In the emerging era of precision medicine and empowering patients to take part in decisions about their clinical care, there is a growing need for user-friendly probabilistic reasoning tools to aid patients and physicians in the correct application of the

Bayes' theorem to ensure that they make well-informed medical decisions.

As explained in the FDA's Guidance document, prior information about a topic that you wish to investigate in more detail can be combined with new data using

Bayes' Theorem.

152) However, "objective Bayesians" (153) use

Bayes' theorem without eliciting prior probabilities from subjective beliefs, avoiding the charge of subjectivism.

Concerning terrorism, we can express

Bayes' Theorem for the probability of identifying a terrorist using the TSA's new behavioral testing screen as follows:

Bayes' theorem can also be applied to the interpretation of clinical trials.

Because of its reference to the assignation of probability for a single event, this subjective interpretation of

Bayes' theorem as a special case of reasoning by induction is rejected by the objectivist conceptions which, by the postulation of the existence of objective laws having more or less restrictive features that govern the behavior of phenomena, transform inductive reasoning into deductive one (6).

In both cases, the general Bayesian framework for continuous distributions uses the opinions of experts as "evidence," and this evidence is used as input to the decision maker's state of knowledge using

Bayes' Theorem.

Bayes' Theorem and the Epistemic Status of Competing Propositions

They can also be used in one form of

Bayes' theorem, as illustrated below, which has application to the Applied Evidence article on open-angle glaucoma in this issue.

In my own experience with using this textbook, students have some anxiety with the material on

Bayes' Theorem, the calculation of a stock's beta, Ohlson's clean surplus theory, and game theory.

Basically, all prior assumptions are made explicit, and the weights and hyperparameters are determined by applying

Bayes' theorem to map the prior assumptions into posterior knowledge after having observed the training data.

Bayes' Theorem (28) is an extremely important development in the history of social science, as well as a somewhat controversial area within statistics.