# Bayes's Theorem

Bayes's Theorem

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• A Bayesian approach to inference implies combining prior judgment with new information to obtain revised judgment. Prior judgment is expressed in a prior probability that a hypothesis is true. The prior probability is subsequently updated with new data that become available to yield the revised posterior probability of the hypothesis. Bayesian updating can be applied to the results of diagnostic tests (which is explained here), to a research hypothesis under investigation, or to a parameter being estimated in a study.

Bayesian Updating of the Probability of Disease

Estimates of probabilities of disease conditional on diagnostic test results are usually not readily available. One is more likely to have an assessment of the probability of a test result among patients with or without the disease. Converting conditional probabilities ...

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