Belief networks are based on this theorem, which is often used to find the credible interval and is avoided by (*) frequentists.
Dempsey and Shafer developed a generalization of this theorem, which provides the basis for hierarchical modeling of transcription factors. In a Hidden Markov Model, the forward-backward algorithm uses this theorem to combine the forward and backward observations. Belief networks are based on this theorem, which is often used to find the credible interval and is avoided by (*) frequentists. Applying this theorem yields the interesting result that it's always beneficial to switch doors in the Monty Hall Problem. It states that the prior probability times the likelihood divided by a normalizer is equal to the conditional probability of an event. For 10 points, name this fundamental theorem of probability named for a British minister.
Dempsey and Shafer developed a generalization of this theorem, which provides the basis for hierarchical modeling of transcription factors.
{Bayes}' Theorem