Reference 2 discusses the application of

Bayes' Theorem to a horse-racing example.

Bayes' theorem tells us that the value of a piece of evidence in testing a particular assertion is determined by its likelihood ratio.

The key for applying

Bayes' theorem to update the probabilistic distributions of uncertain models and their parameters using the measurement data is to create a probability model P with a model parameter vector [theta] or the likelihood function p(D | [theta], [M.sub.j]), which defines the likelihood of getting the measurement data D for a given parameter vector [theta] and a structural model [M.sub.j], where the probability mode parameter vector [theta] contains the structural model parameter vector a and other parameters that describe probabilistic characteristics of the probability mode and are defined subsequently.

Let's analyze SPOT using

Bayes' Theorem and some numerical approximations and conservative assumptions.

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

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, in its general form for continuous probability distributions, follows:

The BACS project is based on

Bayes' theorem, which provides a model for making rational judgements when the only information available is uncertain and incomplete.

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.