Download e-book for kindle: A History of Parametric Statistical Inference from Bernoulli by Anders Hald

By Anders Hald

ISBN-10: 0387464085

ISBN-13: 9780387464084

ISBN-10: 1441923632

ISBN-13: 9781441923639

This publication bargains an in depth heritage of parametric statistical inference. protecting the interval among James Bernoulli and R.A. Fisher, it examines: binomial statistical inference; statistical inference by means of inverse likelihood; the critical restrict theorem and linear minimal variance estimation by way of Laplace and Gauss; mistakes conception, skew distributions, correlation, sampling distributions; and the Fisherian Revolution. energetic biographical sketches of the various major characters are featured all through, together with Laplace, Gauss, Edgeworth, Fisher, and Karl Pearson. additionally tested are the jobs performed by means of DeMoivre, James Bernoulli, and Lagrange.

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Additional info for A History of Parametric Statistical Inference from Bernoulli to Fisher, 1713-1935

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We here only indicate the method of proof and derive the main term. It is assumed that the posterior distribution is unimodal and disappears at the endpoints of its support. The mode is denoted by ˆ  and, like Laplace, we abbreviate p(|x) to p(). As in the binomial case Laplace evaluates the probability integral by developing the integrand into a power series, which he then integrates. 25) and the limits of integration are a = [2 ln{p(ˆ )/p(ˆ   )}]1/2 and b = [2 ln{p(ˆ )/p(ˆ  + )}]1/2 .

Because the median and the mode coincide for a symmetric distribution he needed an argument for choosing between them. This he found by likening estimation to a game of chance in which the player’s expected loss should be minimized. However, he does not explain why a scientists’s “loss” caused by an error of estimation should be measured in the same way as a player’s pecuniary loss. cult so Laplace limits himself to consider the case n = 3. Let the observations be labeled such that x1  x2  x3 .

He obtains an asymptotic expansion, which is improved by Price. Finally, Price considers the expansion for a + b $ 4 and obtains a series that is the expansion of the normal probability integral, but he does not recognize it as such. Also this part of the Essay was overlooked. For the details of the proofs we refer to Hald [113]. Part II STATISTICAL INFERENCE BY INVERSE PROBABILITY. 1 Biography of Laplace Pierre Simon Laplace (1749—1827) was born into a middle-class family at a small town in Normandy, where he spent his first 16 years.

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A History of Parametric Statistical Inference from Bernoulli to Fisher, 1713-1935 by Anders Hald

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