New model diagnostics for spatio-temporal systems in epidemiology and ecology

Abstract

A cardinal challenge in epidemiological and ecological modelling is to develop effective and easily deployed tools for model assessment. The availability of such methods would greatly improve understanding, prediction and management of disease and ecosystems. Conventional Bayesian model assessment tools such as Bayes factors and the deviance information criterion (DIC) are natural candidates but suffer from important limitations because of their sensitivity and complexity. Posterior predictive checks, which use summary statistics of the observed process simulated from competing models, can provide a measure of model fit but appropriate statistics can be difficult to identify. Here, we develop a novel approach for diagnosing mis-specifications of a general spatio-temporal transmission model by embedding classical ideas within a Bayesian analysis. Specifically, by proposing suitably designed non-centred parametrization schemes, we construct latent residuals whose sampling properties are known given the model specification and which can be used to measure overall fit and to elicit evidence of the nature of misspecifications of spatial and temporal processes included in the model. This model assessment approach can readily be implemented as an addendum to standard estimation algorithms for sampling from the posterior distributions, for example Markov chain Monte Carlo. The proposed methodology is first tested using simulated data and subsequently applied to data describing the spread of Heracleum mantegazzianum (giant hogweed) across Great Britain over a 30-year period. The proposed methods are compared with alternative techniques including posterior predictive checking and the DIC. Results show that the proposed diagnostic tools are effective in assessing competing stochastic spatio-temporal transmission models and may offer improvements in power to detect model mis-specifications. Moreover, the latent-residual framework introduced here extends readily to a broad range of ecological and epidemiological models.

A Systematic Bayesian Integration of Epidemiological and Genetic Data

“…An individual j ∈ ξ S ( t ) becomes exposed via primary infection with stochastic rate α and from an infection i ∈ ξ I ( t ) with rate βK ( d ij ; κ ). The term K ( d ij ; κ ) characterises the dependence of the infectious challenge from infective i to susceptible j as a function of distance between them d ij and is known as the spatial kernel function [ 25 , 27 ]. Here, we assume K ( d ij ; κ ) = exp(− κd ij ).…”

“… Having enabled systematic integration of epidemiological and evolutionary process, we characterise and quantify systematically the importance of genetic data for the inference of some important aspects of epidemic dynamics: the inference of the transmission graph, epidemiological parameters and the identification of clusters. Moreover we demonstrate that genetic data may also facilitate model assessment using methods recently developed by the authors [ 27 ]. We demonstrate the reliability of these novel methods using simulated data and their practical utility by analysing a foot-and-mouth outbreak in the UK.…”

Four key challenges in infectious disease modelling using data from multiple sources

“…However, model assessment is already challenging when only one source of data is involved (e.g. see Knock and O’Neill, 2014; Lau et al, 2014 , for examples in the infectious diseases literature), and becomes even more problematic when simultaneously modelling multiple sources of information. Understanding identifiability, detecting and measuring conflict between evidence from the different sources and the influence of each data item on the final results are the main, interlinked, issues.…”

Prediction of Settlement Delay in Critical Illness Insurance Claims by Using the Generalized Beta of the Second Kind Distribution

“…Streftaris and Gibson () and Lau et al . ()), similarly to the work in the previous section. As before, we consider the MCMC estimation process and let be a sampling distribution (such as GB2) for delay j at (post‐convergence) iteration t , where j =1,…, k and t =1,…, N .…”

“…Lau et al . ()). Comparison between candidate models is also considered by using a latent likelihood ratio (LLR) type of test (e.g.…”