Speaker: Eirini Votsi
Title: An introduction to sequential Monte Carlo methods with application in epidemiology
Date: November 2nd, 2015
Time: 02:00 PM
Abstract: Importance sampling refers to a collection of Monte Carlo methods where a mathematical expectation with respect to a target distribution is approximated by a weighted average of random draws from another distribution. It is an important prerequisite for sequential Monte Carlo (SMC) methods. The latter simulated-based methods provide a convenient and attractive approach to computing the posterior distributions of a variable of interest. They are applied when the variable of interest is high-dimensional, a parametric approximation to the posterior distribution is hard to obtain.
In the context of state-space models, where parameters underly the hidden and observation processes, a SMC-based algorithm, the pseudo-marginal Monte-Carlo Markov chain algorithm, could be employed for inference purposes. We aim to bring together the main exponents of the previous topics with the goal of introducing the methods and demonstrating their use by means of an application to epidemiology. In particular, we present a sequential filtering methodology to estimate instantaneous reproduction numbers with special emphasis on epidemics with imported cases. The infection process is modelled as a stochastic state-space process that incorporates observed and hidden information. A new formalization of the estimation of time-varying instantaneous reproduction numbers is presented and its potential benefits are discussed.