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.
Read more about this topic: Inverse Probability
Famous quotes containing the word details:
“Patience is a most necessary qualification for business; many a man would rather you heard his story than granted his request. One must seem to hear the unreasonable demands of the petulant, unmoved, and the tedious details of the dull, untired. That is the least price that a man must pay for a high station.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“Anyone can see that to write Uncle Tom’s Cabin on the knee in the kitchen, with constant calls to cooking and other details of housework to punctuate the paragraphs, was a more difficult achievement than to write it at leisure in a quiet room.”
—Anna Garlin Spencer (1851–1931)