A guide to Bayesian model selection for ecologists

Abstract

The steady upward trend in the use of model selection and Bayesian methods in ecological research has made it clear that both approaches to inference are important for modern analysis of models and data. However, in teaching Bayesian methods and in working with our research colleagues, we have noticed a general dissatisfaction with the available literature on Bayesian model selection and multimodel inference. Students and researchers new to Bayesian methods quickly find that the published advice on model selection is often preferential in its treatment of options for analysis, frequently advocating one particular method above others. The recent appearance of many articles and textbooks on Bayesian modeling has provided welcome background on relevant approaches to model selection in the Bayesian framework, but most of these are either very narrowly focused in scope or inaccessible to ecologists. Moreover, the methodological details of Bayesian model selection approaches are spread thinly throughout the literature, appearing in journals from many different fields. Our aim with this guide is to condense the large body of literature on Bayesian approaches to model selection and multimodel inference and present it specifically for quantitative ecologists as neutrally as possible. We also bring to light a few important and fundamental concepts relating directly to model selection that seem to have gone unnoticed in the ecological literature. Throughout, we provide only a minimal discussion of philosophy, preferring instead to examine the breadth of approaches as well as their practical advantages and disadvantages. This guide serves as a reference for ecologists using Bayesian methods, so that they can better understand their options and can make an informed choice that is best aligned with their goals for inference.

Spatially Heterogeneous Perturbations Homogenize the Regulation of Insect Herbivores

“…One way to address the uncertainty is to combine multifactorial and large-scale experimental approaches that capture direct and indirect human impacts with integrative statistical modeling that can account for these variable influences (Weiher et al 2004;Grace 2006;Grace et al 2012;Hooten and Hobbs 2015). Such an integrative approach, which is the focus of this study, avoids the limitations of global change experiments emphasizing mostly univariate processes (Rösch et al 2013;Shurin et al 2012;Hautier et al 2014;Thébault et al 2014) while analytically accounting for many of the interactive and indirect mechanisms that can determine outcomes to global change (Grace et al 2012).…”

Reconstruction of spatio-temporal temperature from sparse historical records using robust probabilistic principal component regression

“…Often, the optimal γ t is determined by crossvalidation using predictive skill. In the Bayesian framework, the shrinkage can be estimated by cross-validation or by assigning a prior distribution and performing a fully Bayesian inference (Park and Casella, 2008;Hooten and Hobbs, 2015).…”

Multi-Fraction Bayesian Sediment Transport Model

“…The Bayesian framework allows for integration of deterministic functions into a probabilistic framework [14]. Wilcock and Crowe [6] proposed a set of equations that accounts for the transport of different size fractions on the surface of a river bed and their interactions as a function of the proportion of fines contained in the bed surface.…”

“…As established above, the reference stresses are distributions and are not fixed. The analysis leading to Equation (14) had no basis for accounting for uncertainty in the five values of τr,sm. Using the posterior mean values for the mean surface stresses, the present analysis resulted in a somewhat different relationship Equation (15), with the reference stress for BOMC being larger than what was originally specified in [6] for the same sediment.…”