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Abstract:
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Many Bayesian analyses conclude with a summary of the posterior distribution, thus summarizing uncertainty about parameters of interest. This is not enough, as it neglects to state what it is about the parameters that we want actually want to know. Formally, deciding our criteria for a 'good' answer defines a loss function, or utility, and is usually only considered for point estimation problems. For interval estimation, we provide sensible, interpretable loss functions which formally justify some 'standard' but essentially ad-hoc Bayesian intervals. Developing these measures of utility for problems with multiple parameters is straightforward, and the Bayes rules remain attractive and simple. Direct connections can be made with frequentist methods of multiplicity-adjustment.
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