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In other words, there is only a 16% chance that a person testing positive actually has the disease.
In other words, there is only a 16% chance that a person testing positive actually has the disease.
In other words, there is only a 16% chance that a person testing positive actually has the disease.
An extended form of Bayes's theorem is obtained by noting that it applies to [[probability distributions]] as well as to events. Let ''y'' be a (vector valued) observable quantity that we want to use to estimate some unknown, unobservable (vector valued) quantity <math>theta</math>. Prior to seeing the data ''y'', we summarise our knowledge about theta by a probability distribution <math>p(theta)</math>. Assume that we have a model of the relationship between ''y'' and <math>theta</math>. Call this <math>p(y|theta)</math>. We can use Bayes' theorem to update our knowledge of <math>theta</math> by incorporating the information contained in the observed data ''y''.
We have
<math>p(y) = p(\theta)p(y|\theta)/p(y)</math>