The various terms in Bayes’ theorem have formal names.

• The quantity on the far right, \( p(H|I) \), is called the prior probability; it represents our state of knowledge (or ignorance) about the truth of the hypothesis before we have analysed the current data.
• This is modified by the experimental measurements through \( p(D|H,I) \), the likelihood function,
• The denominator \( p(D|I) \) is called the evidence. It does not depend on the hypothesis and can be regarded as a normalization constant.
• Together, these yield the posterior probability, \( p(H|D, I ) \), representing our state of knowledge about the truth of the hypothesis in the light of the data.

In a sense, Bayes’ theorem encapsulates the process of learning.