Bayesian Approach to Statistics

Paul Gustafson

The Bayesian approach to statistics is a general paradigm for drawing inferences from observed data. It is distinguished from other approaches by the use of probabilistic statements about fixed but unknown quantities of interest (as opposed to probabilistic statements about mechanistically random processes such as coin flips). At the heart of Bayesian analysis is Bayes's theorem, which describes how knowledge is updated on observing data. In epidemiology, diagnostic testing provides the most familiar illustration of Bayes's theorem. Say the unobservable variable y is a subject's true disease status (coded as 0/1 for absence/presence). Let q be the investigator-assigned probability that y = 1, in advance of diagnostic testing. One interpretation of how this probability statement reflects knowledge is that the investigator perceives the pretest odds q =(1 − q ) as the basis of a ‘fair bet’ on whether the subject is diseased. If the subject is randomly selected from ...

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