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- W4246044391 abstract "The English physician and philosopher David Hartley (1705–1757), founder of the Associationist school of psychologists, discusses some elementary applications of probability theory in his Observations on Man [118]. On the limit theorems he writes (pp. 338–339): Mr. de Moivre has shown, that where the Causes of the Happening of an Event bear a fixed Ratio to those of its Failure, the Happenings must bear nearly the same Ratio to the Failures, if the Number of Trials be su cient; and that the last Ratio approaches to the first indefinitely, as the number of Trials increases. This may be considered as an elegant Method of accounting for that Order and Proportion, which we every-where see in the Phæomena of Nature. [...] An ingenious Friend has communicated to me a Solution of the inverse Problem, in which he has shewn what the Expectation is, when an event has happened p times, and failed q times, that the original Ratio of the Causes for the Happening or Failing of an Event should deviate in any given Degree from that of p to q. And it appears from this Solution, that where the Number of Trials is very great, the Deviation must be inconsiderable: Which shews that we may hope to determine the Proportions, and, by degrees, the whole Nature, of unknown Causes, by a su cient Observation of their Effects." @default.
- W4246044391 created "2022-05-12" @default.
- W4246044391 date "2007-01-01" @default.
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- W4246044391 title "Bayes’s Posterior Distribution of the Binomial Parameter and His Rule for Inductive Inference, 1764" @default.
- W4246044391 doi "https://doi.org/10.1007/978-0-387-46409-1_4" @default.
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