Editing Inverse probability (section)

== Details ==
In modern terms, given a probability distribution ''p''(''x''|θ) for an observable quantity ''x'' conditional on an unobserved variable θ, the "inverse probability" is the [[posterior distribution]] ''p''(θ|''x''), which depends both on the likelihood function (the inversion of the probability distribution) and a prior distribution. The distribution ''p''(''x''|θ) itself is called the '''direct probability'''.

The ''inverse probability problem'' (in the 18th and 19th centuries) was the problem of estimating a parameter from experimental data in the experimental sciences, especially [[astronomy]] and [[biology]]. A simple example would be the problem of estimating the position of a star in the sky (at a certain time on a certain date) for purposes of [[navigation]]. Given the data, one must estimate the true position (probably by averaging). This problem would now be considered one of [[inferential statistics]].

The terms "direct probability" and "inverse probability" were in use until the middle part of the 20th century, when the terms "[[likelihood function]]" and "posterior distribution" became prevalent.