f an event having occurred in the first sequential position given that a particular event has been observed in the second sequential position.
Bayesian statistics has been expanded to incorporate the expected value criterion. Use of the expected value criterion is a distinct procedure (involving the use of expected values) from that of the Bayesian theorem (involving the revision of prior probability values).
The principal techniques of classical inference are interval estimation and hypothesis testing. The primary concern of Bayesian decision analysis is the choice of a decision act. Although classical statistical techniques are directly concerned with estimating values or with the testing of hypotheses concerning population parameters, the results of these procedures are related to alternative courses of action or to alternative decisions.
Bayesian statistical analysis also is concerned with the selection of the best decision. Whereas classical statistical analysis decision procedures are based entirely on the analysis of data collected through a random sampling of a total population, the decision procedures associated with Bayesian analysis may include the analysis of sample data, but are not dependent upon the availability of such data.
One of the principal applications of Bayesian statistical analysis is the derivation of alternative probabilities to those that may be observed in sample data. Bayes' theorem is used for the purpose of altering probabilities associated with an entire set of probable events, or states, in a decision situation. In the context of such a decision situation, prior probability distribution is that probability distribution which is applicable before any sample data are collected. In Bayesian decision analysis, this type of probability distribution is often subjective, in that the data upon which it is based is itself based on the judgments of individuals. In Bayesian s...