Reference 2 discusses the application of Bayes' Theorem
to a horse-racing example.
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.
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.
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.