the spread of an SIR (susceptible – infective- removed) epidemic that includes both of these features. The analysis includes deriving a threshold parameter which determines whether or not an epidemic with few initial infectives can become established and lead to a major outbreak, and determining the probability and expected final size of a major outbreak. The model is compared and contrasted with standard household and network models and vaccination strategies are briefly considered.

Building multivariate copulas using vines

A vine is a graphical model developed by Cooke, Bedford and Kurowicka that enables us to describe a multivariate copula in terms of a number of conditional and unconditional 2 dimensional copulas. The problem of how one chooses appropriate 2d copulas in practice is however difficult. We look at this as a problem in approximation, and show that under certain conditions we can choose the same finite dimensional family of 2d copulas everywhere to get a given level of approximation. The result is illustrated by a financial data set. The talk describes joint work with Ali Daneshkhah of Strathclyde Business School.