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

By Anders Hald

ISBN-10: 0387464085

ISBN-13: 9780387464084

This e-book deals an in depth historical past of parametric statistical inference. masking the interval among James Bernoulli and R.A. Fisher, it examines: binomial statistical inference; statistical inference through inverse chance; the imperative restrict theorem and linear minimal variance estimation through Laplace and Gauss; blunders idea, skew distributions, correlation, sampling distributions; and the Fisherian Revolution. energetic biographical sketches of a number of the major characters are featured all through, together with Laplace, Gauss, Edgeworth, Fisher, and Karl Pearson. additionally tested are the jobs performed via DeMoivre, James Bernoulli, and Lagrange.

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In 1774 Bayes’s paper, [3], was not known among French probabilists. However, by 1781 Laplace knew Bayes’s paper and this may have induced him to derive his principle from a two-stage model with equal probabilities for the causes. In 1786 he points out that the theory of inverse probability is based on the relation P (Ci |E) = P (Ci E)/P (E), and assuming that P (Ci ) = 1/n, i = 1, . . 2) in agreement with his 1774 principle. cient reason, also called the principle of indierence. This distinction is clearly explained by Cournot ([33], Chapter 8), who notes that the first interpretation is unambiguous and uncontestable, whereas the second is subjective and arbitrary.

Minimize the sum of the absolute values of the residuals under S the restriction that the sum of the residuals equals zero; thatSis, minimize |yi  a  bxi | with respect to a and b under the restriction (yi  a  bxi ) = 0. Boscovich was the first to formulate a criterion for fitting a straight line to data based on the minimization of a function of the residuals. His formulation and solution are purely verbal, supported by a diagram that explains the method of minimization. We give an algebraic solution that follows his mode of reasoning.

2 Laplace’s Theory of Inverse Probability, 1774 35 example of optimum estimation can be found, the derivation and characterization of an estimator that minimized a particular measure of posterior expected loss. After more than two centuries, we mathematical statisticians cannot only recognize our roots in this masterpiece of our science, we can still learn from it. 2 The Principle of Inverse Probability and the Symmetry of Direct and Inverse Probability, 1774 In the “Memoir on the Probability of Causes of Events” Laplace [148] begins by discussing direct and inverse probability by means of the urn model.

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