Download e-book for kindle: A History of Inverse Probability: From Thomas Bayes to Karl by Andrew I. Dale

By Andrew I. Dale

ISBN-10: 0387988076

ISBN-13: 9780387988078

It is a heritage of using Bayes theoremfrom its discovery by means of Thomas Bayes to the increase of the statistical rivals within the first a part of the 20 th century.

The booklet focuses rather at the improvement of 1 of the elemental features of Bayesian data, and during this re-creation readers will locate new sections on members to the theory.

furthermore, this variation comprises amplified dialogue of correct paintings.

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Additional info for A History of Inverse Probability: From Thomas Bayes to Karl Pearson (2nd Edition)

Example text

I Suppose the squa re table or plane ABCD to be so mad e and levelled, that if either of the balls 0 or W be thrown upon it , thereshall be the same probability that it rests upon any one equa l partof the plane as another, and that it must necessarily rest somewhereupon it. 10 On inverse probability 2. I supposethat the ball W shall be 1st thrown, and through the point where it rests a lineos shall be drawn parallel to AD, and meetingCD and AB in sand 0; and that afterwardsthe ball 0 shall be thrown p + q or n times, and that its resting betweenAD and os after a single throw be called the happening of the event M in a single trial.

Care must of course betaken not to confuse themethodof maximum likelihood with likelihood pure andsimple (though, as Oscar Wilde said of Truth, likelihood "is rarely pure and neversimple"). A . Fisher, is offered as analternative mode of inference forthose unhappy with both inverse probability and significance tests. The main building-block here is L[HIR], the likelihood of the hypothesisH given R, a quantity which, having H as variable and R as constant,is defined as being proportional to Pr[RIH], the probability of (the variable) R given (the hypothesis) H.

Ii . 490] said 22, Felix qui potui t rerum cognoscerecausam. With goodwill one can then see Bayes's original problem as the obtaining of the probability thata value x li es in a certain interval (the cause) given the result of an experiment (the effect ), while the second of Pri ce's exa mples cite d above (one that relies on Bayes's Theorem for its solution) gives the proba bility of a further observation given cert ain data . To explore a bit further the connexion betweenBern oulli's Theorem, its inverse and Bayes's T heorem-" , considera binary experiment withconst an t probability p of success, and supposetha t n independ ent rials t have been run.

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A History of Inverse Probability: From Thomas Bayes to Karl Pearson (2nd Edition) by Andrew I. Dale

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