Bayesian probability

lastmod 2018-08-17created 2015-12-287 edits

Bayesian probability is an interpretation of probability that treats probability as 'a measure of a state of knowledge'. This differs from interpretations that regard probability as frequency of occurrence or as a physical property of some system. It is named after Thomas Bayes, the 18th-century statistician who pioneered the field.

According to John Earman, there are two viewpoints in Bayesian probability. From the objective viewpoint, the rules of Bayesian statistics can be justified rationally and universally and can be explained as an extension of logic. On the other hand, from the viewpoint of subjectivist probability theory, a state of knowledge can be measured as a personal degree of belief. Many modern machine learning methods are built on objective Bayesian principles. Bayesian probability is one of the most popular of the various concepts of probability and is widely applied in psychology, sociology, and economic theory. To evaluate the probability of a hypothesis, a prior probability is first specified and then updated to a new probability value in light of new relevant data. Bayes' theorem provides the standard procedure and formula needed for calculating such probabilities.

Overview

• Namuwiki: Bayes' theorem

Bayes' theorem was devised in the 1740s by Thomas Bayes, an English minister. Bayes' theorem is an algorithm that infers the probability of an event based on prior experience and current evidence. For example, suppose that about 1% of the world's population is known to suffer from some disease I, that there is a test with 90% accuracy for determining whether someone has disease I, and that a person takes this test and gets a positive result; what is the probability that this person actually has disease I? According to Bayes' theorem, this probability is about 8%.

Documentation

Bayesian Reasoning and Machine Learning

http://web4.cs.ucl.ac.uk/staff/D.Barber/pmwiki/pmwiki.php?n=Brml.Online

http://web4.cs.ucl.ac.uk/staff/D.Barber/textbook/020217.pdf

Bayes' theorem

• Wikipedia (en) Description of Bayes' theorem
• An easy way to solve Bayes' theorem
• [Recommended] AI Study: Bayes' Theorem

In probability theory and statistics, Bayes' theorem (English: Bayes’ theorem) is a theorem that describes the relationship between the prior and posterior probabilities of two random variables. Under the Bayesian interpretation of probability, Bayes' theorem determines how the posterior probability is updated when new evidence is presented.

See also

• Probability theory
• Machine learning
• Maximum a posteriori estimation (MAP)
• Maximum likelihood estimation (MLE)

Favorite site

• Wikipedia (en) Description of Bayesian probability
• Bayesian inference - Part 1
• Bayes' theorem and MLE, MAP ¹

References