Simulation-based Bayesian inference for epidemic models

Abstract

A powerful and flexible method for fitting dynamic models to missing and censored data is to use the Bayesian paradigm via data-augmented Markov chain Monte Carlo (DA-MCMC). This samples from the joint posterior for the parameters and missing data, but requires high memory overheads for large-scale systems. In addition, designing efficient proposal distributions for the missing data is typically challenging. Pseudo-marginal methods instead integrate across the missing data using a Monte Carlo estimate for the likelihood, generated from multiple independent simulations from the model. These techniques can avoid the high memory requirements of DA-MCMC, and under certain conditions produce the exact marginal posterior distribution for parameters. A novel method is presented for implementing importance sampling for dynamic epidemic models, by conditioning the simulations on sets of validity criteria (based * Corresponding author. Tel.: (+44) 1223 337685.Email address: tjm44@cam.ac.uk (Trevelyan J. McKinley) January 16, 2013 on the model structure) as well as the observed data. The flexibility of these techniques is illustrated using both removal time and final size data from an outbreak of smallpox. It is shown that these approaches can circumvent the need for reversible-jump MCMC, and can allow inference in situations where DA-MCMC is impossible due to computationally infeasible likelihoods. Preprint submitted to Elsevier

Efficient $$\hbox {SMC}^2$$ SMC 2 schemes for stochastic kinetic models

“…We find that the DA scheme suffers intolerably poor mixing due to dependence between the latent infection times and the static parameters (see also McKinley et al (2014)). The pMCMC scheme, which can be seen as the pseudo-marginal analogue of an idealised marginal scheme, offers over an order of magnitude increase in terms of overall efficiency (as measured by autocorrelation time for a fixed computational budget) over DA.…”

“…Application areas include (but are not limited to) systems biology (Golightly and Wilkinson 2005;Wilkinson 2012), predator-prey interaction (Ferm et al 2008;Boys et al 2008) and epidemiology (Lin and Ludkovski 2013;McKinley et al 2014). Here, we focus on the MJP representation of a stochastic kinetic model (SKM), whereby transitions of species in a reaction network are described probabilistically via an instantaneous reaction rate or hazard, which depends on the current system state and a set of rate constants, with the latter typically the object of inference.…”

“…Recently proposed pseudomarginal MCMC schemes, e.g. particle MCMC (pMCMC) (Andrieu et al 2010), offer a promising alternative and have been successfully applied in both the epidemiology (McKinley et al 2014) and systems biology (Golightly and Wilkinson 2015) literature. However, these 'global' inference schemes require careful selection and tuning of proposal mechanisms and must be restarted from scratch upon receipt of new observations or when assimilating information from multiple data sets.…”

Stability of noisy Metropolis–Hastings

“…As a consequence, the resulting chain can get "stuck" and may not move after a considerable number of iterations. In order to overcome this issue, a subtly different algorithm is performed in some practical problems (see, e.g., McKinley et al 2014). The basic idea is to refresh, independently from the past, the value of the current weight at every iteration.…”

How big is an outbreak likely to be? Methods for epidemic final-size calculation

“…This is typically not a trivial task. Another approach which is gaining in popularity is to use simulation-based methods, such as Approximate Bayesian Computation or pseudo-marginal methods [58,[61][62][63]. This approach relies on the ability to simulate data efficiently, and hence our comparison of three Monte Carlo methods will facilitate the use of such simulation-based inference methods.…”