Bayesian Analysis for Inference of an Emerging Epidemic: Citrus Canker in Urban Landscapes

Neri, Franco M.; Cook, Alex R.; Gibson, Gavin J.; Gottwald, Tim R.; Gilligan, Christopher A.

where Q j (t) is the infectious pressure for host j at time t (Equation 2b). However, the data are actually censored, and the likelihood involves integrating over the unobserved infection times consistent with the data: f censored dataDa,b,e ð Þ Ð f uncensored dataDa,b,e ð Þ dt. The posterior for a,b,e ð Þ can then be obtained by extending the parameter vector to a,b,e,t 1 ,t 2 , . . . ð Þ [H, i.e. including the unobserved event times as parameters, and using MCMC to explore the augmented parameter space H [34, 35] (for recent applications see e.g. [21, [36] [37] [38] ). The marginal for a,b,e ð Þis the desired posterior. Independent uniform priors over the regions of interest were taken for all parameters, with support coinciding with the following intervals: 0, 1 ½ km for a; 0, 1 ½ days 21 km 2 for b; 0, 1 ½ days 21 for e. A Metropolis-Hastings algorithm with independent Gaussian proposal distributions [39] was used for parameters a, b, e, adjusting the width of the distributions to obtain an acceptance rate between 0.2 and 0.4 for each parameter. The proposal distribution for augmented infection times was constant over the corresponding censoring intervals. Each Monte Carlo chain was run for 100000-250000 steps (depending on the system size and the temporal window used, see below), and a burnin period corresponding to the initial 10% of the chain was discarded before the analysis, to ensure that convergence had been reached.