Choosing priors in Bayesian ecological models by simulating from the prior predictive distribution

Abstract

Bayesian data analysis is increasingly used in ecology, but prior specification remains focused on choosing non-informative priors (e.g., flat or vague priors). One barrier to choosing more informative priors is that priors must be specified on model parameters (e.g., intercepts, slopes, and sigmas), but prior knowledge often exists on the level of the response variable. This is particularly true for common models in ecology, like generalized linear mixed models that have a link function and potentially dozens of parameters, each of which needs a prior distribution. We suggest that this difficulty can be overcome by simulating from the prior predictive distribution and visualizing the results on the scale of the response variable. In doing so, some common choices for non-informative priors on parameters can easily be seen to produce biologically impossible values of response variables. Such implications of prior choices are difficult to foresee without visualization. We demonstrate a workflow for prior selection using simulation and visualization with two ecological examples (predator-prey body sizes and spider responses to food competition). This approach is not new, but its adoption by ecologists will help to better incorporate prior information in ecological models, thereby maximizing one of the benefits of Bayesian data analysis.

Individual size distributions across North American streams vary with local temperature

“…The prior for the random year intercepts was set to Exponential (5) to improve model convergence. To ensure that the prior distributions contained reasonable prior predictions but did not overwhelm the posterior inference, we used prior predictive simulation and prior sensitivity analysis (see Supporting Information S4–S7; Gabry et al, 2019, Wesner & Pomeranz, 2021).…”

Larger but younger fish when growth outpaces mortality in heated ecosystem

“…The other seven models include some or all parameters as parameters common for the two areas, e.g., substituting 𝐿 &./01 and 𝐿 &8/9:1 with 𝐿 &1 . To aid convergence of this non-linear model, we used informative priors chosen after visualizing draws from prior predictive distributions (Wesner & Pomeranz 2021) using probable parameter values (Supporting Information, Fig. S1, S7).…”

Geography, taxonomy, and ecological guild: Factors impacting freshwater macroinvertebrate gut microbiomes

“…We then compared these models using the Watanabe‐Akaike Information Criterion (WAIC) (Hooten & Hobbs, 2015 ). Priors for each parameter were chosen using prior predictive simulation (Wesner & Pomeranz, 2021 ) and are justified in the Appendix S1 .…”