Bayesian estimation for percolation models of disease spread in plant populations

Gavin J. Gibson, Wilfred Otten, J. A. N. Filipe, Alex R. Cook, Glenn Marion, Christopher A. Gilligan

Research output: Contribution to journalArticle

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Abstract

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.
Original languageEnglish
Pages (from-to)391-402
Number of pages12
JournalStatistics and Computing
Volume16
Issue number4
DOIs
StatePublished - Dec 2006

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Model
Posterior distribution
Testing
Partial observation
Spatio-temporal model
Sampling distribution
Markov chain Monte Carlo methods
Bayesian estimation
Physical process
Bayesian methods
Bayesian analysis
Statistical method
Susceptibility
Infection
Nearest neighbor
Time-varying
Scenarios
Experiment
Sampling
Statistical methods

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Gibson, G. J., Otten, W., Filipe, J. A. N., Cook, A. R., Marion, G., & Gilligan, C. A. (2006). Bayesian estimation for percolation models of disease spread in plant populations. Statistics and Computing, 16(4), 391-402. DOI: 10.1007/s11222-006-0019-z

Gibson, Gavin J.; Otten, Wilfred; Filipe, J. A. N.; Cook, Alex R.; Marion, Glenn; Gilligan, Christopher A. / Bayesian estimation for percolation models of disease spread in plant populations.

In: Statistics and Computing, Vol. 16, No. 4, 12.2006, p. 391-402.

Research output: Contribution to journalArticle

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Gibson, GJ, Otten, W, Filipe, JAN, Cook, AR, Marion, G & Gilligan, CA 2006, 'Bayesian estimation for percolation models of disease spread in plant populations' Statistics and Computing, vol 16, no. 4, pp. 391-402. DOI: 10.1007/s11222-006-0019-z

Bayesian estimation for percolation models of disease spread in plant populations. / Gibson, Gavin J.; Otten, Wilfred; Filipe, J. A. N.; Cook, Alex R.; Marion, Glenn; Gilligan, Christopher A.

In: Statistics and Computing, Vol. 16, No. 4, 12.2006, p. 391-402.

Research output: Contribution to journalArticle

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AU - Gibson,Gavin J.

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AU - Gilligan,Christopher A.

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Gibson GJ, Otten W, Filipe JAN, Cook AR, Marion G, Gilligan CA. Bayesian estimation for percolation models of disease spread in plant populations. Statistics and Computing. 2006 Dec;16(4):391-402. Available from, DOI: 10.1007/s11222-006-0019-z