Bayesian estimation for percolation models of disease spread in plant populations
 G. J. Gibson,
 W. Otten,
 J. A. N. Filipe,
 A. Cook,
 G. Marion,
 C. A. Gilligan
 … show all 6 hide
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Statistical methods are formulated for fitting and testing percolationbased, spatiotemporal models that are generally applicable to biological or physical processes that evolve in spatially distributed populations. The approach is developed and illustrated in the context of the spread of Rhizoctonia solani, a fungal pathogen, in radish but is readily generalized to other scenarios. The particular model considered represents processes of primary and secondary infection between nearestneighbour hosts in a lattice, and timevarying susceptibility of the hosts. Bayesian methods for fitting the model to observations of disease spread through space and time in replicate populations are developed. These use Markov chain Monte Carlo methods to overcome the problems associated with partial observation of the process. We also consider how model testing can be achieved by embedding classical methods within the Bayesian analysis. In particular we show how a residual process, with known sampling distribution, can be defined. Model fit is then examined by generating samples from the posterior distribution of the residual process, to which a classical test for consistency with the known distribution is applied, enabling the posterior distribution of the Pvalue of the test used to be estimated. For the Rhizoctoniaradish system the methods confirm the findings of earlier nonspatial analyses regarding the dynamics of disease transmission and yield new evidence of environmental heterogeneity in the replicate experiments.
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 Title
 Bayesian estimation for percolation models of disease spread in plant populations
 Journal

Statistics and Computing
Volume 16, Issue 4 , pp 391402
 Cover Date
 20061201
 DOI
 10.1007/s112220060019z
 Print ISSN
 09603174
 Online ISSN
 15731375
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Spatiotemporal modeling
 Stochastic modelling
 Fungal pathogens
 Bayesian inference
 Markov chain Monte Carlo
 Industry Sectors
 Authors

 G. J. Gibson ^{(1)}
 W. Otten ^{(2)}
 J. A. N. Filipe ^{(2)} ^{(3)}
 A. Cook ^{(1)} ^{(4)}
 G. Marion ^{(4)}
 C. A. Gilligan ^{(2)}
 Author Affiliations

 1. Department of Actuarial Mathematics & Statistics and the Maxwell Institute for Mathematical Sciences, HeriotWatt University, Riccarton, Edinburgh, EH14 4AS
 2. Department of Plant Sciences, University of Cambridge, Downing Street, Cambridge, CB2 3EA, UK
 3. Infectious Disease Epidemiology Unit, London School of Hygiene & Tropical Medicine, Keppel Street, London, WC1E 7HT
 4. Biomathematics & Statistics Scotland, James Clerk Maxwell Building, The King’s Buildings, Edinburgh, EH9 3JZ