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Bayes' theorem (view source)

Revision as of 01:44, August 3, 2018

38 bytes removed ,  01:44, August 3, 2018
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where X and Y are independent statements, I is available background information, and
 
where X and Y are independent statements, I is available background information, and
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<math>P(X|Y,I)</math> is the [[posterior probability]] for ''X'' given ''Y'' and ''I'',
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<math>P(X|Y,I)</math> is the posterior probability for ''X'' given ''Y'' and ''I'',
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<math>P(Y|X,I)</math> is the [[likelihood]] for ''Y'' given ''X'' and ''I'',
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<math>P(Y|X,I)</math> is the likelihood for ''Y'' given ''X'' and ''I'',
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<math>P(X|I)</math> is the [[prior probability]] for ''X'' given only ''I'', and
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<math>P(X|I)</math> is the prior probability for ''X'' given only ''I'', and
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<math>P(Y|I)</math> is sometimes called the [[evidence (statistics)|evidence]] or probability for ''Y'' given only ''I''.
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<math>P(Y|I)</math> is sometimes called the evidence or probability for ''Y'' given only ''I''.
    
In a scientific context, ''X'' may be a [[hypothesis]], and ''Y'' may be experimental [[data]].  The theorem can then be used to determine the degree of belief in the hypothesis by using the experimental data.
 
In a scientific context, ''X'' may be a [[hypothesis]], and ''Y'' may be experimental [[data]].  The theorem can then be used to determine the degree of belief in the hypothesis by using the experimental data.
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