Relationship between bayesian and frequentist sample size determination

Sample size determination is among the most commonly encountered tasks in statistical practice. A broad range of frequentist and Bayesian methods for sample size determination can be described as choosing the smallest sample that is sufficient to achieve some set of goals. An example for the frequentist is seeking the smallest sample size that is sufficient to achieve a desired power at a specified significance level. An example for the Bayesian is seeking the smallest sample size necessary to obtain, in expectation, a desired rate of correct classification of the hypothesis as true or false. This article explores parallels between Bayesian and frequentist methods for determining sample size. We provide a simple but general and pragmatic framework for investigating the relationship between the two approaches, based on identifying mappings to connect the Bayesian and frequentist inputs necessary to obtain the same sample size. We illustrate this mapping with examples, highlighting a somewhat surprising "approximate functional correspondence" between power-based and information-based optimal sample sizes.