An introduction to Bayesian inference for ecological research and environmental decision-making

In our statistical practice, we ecologists work comfortably within the hypothetico-deductive epistemology of Popper and the frequentist statistical methodology of Fisher. Consequently, our null hypotheses do not often take into account pre-existing data and do not require parameterization, our experiments demand large sample sizes, and we rarely use results from one experiment to predict the outcomes of future experiments. Comparative statistical statements such as ''we reject the null hypothesis st the 0.05 level,'' which reflect the likelihood of our data given our hypothesis, are of little use in communicating our results to nonspecialists or in describing the degree of certitude we have in our conclusions. In contrast, Bayesian statistical inference requires the explicit assignment of prior probabilities, based on existing information, to the outcomes of experiments. Such an assignment forces the parameterization of null and alternative hypotheses. The results of these experiments, regardless of sample size, then can be used to compute posterior probabilities of our hypotheses given the available data. Inferential conclusions in a Bayesian mode also are mon meaningful in environmental policy discussions: e.g., ''our experiments indicate that there is a 95% probability that acid deposition will affect northeastern conifer forests.'' Based on comparisons with current statistical practice in ecology, I argue that a ''Bayesian ecology'' would (a) make better use of pre-existing data; (b) allow stronger conclusions to be drawn from large-scale experiments with few replicates; and (c) be more relevant to environmental decision-making.