External Seminar: Dennis Prangle (Newcastle)

[Statistics & Probability Seminar]

Rare event methods for approximate Bayesian computation

Many stochastic mathematical models are hard to fit due to only partial observations being available. An example is fitting infectious disease epidemic models. This is straightforward if the times of all population events (e.g. infection and removal) are known, but in reality only some of these are observed.

One approach to this problem is approximate Bayesian computation (ABC). This is useful in situations where simulation of data from the model can be performed quickly. The idea is to find parameter values such that corresponding model simulations match the observations well. A problem is that this scales poorly to high dimensional data, as good matches become extremely rare.

This talk will review the basics of ABC and present recent work on improving its performance using rare event methods. The idea is to estimate the rare probability of a simulation matching the data well. To do this we introduce latent variables, which represent all the random unobservable quantities which drive the simulation. Our method uses a systematic search of the space of latent variables to estimate the rare probability of interest, and uses this in parameter inference. I'll present theoretical and empirical support for our method, and discuss future prospects for using latent variables in ABC.