A Variational Bayes Approach to the Analysis of Occupancy Models

<div><p>Detection-nondetection data are often used to investigate species range dynamics using Bayesian occupancy models which rely on the use of Markov chain Monte Carlo (MCMC) methods to sample from the posterior distribution of the parameters of the model. In this article we develop two Variational Bayes (VB) approximations to the posterior distribution of the parameters of a single-season site occupancy model which uses logistic link functions to model the probability of species occurrence at sites and of species detection probabilities. This task is accomplished through the development of iterative algorithms that do not use MCMC methods. Simulations and small practical examples demonstrate the effectiveness of the proposed technique. We specifically show that (under certain circumstances) the variational distributions can provide accurate approximations to the true posterior distributions of the parameters of the model when the number of visits per site (<i>K</i>) are as low as three and that the accuracy of the approximations improves as <i>K</i> increases. We also show that the methodology can be used to obtain the posterior distribution of the predictive distribution of the proportion of sites occupied (PAO).</p>