Fast and efficient approaches to large-scale occupancy models - Clark, Allan Ernest (Department of Statistical Sciences, 2023)
Bayesian occupancy models are important statistical tools that are used to investigate species range dynamics, species interactions as well as undercover key biological processes that drive occupancy (and detection) in a particular region. The results from these models are used to answer pressing conservation questions and are often used to develop responses to them. My original contribution to knowledge is the development of statistical methods that use detection-nondetection data commonly collected when undertaking occupancy modelling. The efficacy of these methods are investigated and applied to various South African detection-nondetection data sets. I developed two Variational Bayes approximations to the posterior distribution of the parameters of a single season site occupancy model that uses logistic or probit link functions to model the probability of species occurrence at sites and species detection probabilities. The results suggest that under certain circumstances, the variational distributions provide accurate approximations to the true posterior distributions of the parameters of the model when the survey occasions are as low as three and the accuracy of the approximations improves as the sampling occasions increase. Approximate methods could be implemented when the detection probability is at least 0.5 and when there are at least three sampling occasions. The link between logistic regression and occupancy modelling was exploited to develop a Gibbs sampler required to obtain posterior samples from the posterior distribution of the parameters of various occupancy model types (nonspatial, spatial and multi-species) when logit link functions are used to model the regression effects of the detection and occupancy processes. For the nonspatial occupancy model, the Gibbs sampling algorithm developed produces posterior samples that are identical to those obtained when using JAGS and Stan and that in certain cases the posterior chains mix faster than those obtained when using JAGS, stocc, and Stan. The Gibbs sampling algorithm developed for the multi-species occupancy model produces posterior samples that are identical to those obtained when using Stan, resulting in faster implementation times and a larger expected sampling rate than Stan. The algorithms are implemented in the R package Rcppocc and MSO which is freely available on GitHub (https://github.com/AllanClark/Rcppocc, https://github.com/ AllanClark/MSO).