In the study of probability, two events A and B are said to be independent events if neither event influences or effects the other. For example, tossing a coin twice yields independent events because whether the coin shows heads or tails on the second...

. Theorem of PROBABILITY calculus, variously formulated and developed by and after T.Bayes (1702–61). Briefly, where p and q are propositions, the probability of p, given q, is that of q, given p, multiplied by the prior probability of p and...

Bayes, Bayes' Theorem, Bayesian Approach to Philosophy of Science The posthumous publication, in 1763, of Thomas Bayes's "Essay Towards Solving a Problem in the Doctrine of Chances" inaugurated a revolution in the...

Bayes' theorem (also known as Bayes' rule or Bayes' law) is a result in probability theory, which relates the conditional and marginal probability distributions of random variables. In some interpretations of probability, Bayes' theorem tells how to...

The application of Bayes factors for statistical hypothesis testing in genetics, sports, ecology, sociology and psychology is considered. The measure, which was introduced by Jeffreys in his 1935 book 'Theory of Probability,' represents the 'posterior odds of the null hypothesis when the prior probability...

Bayes factors are applied in multiple and partial settings for statistical hypotheses testing. The multiple case generates an intermediate analysis effect between standard testing and point estimation. Bayes factors are also shown to extend applications for point null hypothesis, model choice, discriminant analysis and...