Bayesian estimation for percolation models of disease spread in plant populations
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Statistical methods are formulated for fitting and testing percolation-based, spatio-temporal 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 nearest-neighbour hosts in a lattice, and time-varying 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 P-value of the test used to be estimated. For the Rhizoctonia-radish system the methods confirm the findings of earlier non-spatial analyses regarding the dynamics of disease transmission and yield new evidence of environmental heterogeneity in the replicate experiments.
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- Bayesian estimation for percolation models of disease spread in plant populations
Statistics and Computing
Volume 16, Issue 4 , pp 391-402
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- Spatio-temporal modeling
- Stochastic modelling
- Fungal pathogens
- Bayesian inference
- Markov chain Monte Carlo
- Industry Sectors
- Author Affiliations
- 1. Department of Actuarial Mathematics & Statistics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt 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