title: Marginal Bayesian nonparametric model for time to disease arrival of threatened amphibian populations.
abstract: The global emergence of Batrachochytrium dendrobatidis (Bd) has caused the extinction of hundreds of amphibian species worldwide. It has become increasingly important to be able to precisely predict time to Bd arrival in a population. The data analyzed herein present a unique challenge in terms of modeling because there is a strong spatial component to Bd arrival time and the traditional proportional hazards assumption is grossly violated. To address these concerns, we develop a novel marginal Bayesian nonparametric survival model for spatially correlated right-censored data. This class of models assumes that the logarithm of survival times marginally follow a mixture of normal densities with a linear-dependent Dirichlet process prior as the random mixing measure, and their joint distribution is induced by a Gaussian copula model with a spatial correlation structure. To invert high-dimensional spatial correlation matrices, we adopt a full-scale approximation that can capture both large- and small-scale spatial dependence. An efficient Markov chain Monte Carlo algorithm with delayed rejection is proposed for posterior computation, and an R package spBayesSurv is provided to fit the model. This approach is first evaluated through simulations, then applied to threatened frog populations in Sequoia-Kings Canyon National Park.
authors.affiliation: Department of Statistics, University of South Carolina, Columbia, South Carolina, U.S.A.
authors.forename: Haiming
authors.initials: H
authors.lastname: Zhou
authors.affiliation: Department of Statistics, University of South Carolina, Columbia, South Carolina, U.S.A.
authors.forename: Timothy
authors.initials: T
authors.lastname: Hanson
authors.affiliation: Sierra Nevada Aquatic Research Laboratory, University of California, Mammoth Lakes, California, U.S.A.
authors.forename: Roland
authors.initials: R
authors.lastname: Knapp
mesh_terms: D000465:Algorithms; D000663:Amphibians / Q000382:microbiology; D000818:Animals; D001499:Bayes Theorem; D001699:Biometry / Q000379:methods; D008411:Chytridiomycota / Q000472:pathogenicity; D003198:Computer Simulation; D056727:Endangered Species / Q000706:statistics & numerical data*; D008390:Markov Chains; D008954:Models, Biological; D015233:Models, Statistical; D009010:Monte Carlo Method; D009181:Mycoses / Q000662:veterinary; D011157:Population Dynamics / Q000706:statistics & numerical data; D018709:Statistics, Nonparametric; D013997:Time Factors
keywords: Bayesian nonparametric; Copula; Delayed rejection; Dependent Dirichlet process; Full-scale approximation; Point-referenced; Proportional hazards; Spatial survival data