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Statistical ThoughtA Perspective and History$
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Shoutir Kishore Chatterjee

Print publication date: 2003

Print ISBN-13: 9780198525318

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198525318.001.0001

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BEGINNING OF THE PRO-SUBJECTIVE APPROACH

BEGINNING OF THE PRO-SUBJECTIVE APPROACH

Chapter:
(p.194) 7 BEGINNING OF THE PRO-SUBJECTIVE APPROACH
Source:
Statistical Thought
Author(s):

Shoutir Kishore Chatterjee

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198525318.003.0007

Around the middle of the 18th century, Bayes conceived the idea of treating an unknown parameter as a subjective random variable distributed according to a prior, and inferring about it from its conditional (posterior) distribution given the observations. He considered the particular case of a binomial parameter subject to a uniform prior, and following the pro-subjective approach used the posterior to derive an interval estimate. Later, Laplace stated the result in its general form and employed it extensively for pro-subjective inference of various types in different situations, often basing his computation on the asymptotic normality of the posterior distribution. In a novel application, Laplace used pro-subjective reasoning and the data from a sample survey to estimate the size of the population of France.

Keywords:   Bayes, binomial parameter, subjective prior, posterior, Laplace, pro-subjective inference, population estimation

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