Process & Systems Modelling

Assessing the adequacy of models for spatio-temporal processes in epidemiology & ecology

Stochastic spatio-temporal models play an increasingly important role in epidemiological and ecological studies of disease, invasive aliens and endemic species responses to climate changes. The dynamics of such systems can be extremely sensitive to the particular choice of model, with important implications for the design of control and risk management strategies.

Conventional Bayesian model assessment techniques (e.g. Bayes factor and Deviance Information Criterion) focus on relative model fit but do not readily offer insights in to which aspects of the model are at fault. Alternatively, posterior predictive checks can provide useful measures of model adequacy but are based on summary statistics which can be difficult to identify. We have therefore developed a novel approach for diagnosing misspecifications in a general spatio-temporal transmission model by embedding classical analysis of residuals within a Bayesian framework using latent residuals for each sub-process whose sampling properties are known given the specification of the fitted model. Application to simulated data suggests that our approach is more sensitive in detecting misspecification of the spatial transmission kernel than standard posterior predictive checks.

transmitabilityscenario bar graphsspacer Inferred distributions of residuals related to a spatial dispersal process. In Scenario I a light tailed dispersal process (model II) is fitted to data generated from the heavy tailed model I, with the situation reversed in Scenario II. Deviations from the known distribution (here uniform on the unit interval) of residuals related to the fitted spatial dispersal process indicate that extreme dispersal distances are under-represented in Scenario I and over represented in Scenario II.

Further details from: Glenn Marion

Article date 2013

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Statistical Genomics and Bioinformatics

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