Inference on historical Ebola outbreaks using hierarchical models: a particle filtering approach

Abstract

Particle filters are commonly used to estimate the likelihood for epidemic models when it is analytically intractable. These methods marginalise over missing data and do not suffer from the scaling issues present in traditional data-augmented Markov chain Monte Carlo methods. In this thesis we present a particle filtering methodology which extends upon recent advances in the field to simulate realisations of a process which are consistent with observations of two events from the same outbreak, such as symptom onsets and recoveries. This particle filtering approach is used in a particle marginal Metropolis-Hastings (pmMH) algorithm to fit a hierarchical model to four outbreaks of Ebola simultaneously for the first time. We estimated R₀ above 1 for all four outbreaks (as expected by the threshold theorem), with three of the outbreaks having values above 3. Our results also indicated that transmission began to reduce before the implementation of major intervention measures, which may be due to changes in community awareness. An additional area of work in this thesis relates to the efficiency of pmMH methods. Mixing of the overall Markov chain is crucial to the efficiency of a pmMH method, and is controlled by the variance in the log-likelihood estimates from the particle filter at the maximum a posteriori (MAP). This variance is in turn controlled by the number of particles used. We develop a more sophisticated methodology for estimating the MAP when only noisy estimates of the log-likelihood are available. This enables a priori tuning of the inference methods and the possibility of automating the tuning process.