Intrinsic Bayesian Analysis for Occupancy Models

Abstract: Occupancy models are typically used to determine the probability of a species being present at a given site while accounting for imperfect detection. The survey data underlying these models often include information on several predictors that could potentially characterize habitat suitability and species detectability. Because these variables might not all be relevant, model selection techniques are necessary in this context. In practice, model selection is performed using the Akaike Information Criterion (AIC), as few other alternatives are available. This paper builds an objective Bayesian variable selection framework for occupancy models through the intrinsic prior methodology. The procedure incorporates priors on the model space that account for test multiplicity and respect the polynomial hierarchy of the predictors when higher-order terms are considered. The methodology is implemented using a stochastic search algorithm that is able to thoroughly explore large spaces of occupancy models. The proposed strategy is entirely automatic and provides control of false positives without sacrificing the discovery of truly meaningful covariates. The performance of the method is evaluated and compared to AIC through a simulation study. The method is illustrated on two datasets previously studied in the literature.