BAYESIAN PROBABILITY

Bayesianism is the philosophical tenet that the mathematical theory of probability applies to the degree of plausibility of statements, or to the degree of belief of rational agents in the truth of statements. It is opposed to frequentism, which rejects degree-of-belief interpretations of mathematical probability, and assigns probabilities instead to random events according to their relative frequencies of occurrence. Whereas a frequentist might assign probability 1/2 to the event of getting a head when a coin is tossed (but only if the frequentist knows that that is the relative frequency) a Bayesian might assign probability 1/2 to the proposition that there was life on Mars a billion years ago, without intending that assignment to assert anything about any relative frequency.

The terms subjectivism, subjective probability, personal probability, epistemic probability and logical probability are used to describe what Bayesians believe in. Not all of these terms are synonymous, however.

Advocates of "logical probability" would like to codify techniques whereby if two people have the same prior information relevant to the truth of an uncertain proposition, then they would assign the same probability. No one has any idea how to do that except in simple cases, and then the validity of proposed methods is subject to philosophical controversy. The most sophisticated proponents of this view have been Sir Harold Jeffreys and Edwin Jaynes.

"Subjective probability" is supposed to measure how sure someone is of an uncertain proposition.

The Bayesian approach is in contrast to frequency probability where probability is held to be derived from observed or imagined frequency distributions or proportions of populations. The difference has many implications for the methods by which statistics is practiced when following one model or the other.

History of Bayesian probability

Bayesianism is named after Thomas Bayes, the originator of Bayes' theorem. This theorem is often used to update the plausibility of a given statement in light of new evidence. Laplace (1812) rediscovered the theorem and put it to good use in solving problems in celestial mechanics, medical statistics and, by some accounts, even jurisprudence.

For instance, he estimated the mass of Saturn, given orbital data that were available to him from various astronomical observations. He presented the result together with an indication of its uncertainty, stating it like this: `It is a bet of 11000 to 1 that the error in this result is not within 1/100th of its value'. He would have won the bet, as another 150 years' accumulation of data has changed the estimate by only 0.63%. According to the frequency probability definition, however, we are not permitted to use probability theory to tackle this problem. This is because the mass of Saturn is a constant and not a random variable, therefore, it has no frequency distribution and so probability theory cannot be used.

Bayesianism has been championed by L. J. Savage, Bruno de Finetti, Edwin Jaynes, Frank P. Ramsey, and others. They created the idea of defining rational belief as an abstraction of betting behavior subject to the constraint that one doesn't want to be inconsistent in his behavior. A series of critiques of statistical methods was based on this concept and formed the basis of debate from the 1950s and statisticians remain divided on the issue.

See uncertainty

Applications of Bayesian probability

Today, there are a variety of applications of personal probability that have gained wide acceptance. Some schools of thought emphasise Cox's theorem and Jaynes' principle of maximum entropy as cornerstones of the theory, while others may claim that Bayesian methods are more general and give better results in practice than frequency probability.

Multi-dimensional Bayesian probability techniques have been a fundamental part of computerized pattern recognition techniques since the late 1950s. There is growing interest in using Bayesian probability to filter spam. For example: Bogofilter, SpamAssassin and Mozilla.

External links

On-line textbook: Information Theory, Inference, and Learning Algorithms, by David MacKay, has many chapters on Bayesian methods, including introductory examples; compelling arguments in favour of Bayesian methods (in the style of Edwin Jaynes); state-of-the-art Monte Carlo methods, message-passing methods, and variational methods; and examples illustrating the intimate connections between Bayesian inference and data compression.

Modern Translation: BAYESIAN PROBABILITY

Language		Translations for "BAYESIAN PROBABILITY"; alternative meanings/domain in parentheses.
Danish		Bayes'regel (Bayesian inference, Bayesian logic, Bayes'Rule, statistical inference), Bayes'logik (Bayesian inference, Bayesian logic, Bayes'Rule, statistical inference). (various references)

Dutch		Bayes-regel (Bayesian inference, Bayesian logic, Bayes'Rule, statistical inference), Bayes-logica (Bayesian inference, Bayesian logic, Bayes'Rule, statistical inference). (various references)

Finnish		Bayes-logiikka (Bayesian inference, Bayesian logic, Bayes'Rule, statistical inference), Bayesin logiikka (Bayesian inference, Bayesian logic, Bayes'Rule, statistical inference). (various references)

French		modèle bayésien (Bayesian inference, Bayesian logic, Bayes'Rule), formule de Bayes (Bayesian inference, Bayesian logic, Bayes'Rule), approche bayésienne (Bayesian inference, Bayesian logic, Bayes'Rule). (various references)

German		Bayesche Wahrscheinlichkeitstheorie (Bayesian inference, Bayesian logic, Bayes'Rule, statistical inference). (various references)

Greek		νόμος του Bayes (Bayesian inference, Bayesian logic, Bayes'Rule, statistical inference), λογική του Bayes (Bayesian inference, Bayesian logic, Bayes'Rule, statistical inference). (various references)

Italian		teorema di Bayes (Bayesian inference, Bayesian logic, Bayes'Rule, Bayes'theorem, statistical inference), regola di Bayes (Bayes'decision rule, Bayesian inference, Bayesian logic, Bayes'Rule, statistical inference). (various references)

Pig Latin		ayesianbay obabilitypray

Portuguese		método de Bayes (Bayesian inference, Bayesian logic, Bayes'Rule, statistical inference). (various references)

Spanish		regla de Bayes (Bayesian inference, Bayesian logic, Bayes'Rule, statistical inference), lógica Bayesiana (Bayesian inference, Bayesian logic, Bayes'Rule, statistical inference). (various references)

Swedish		Bayesisk logik (Bayesian inference, Bayesian logic, Bayes'Rule, statistical inference), Bayes formel (Bayesian inference, Bayesian logic, Bayes'Rule, statistical inference). (various references)
Source: compiled by the editor from various translation references.

Anagrams: BAYESIAN PROBABILITY

Alternative Orthography: BAYESIAN PROBABILITY

Hexadecimal (or equivalents, 770AD-1900s) (references)

42 41 59 45 53 49 41 4E 50 52 4F 42 41 42 49 4C 49 54 59

Leonardo da Vinci (1452-1519; backwards) (references)

Binary Code (1918-1938, probably earlier) (references)

01000010 01000001 01011001 01000101 01010011 01001001 01000001 01001110 00100000 01010000 01010010 01001111 01000010 01000001 01000010 01001001 01001100 01001001 01010100 01011001

HTML Code (1990) (references)

&#66 &#65 &#89 &#69 &#83 &#73 &#65 &#78 &#32 &#80 &#82 &#79 &#66 &#65 &#66 &#73 &#76 &#73 &#84 &#89

ISO 10646 (1991-1993) (references)

0042 0041 0059 0045 0053 0049 0041 004E 0050 0052 004F 0042 0041 0042 0049 004C 0049 0054 0059

Encryption (beginner's substitution cypher): (references)

Domain	Definition
Computing	Approach to inexact reasoning which consists in calculating the probability, e. g. of a disease, in light of specified evidence from the a priori probability of the disease and the conditional probability relating the observations to the diseases. Source: European Union. (references)
Source: compiled by the editor from various references; see credits.

Scrabble® Enable2K-Verified Anagrams
	Words within the letters "a-a-a-b-b-b-e-i-i-i-l-n-o-p-r-s-t-y-y"
	-5 letters: inseparability.
Source: compiled by the editor from various references; see credits. SCRABBLE® is a registered trademark. All intellectual property rights in and to the game are owned in the U.S.A and Canada by Hasbro Inc., and throughout the rest of the world by J.W. Spear & Sons Limited of Maidenhead, Berkshire, England, a subsidiary of Mattel Inc. Mattel and Spear are not affiliated with Hasbro.

BAYESIAN PROBABILITY

Specialty Definition: BAYESIAN PROBABILITY

Computing

Specialty Definition: Bayesian probability

History of Bayesian probability

Applications of Bayesian probability

External links

Modern Translation: BAYESIAN PROBABILITY

Danish

Dutch

Finnish

French

German

Greek

Italian

Pig Latin

Portuguese

Spanish

Swedish

Anagrams: BAYESIAN PROBABILITY

Scrabble® Enable2K-Verified Anagrams

Alternative Orthography: BAYESIAN PROBABILITY

42 41 59 45 53 49 41 4E 50 52 4F 42 41 42 49 4C 49 54 59

01000010 01000001 01011001 01000101 01010011 01001001 01000001 01001110 00100000 01010000 01010010 01001111 01000010 01000001 01000010 01001001 01001100 01001001 01010100 01011001

&#66 &#65 &#89 &#69 &#83 &#73 &#65 &#78 &#32 &#80 &#82 &#79 &#66 &#65 &#66 &#73 &#76 &#73 &#84 &#89

0042 0041 0059 0045 0053 0049 0041 004E 0050 0052 004F 0042 0041 0042 0049 004C 0049 0054 0059

363559395343354825052493635364346435459

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