A case study in non-centering for data augmentation: Stochastic epidemics

Abstract

In this paper, we introduce non-centered and partially non-centered MCMC algorithms for stochastic epidemic models. Centered algorithms previously considered in the literature perform adequately well for small data sets. However, due to the high dependence inherent in the models between the missing data and the parameters, the performance of the centered algorithms gets appreciably worse when larger data sets are considered. Therefore non-centered and partially non-centered algorithms are introduced and are shown to out perform the existing centered algorithms.

A tutorial introduction to Bayesian inference for stochastic epidemic models using Approximate Bayesian Computation

“…A variety of extensions appear in the literature such as the household model (O'Neill et al, 2000), spatial epidemic models (Jewell et al, 2009b) and random graph models (Britton and O'Neill, 2002). It is beyond the scope of this paper to discuss these extensions in detail, but we briefly describe the SIR epidemic model upon a Bernoulli random graph studied using MCMC in Britton and O'Neill (2002) and Neal and Roberts (2005).…”

Efficient MCMC for temporal epidemics via parameter reduction

“…Typically, updating of the infection times is done one at a time, either a randomly chosen infection time Neal and Roberts (2005) or all infection times sequentially Jewell et al (2009) per MCMC iteration. Then the components of θ are updated individually in a sequential order.…”

“…The conditional distribution of I i given the remainder of the data and the parameters is not of a convenient form for a Gibbs step. However, we know that the infectious period distributions follow Gamma(α, δ) and therefore it is convenient to use an independent sampler for I i , proposing I i = R i − Gamma(α, δ), see, for example, Neal and Roberts (2005). For the components of θ it is possible in some cases to use a Gibbs step, since for example, from (2),…”

“…The above MCMC algorithm is easy to implement but not very efficient and if m is large and all infection times are updated per iteration, it can take a long time per iteration. The key problem is the intrinsic dependence between I and θ, see Neal and Roberts (2005). A solution proposed by Neal and Roberts (2005) and subsequently used in Jewell et al (2009), is a non-centered parameterisation.…”

“…The key problem is the intrinsic dependence between I and θ, see Neal and Roberts (2005). A solution proposed by Neal and Roberts (2005) and subsequently used in Jewell et al (2009), is a non-centered parameterisation. That is, to reparameterise the model to express the infectious period of individual i as R i − I i = U i /δ, or equivalently to write I i = R i − U i /δ, where U i ∼ Gamma(α, 1) and U i is a priori independent of δ.…”