On the use of prior distributions in bayesian inference applied to Ecology: an ecological example using binomial proportions in exotic plants, Central Chile

Abstract

Abstract Background The use of Bayesian inference (BI) is a common methodology for data analysis in Ecology and Evolution. This statistical approach is particularly useful in cases which information is scarce, because allows formalizing sources of information, other than sampling data (priors), obtained from technical reports, expert opinions and beliefs. Recent reviews detected that most ecological studies use non-informative priors without any justification, ignoring other sources of independent information available to construct informative priors. In this study, we examined how the selection of informative or non-informative priors, affects hypothesis testing. We compared the proportion of occupied sites (occupancy) in four exotic plant species living in two contrasting environments in Central Chile. Given that occupancy is related to binomial proportions, we developed a statistical procedure based on beta distribution, to compare occupancies using Bayes factor. Results Bayes factor obtained from different non-informative priors led to similar inferences relative to H0. The use of informative prior drastically changed our decisions about H0 in three of four plant species. Conclusions The selection of priors is critical because they determine hypothesis testing. The use of independent information will improve our inferences, which is precisely the strength of BI. We hypothesize that the reluctance to use informative priors in ecological studies reflects extreme positivism and the use of non-informative priors is a strategy to avoid subjectivity; by doing that, ecologists depart from the philosophy of BI which accepts that the subjective knowledge is a valid, and sometimes the only alternative, to know the world.

Keywords

• Bayesian inference
• Bayes factor
• Binomial proportions
• Prior distribution
• Posterior distribution