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September 2016 Bayesian nonparametric dependent model for partially replicated data: The influence of fuel spills on species diversity
Julyan Arbel, Kerrie Mengersen, Judith Rousseau
Ann. Appl. Stat. 10(3): 1496-1516 (September 2016). DOI: 10.1214/16-AOAS944


We introduce a dependent Bayesian nonparametric model for the probabilistic modeling of membership of subgroups in a community based on partially replicated data. The focus here is on species-by-site data, that is, community data where observations at different sites are classified in distinct species. Our aim is to study the impact of additional covariates, for instance, environmental variables, on the data structure, and in particular on the community diversity. To this end, we introduce dependence a priori across the covariates and show that it improves posterior inference. We use a dependent version of the Griffiths–Engen–McCloskey distribution defined via the stick-breaking construction. This distribution is obtained by transforming a Gaussian process whose covariance function controls the desired dependence. The resulting posterior distribution is sampled by Markov chain Monte Carlo. We illustrate the application of our model to a soil microbial data set acquired across a hydrocarbon contamination gradient at the site of a fuel spill in Antarctica. This method allows for inference on a number of quantities of interest in ecotoxicology, such as diversity or effective concentrations, and is broadly applicable to the general problem of community response to environmental variables.


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Julyan Arbel. Kerrie Mengersen. Judith Rousseau. "Bayesian nonparametric dependent model for partially replicated data: The influence of fuel spills on species diversity." Ann. Appl. Stat. 10 (3) 1496 - 1516, September 2016.


Received: 1 July 2015; Revised: 1 February 2016; Published: September 2016
First available in Project Euclid: 28 September 2016

zbMATH: 06775275
MathSciNet: MR3553233
Digital Object Identifier: 10.1214/16-AOAS944

Keywords: Bayesian nonparametrics , covariate-dependent model , Gaussian processes , Griffiths–Engen–McCloskey distribution , partially replicated data , stick-breaking representation

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.10 • No. 3 • September 2016
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