Andrew I. Dale's A History of Inverse Probability: From Thomas Bayes to Karl PDF
By Andrew I. Dale
This can be a historical past of using Bayes theoremfrom its discovery by way of Thomas Bayes to the increase of the statistical opponents within the first a part of the 20 th century. The ebook focuses really at the improvement of 1 of the basic points of Bayesian records, and during this re-creation readers will locate new sections on individuals to the idea. additionally, this version contains amplified dialogue of suitable paintings.
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Extra info for A History of Inverse Probability: From Thomas Bayes to Karl Pearson
None other than the uniform distribution for p has the property of the corollary to Proposition 8. As Murray  has it the assumption "all values of p are equally likely" is equivalent to the assumption "any number x of successes in n trials is just as likely as any other number y, x ~ n, y ~ n". 129] In his elegant note Murray verified that part of this quotation which was not proved by Bayes. A shorter proof than his would be provided by noting that the uniform distribution does yield the appropriate sequence of moments, and then using the uniqueness theorem for moment generating functions 15 • Several writers have of course disparaged Bayes's argument 16 : it might be of interest to look at the discussion presented by Hacking , according to whom Bayes argued as follows: (i) Before any trials on the billiard table 17 , and before the point o is discovered, there is no reason to suppose M will happen any number of times rather than any other possible number and, he might have added, there is no reason to prefer any value of P(M) [the probability of M] to any other18.
Bayes was, however, licensed as a preacher, though not ordained. The manuscript volume in the library of Edinburgh University that contains the list of theologues also contains a list of books. The range of topics covered seems too narrow for this to be a listing of books in the University library, and it is possible that the works listed were for the particular use of the theologues. But be that as it may: only two of these books are recognizable as being distinctly mathematical: they are (i) Keckermanni systema mathem: and, (ii) Speedwells geometrical problems.
393] But, by the Corollary to Proposition 8, this is precisely the situation of the proposed model. In what follows therefore I shall take for granted that the rule given concerning the event M [Le. success] in prop. 9. is also the rule to be used in relation to any event concerning the probability of which nothing at all is known antecedently to any trials made or observed concerning it. And such an event I shall call an unknown event. 393-394] Then, following a corollary in which, in essence, the table is assumed to be of unit area, one finds Proposition 10, which provides the solution to the problem initially posed33 : Proposition 10.
A History of Inverse Probability: From Thomas Bayes to Karl Pearson by Andrew I. Dale