Where does posterior collide?

In Bayesian statistics the posterior is the probability distribution of an unknown quantity after data have been observed: it is obtained by combining a prior distribution with the likelihood of the data through Bayes' theorem, and it is the central object from which estimates, such as the posterior mean, and credible intervals are read. Bayes' 1763 An Essay towards Solving a Problem in the Doctrine of Chances introduced the rule for updating a probability in light of evidence that this distribution formalises. The referent is a whole distribution over the possible values of a parameter, revised by evidence, not a place at the back of a body or a kind of knowledge won from experience.[1]

Unit

A full probability distribution over a parameter, one per model and dataset

Recovery means

Not applicable

Measured by

Computed by Bayes' theorem, by conjugate updating or by sampling methods such as Markov chain Monte Carlo, then summarised by its mean and credible intervals

In philosophy the word marks knowledge that is posterior to experience, that is, knowledge whose justification depends on observation, which is usually written as a posteriori and set against a priori knowledge that holds independently of experience. Kant's 1781 Critique of Pure Reason made this contrast central, asking which of our judgements could be known before any experience and which could only be established through it. Here posterior names an order of justification, coming after experience, not a direction on the body or an updated probability distribution, though its root idea of coming after is shared with the statistical posterior that comes after the data.[2]

Unit

A status of a claim: its justification rests on experience

Recovery means

Not applicable

Measured by

Judged by philosophical analysis of whether a claim's warrant depends on observation or holds independently of it