Latent likelihood ratio tests for assessing spatial kernels in epidemic models
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Mathematical Biology
Latent likelihood ratio tests for assessing spatial kernels in epidemic models David Thong1
· George Streftaris1 · Gavin J. Gibson1
Received: 30 September 2019 / Revised: 10 August 2020 © The Author(s) 2020
Abstract One of the most important issues in the critical assessment of spatio-temporal stochastic models for epidemics is the selection of the transmission kernel used to represent the relationship between infectious challenge and spatial separation of infected and susceptible hosts. As the design of control strategies is often based on an assessment of the distance over which transmission can realistically occur and estimation of this distance is very sensitive to the choice of kernel function, it is important that models used to inform control strategies can be scrutinised in the light of observation in order to elicit possible evidence against the selected kernel function. While a range of approaches to model criticism is in existence, the field remains one in which the need for further research is recognised. In this paper, building on earlier contributions by the authors, we introduce a new approach to assessing the validity of spatial kernels—the latent likelihood ratio tests—which use likelihood-based discrepancy variables that can be used to compare the fit of competing models, and compare the capacity of this approach to detect model mis-specification with that of tests based on the use of infection-link residuals. We demonstrate that the new approach can be used to formulate tests with greater power than infection-link residuals to detect kernel mis-specification particularly when the degree of mis-specification is modest. This new tests avoid the use of a fully Bayesian approach which may introduce undesirable complications related to computational complexity and prior sensitivity. Keywords Spatio-temporal epidemic models · Bayesian inference · Latent likelihood ratio tests · Latent processes Mathematics Subject Classification 62F15 · 92-08 · 92D30 · 62M30
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00285020-01529-3) contains supplementary material, which is available to authorized users.
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David Thong [email protected]
Extended author information available on the last page of the article
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1 Introduction Selection of spatial kernel functions in spatio-temporal epidemic models is a question of paramount practical importance. It is recognised (Shaw and Royle 1993; Gibson and Austin 1996) that predictions regarding the speed of epidemic spread or propensity for transmission over long distances are very sensitive to the choice of spatial kernel function. The control of epidemics such as foot and mouth disease (FMD) in the UK (Keeling 2001; Bates 2016; Chis Ster et al. 2009; Ferguson 2001; Ferguson et al. 2001; Jewell et al. 2009; Morris et al. 2001; BBC News 2011; Ster and Ferguson 2007; Streftaris and Gibson 2004a; Tildesley et al. 2008) or citrus canker in the USA (Neri et al. 2014; Gottwald et al
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