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Suggestions for Presenting the Results of Data Analyses

Bayesian Methods

Although Bayesian methods date back over 2 centuries, they are not familiar to most biologists. Bayesian analysis allows inference from a posterior distribution that incorporates information from the observed data, the model, and the prior distribution (Schmitt 1969, Ellison 1996, Barnett 1999, Wade 2000). Bayesian methods often require substantial computation and have been increasingly applied since computers have become widely available (Lee 1997).

In reporting results, authors should consider readers' lack of familiarity with Bayesian summaries such as odds ratios, Bayes factors, and credible intervals. The clarity of a presentation can be greatly enhanced by a simple explanation after the first references to such quantities: "A Bayes factor of 4.0 indicates that the ratio of probabilities for Model 1 and Model 2 is 4 times larger when computed using the posterior rather than the prior."

Presentations of Bayesian analyses should report the sensitivity of conclusions to the choice of the prior distribution. This portrayal of sensitivity can be accomplished by including overlaid graphs of the posterior distributions for a variety of reasonable priors or by tabular presentations of credible intervals, posterior means, and medians.

An analysis based on flat priors representing limited or vague prior knowledge should be included in the model set. When the data seem to contradict prevailing thought, the strength of the contradiction can be assessed by reporting analyses based on priors reflecting prevailing thought.

Generally, Bayesian model-checking should be reported. Model-checks vary among applications, and there are a variety of approaches even for a given application (Carlin and Lewis 1996, Gelman and Meng 1996, Gelman et al. 1995). One particularly simple and easily implemented check is a posterior predictive check (Rubin 1984). The credibility of the results will be enhanced by a brief description of model-checks performed, especially as these relate to questionable aspects of the model. A lengthy report of model-checks will usually not be appropriate, but the credibility of the published paper will often be enhanced by reporting the results of model-checks.

The implementation of sophisticated methods for fitting models, such as Markov Chain Monte Carlo (MCMC; Geyer 1992) should be reported in sufficient detail. In particular, MCMC requires diagnostics to indicate that the posterior distribution has been adequately estimated.

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