The Importance of Prior Choice in Model Selection: a Density Dependence Example

Abstract: We perform a Bayesian analysis on abundance data for ten species of North American duck, using the results to investigate the evidence in favour of biologically motivated hypotheses about the causes and mechanisms of density dependence in these species. We explore the capabilities of our methods to detect density dependent effects, both by simulation and through analyzes of real data. The effect of the prior choice on predictive accuracy is also examined. We conclude that our priors, which are motivated by considering the dynamics of the system of interest, offer clear advances over the priors used by previous authors for the duck data sets. We use this analysis as a motivating example to demonstrate the importance of careful parameter prior selection if we are to perform a balanced model selection procedure. We also present some simple guidelines that can be followed in a wide variety of modelling frameworks where vague parameter prior choice is not a viable option. These will produce parameter priors that not only greatly reduce bias in selecting certain models, but improve the predictive ability of the resulting model-averaged predictor.