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A History of Parametric Statistical Inference from Bernoulli to Fisher, 1713–1935The Multivariate Posterior Distribution

A History of Parametric Statistical Inference from Bernoulli to Fisher, 1713–1935: The... [Irénée Jules Bienaymé (1796–1878) proposes to generalize Laplace’s inverse probability analysis of the binomial. Using the principle of inverse probability on the multinomial he gets the posterior distribution 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ p_n \left( {\theta _1 ,...,\theta _k |n_1 ,...,n_k } \right)\alpha \theta _1^{n_1 } ...\theta _k^{n_k } ,0 < \theta _i < 1,\sum \theta _i = 1, $$\end{document} where the ns are nonnegative integers and Σni = n. In normed form this distribution is today called the Dirichlet distribution. The posterior mode is hi = ni/n, Σhi = 1.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A History of Parametric Statistical Inference from Bernoulli to Fisher, 1713–1935The Multivariate Posterior Distribution

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Publisher
Springer New York
Copyright
© Springer Science+Business Media, LLC 2007
ISBN
978-0-387-46408-4
Pages
67 –68
DOI
10.1007/978-0-387-46409-1_9
Publisher site
See Chapter on Publisher Site

Abstract

[Irénée Jules Bienaymé (1796–1878) proposes to generalize Laplace’s inverse probability analysis of the binomial. Using the principle of inverse probability on the multinomial he gets the posterior distribution 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ p_n \left( {\theta _1 ,...,\theta _k |n_1 ,...,n_k } \right)\alpha \theta _1^{n_1 } ...\theta _k^{n_k } ,0 < \theta _i < 1,\sum \theta _i = 1, $$\end{document} where the ns are nonnegative integers and Σni = n. In normed form this distribution is today called the Dirichlet distribution. The posterior mode is hi = ni/n, Σhi = 1.]

Published: Jan 1, 2007

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