# Bayesian updating definition dating the enemey

The evidence is then obtained and combined through an application of Bayes’s theorem to provide a posterior probability distribution for the parameter.The posterior distribution provides the basis for statistical inferences concerning the parameter.Bayesian analysis, a method of statistical inference (named for English mathematician Thomas Bayes) that allows one to combine prior information about a population parameter with evidence from information contained in a sample to guide the statistical inference process.A prior probability distribution for a parameter of interest is specified first.Thomas Bayes was an English minister in the first half of the 18th century, whose (now) most famous work, “An Essay toward Solving a Problem is the Doctrine of Chances,” was brought to the attention of the Royal Society in 1763 – two years after his death – by his friend Richard Price.The essay, the key to what we now know as Bayes's Theorem, concerned how we should adjust probabilities when we encounter new data.Bayesian proponents argue that, if a parameter value is unknown, then it makes sense to specify a probability distribution that describes the possible values for the parameter as well as their likelihood.The Bayesian approach permits the use of objective data or subjective opinion in specifying a prior distribution.

Bayesian methods have been used extensively in statistical decision theory ( statistics: Decision analysis).

This contrasted with the more skeptical viewpoint of the Scottish philosopher David Hume, who argued that since we could not be certain that the sun would rise again, a prediction that it would was inherently no more rational than one that it wouldn't.

The Bayesian viewpoint, instead, regards rationality as a probabilistic matter.

In this context, Bayes’s theorem provides a mechanism for combining a prior probability distribution for the states of nature with sample information to provide a revised (posterior) probability distribution about the states of nature.

These posterior probabilities are then used to make better decisions.