Bayesian model selection: The steepest mountain to climb

• Bayesian hierarchical models are becoming increasingly common.
• Selecting competing models can be potentially difficult in a Bayesian framework.
• We provide a “how to” contribution that can aid ecologists to address this task.
• We treat the comparison of non-nested models and the selection of variables in GLMs.
• We clarify theoretical and practical aspects on the use of two Gibbs sampler based strategies.

Following the advent of MCMC engines Bayesian hierarchical models are becoming increasingly common for modelling ecological data. However, the great enthusiasm for model fitting has not yet encompassed the selection of competing models, despite its fundamental role in the inferential process. This contribution is intended as a starting guide for practical implementation of Bayesian model and variable selection into a general purpose software in BUGS language. We explain two well-known procedures, the product space method and the Gibbs variable selection, clarifying theoretical aspects and practical guidelines through applied examples on the comparison of non-nested models and on the selection of variables in a generalized linear model problem. Despite the relatively wide range of available techniques and the difficulties related to the maximization of sampling efficiency, for their conceptual simplicity and ease of implementation the proposed methods represent useful tools for ecologists and conservation biologists that want to close the loop of a Bayesian analysis.