Download A History of Parametric Statistical Inference from Bernoulli by Anders Hald PDF

By Anders Hald

This is a background of parametric statistical inference, written by means of some of the most very important historians of records of the twentieth century, Anders Hald. This publication may be seen as a follow-up to his most up-to-date books, even though this present textual content is far extra streamlined and comprises new research of many principles and advancements. and in contrast to his different books, which have been encyclopedic through nature, this e-book can be utilized for a path at the subject, the one necessities being a simple path in chance and statistics.

The ebook is split into 5 major sections:

* Binomial statistical inference;

* Statistical inference by way of inverse probability;

* The vital restrict theorem and linear minimal variance estimation by way of Laplace and Gauss;

* errors concept, skew distributions, correlation, sampling distributions;

* The Fisherian Revolution, 1912-1935.

Throughout all of the chapters, the writer presents full of life biographical sketches of the various major characters, together with Laplace, Gauss, Edgeworth, Fisher, and Karl Pearson. He additionally examines the jobs performed via DeMoivre, James Bernoulli, and Lagrange, and he presents an obtainable exposition of the paintings of R.A. Fisher.

This ebook might be of curiosity to statisticians, mathematicians, undergraduate and graduate scholars, and historians of science.

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

Example text

For  = h + t he finds 1 1 ln p(|n, h) = ln p(h|n, h) nt2 (h1 +k1 )+ nt3 (h2 +k2 )· · · , k = 1h. 10) p(h|n, h)  n/2hk. 9). 8). He completes this result by giving the first proof of the fact that the integral of the normal density function equals 1. 3 Posterior Consistency and Asymptotic Normality, 1774 39 and he later ([149], Art. 23) gave a simpler proof by evaluating the double integral ] 4] 4 ] 4 1 exp[s(1 + x2 )]dsdx = (1 + x2 )1 dx = , 2 0 0 0 and using the transformations s = u2 and sx2 = t2 to show that the integral equals ] 4 ] 4 2 exp(u2 )du exp(t2 )dt.

16) gives an approximation to the likelihood function. 16) by the corresponding ps, as shown above for k = 2. This is the generalization of de Moivre’s result. When K. Pearson in the 1920s lectured on the history of statistics, he ([212], pp. 596—603) discovered Lagrange’s result and remarked that it was the basis for his [203] "2 goodness-of-fit test. 3 De Morgan’s Continuity Correction, 1838 Augustus de Morgan (1806—1871) improves de Moivre’s approximation by introducing a “continuity correction” ([187], p.

P (E|Cn ) Inverse probability P (C1 |E), . . , P (Cn |E) Direct probability corresponds to probabilistic deduction and inverse probability to probabilistic induction. It is a remarkable fact that Laplace considers conditional probabilities only. His principle amounts to the symmetry relation P (Ci |E) 2 P (E|Ci ), i = 1, . . , n, 36 5 Laplace’s Theory of Inverse Probability which is the form he ordinarily uses. His intuitive reasoning may have been as follows: If the probability of the observed event for a given cause is large relative to the other probabilities then it is relatively more likely that the event has been produced by this cause than by any other cause.

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