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.
Year
2014
Category
Refereed journal