A History of Parametric Statistical Inference from Bernoulli by Anders Hald

By Anders Hald

This publication bargains a close background of parametric statistical inference. overlaying the interval among James Bernoulli and R.A. Fisher, it examines: binomial statistical inference; statistical inference by means of inverse chance; the principal restrict theorem and linear minimal variance estimation by way of Laplace and Gauss; mistakes conception, skew distributions, correlation, sampling distributions; and the Fisherian Revolution. full of life biographical sketches of a few of the major characters are featured all through, together with Laplace, Gauss, Edgeworth, Fisher, and Karl Pearson. additionally tested are the jobs performed through DeMoivre, James Bernoulli, and Lagrange.

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Extra resources for A History of Parametric Statistical Inference from Bernoulli to Fisher, 1713-1935

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4) by substituting wi |Xi | for |Xi |. Bowditch ([20] Vol. 438) points out that the method of least absolute deviations is preferable to the method of least squares for estimating the slope of the line if extreme errors occur. The method of least absolute deviations had drawbacks compared with the method of averages and the method of least squares: (1) the estimate of the slope is nonlinear and complicated to calculate, and (2) the method was restricted to one independent variable. The method therefore disappeared from statistical practice until the second half of the twentieth century when questions of robustness of estimates were discussed.

6) which depends on the supposition that P (U ) is uniformly distributed on [0, 1]. Thus ends the inferential part of Bayes’s paper. He does not discuss where to find unknown events in nature; his paper contains no philosophy of science, no examples, and no data. Price [226] attempts to remedy this defect in his commentary. As examples he discusses the drawings from a lottery and the probability of a sunrise tomorrow. ” He (p. ” This implies that in the natural sciences “unknown events” are the exception rather than the rule.

He was elected a Fellow of the Royal Society in 1742. When Bayes died in 1761 his relatives asked Richard Price (1723—1791), another Presbyterian minister, to examine the mathematical papers left by Bayes. Price found a paper on Stirling’s formula and the paper “An Essay Towards Solving a Problem in the Doctrine of Chances,” which he got published in two parts in the Phil. Trans. ([226], [227]) with introductory letters, comments, and extensions by himself. Bayes’s mathematics is correct, but his verbal comments are obscure and have caused much discussion, which recently has led to a new interpretation of his criterion for the application of his rule for inductive inference.

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