Abstract
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 (K) are as low as three and that the accuracy of the approximations improves as K 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).
Highlights
Bayesian analysis is a coherent statistical paradigm whereby prior information regarding the research area is blended with that of information obtained from the observed data [1]
We developed two new methods of approximating the posterior distribution of the parameters of a Bayesian single season occupancy model that use logistic link functions
We believe that the approximation results obtained using the probit link function would be similar to those obtained using the tangent based method and did not explicitly consider this link function
Summary
Bayesian analysis is a coherent statistical paradigm whereby prior information regarding the research area is blended with that of information obtained from the observed data [1]. Subjective prior information is elicited either from expertise in the field or based on prior research (meta analyses). Informative priors are increasingly being used in ecology ([2, 3]) and even in the absence of prior information many ecologists are using Bayesian methods [4]. One class of model that is often analysed in a Bayesian way is the occupancy model [5]. The single season occupancy model was formulated by using ideas borrowed from closed population mark-recapture models. In this model n sites are visited a number of times (K) in order to estimate the occupancy (ψ) and detection probability (denoted throughout as d) of a species associated with each site. In this model n sites are visited a number of times (K) in order to estimate the occupancy (ψ) and detection probability (denoted throughout as d) of a species associated with each site. (The term detection probability should be read as conditional detection probability throughout the text.) These methods are useful when studying the PLOS ONE | DOI:10.1371/journal.pone.0148966 February 29, 2016
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