A Gibbs sampler for multi-species occupancy models

Abstract

Multi-species occupancy (MSO) models use detection-nondetection data from several species observed at different locations to estimate the probability that a particular species occupies a particular geographical region. The models are particularly useful for estimating the occupancy probabilities associated with rare species since they are seldom observed when undertaking field surveys. In this paper, we develop Gibbs sampling algorithms that can be used to fit various Bayesian MSO models to detection-nondetection data. Bayesian analysis of these models can be undertaken using statistical packages such as JAGS, Stan and NIMBLE , however, since these packages were not developed specifically to fit occupancy models, one often experiences long run-times when undertaking analysis. In a single season (single species) nonspatial and spatial occupancy modelling context, Clark and Altwegg (2019), show that special purpose Gibbs samplers can produce posterior chains that mix faster and have larger expected sampling rates (Holmes & Held, 2006) than those obtained using JAGS and Stan. These results suggest that such algorithms could potentially lead to significant reductions in the run-times of MSO models. This paper illustrates how to fit MSO models when the detection and occupancy processes are modelled using logistic link functions and apply these methods to a camera-trapping study undertaken by 1 Drouilly, Clark, and O’Riain (2018). Variable selection is undertaken using a reversible-jump Markov chain Monte Carlo (Barker & Link, 2013) algorithm. We found that the Gibbs sampling algorithm developed produces posterior samples that are identical to those obtained when using Stan, resulting in faster run-times and has a larger expected sampling rate than Stan when analysing the above-referenced data set.