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Background

Decision theory is a well-developed branch of statistics. We do not intend to provide a full review of Bayesian decision theory here; we refer the interested reader to Robert (2007) and chapter 13 of Jaynes (2003) for nice introductions to the topic. Despite the large statistical literature on decision theory, these techniques have been used relatively rarely in discussions of systematic methodology. There are some notable exceptions. Wheeler (1991) presented a decision-theory argument for choosing among trees using a 0-1 loss function (see the section on “all-or-nothing” losses below). Jermiin et al.(1997) used frequentist and Bayesian decision theory arguments in the justification for their methods for constructing a majority-rule consensus of trees with likelihoods that are close to the maximum likelihood score. Minin et al.(2003) developed a model selection methodology from decision theory, and Abdo et …