Bayesian methods for hierarchical models: are ecologists making a Faustian bargain?

It is unquestionably true that hierarchical models represent an order of magnitude increase in the scope and complexity of models for ecological data. The past decade has seen a tremendous expansion of applications of hierarchical models in ecology. The expansion was primarily due to the advent of the Bayesian computational methods. We congratulate the authors for writing a clear summary of hierarchical models in ecology. While we agree that hierarchical models are highly useful to ecology, we have reservations about the Bayesian principles of statistical inference commonly used in the analysis of these models. One of the major reasons why scientists use Bayesian analysis for hierarchical models is the myth that for all practical purposes, the only feasible way to fit hierarchical models is Bayesian. Cressie et al. (2009) do perfunctorily mention the frequentist approaches but are quick to launch into an extensive review of the Bayesian analyses. Frequentist inferences for hierarchical models such as those based on maximum likelihood are beginning to catch up in ease and feasibility (De Valpine 2004, Lele et al. 2007). The recent ''data cloning'' algorithm, for instance, ''tricks'' the Bayesian MCMC setup into providing maximum likelihood estimates and their standard errors (Lele et al. 2007). A natural question that a scientist should ask is: if one has a hierarchical model for which full frequentist (say, based on ML estimation) as well as Bayesian inferences are available, which should be used and why? This can only be answered based on the philosophical underpinnings. The convenience criterion, commonly used to justify the use of Bayesian approach, no longer applies, given the recent advances in the frequentist computational approaches. Although the Bayesian computational algorithms made statistical inference for such models possible, it is not clear to us that the Bayesian inferential philosophy necessarily leads to good science. In return for seemingly confident inferences about important quantities in the face of poor data and vast natural uncertainties, are ecologists making a Faustian bargain? We begin by stating our reservations about the scientific philosophy advocated by the authors. The authors claim that modeling is for synthesis of information (Cressie 2009). Furthermore, they claim that subjectivity is unavoidable. We completely disagree with both these statements. In our opinion, the fundamental goal of modeling in science is to understand the mechanisms underlying the natural phenomena. Models are quantitative hypotheses about mechanisms that help us connect our prospective understandings to observable phenomena. …