The Annals of Applied Statistics

Bayesian nonparametric dependent model for partially replicated data: The influence of fuel spills on species diversity

Julyan Arbel, Kerrie Mengersen, and Judith Rousseau

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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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Ann. Appl. Stat. Volume 10, Number 3 (2016), 1496-1516.

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

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


Arbel, Julyan; Mengersen, Kerrie; Rousseau, Judith. Bayesian nonparametric dependent model for partially replicated data: The influence of fuel spills on species diversity. Ann. Appl. Stat. 10 (2016), no. 3, 1496--1516. doi:10.1214/16-AOAS944.

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Supplemental materials

  • Supplement to “Bayesian nonparametric dependent model for partially replicated data: The influence of fuel spills on species diversity”. The supplementary material contains details about posterior computation and inference in the Dep-GEM model, additional results and omitted proofs that complement the analysis of the main text. It is available as Arbel, Mengersen and Rousseau (2016).