Accession Number : AD0667926

Title :   THE VALUE OF PRIOR INFORMATION.

Descriptive Note : Technical rept.,

Corporate Author : WISCONSIN UNIV MADISON DEPT OF STATISTICS

Personal Author(s) : Draper,Norman R. ; Guttman,Irwin

Report Date : DEC 1967

Pagination or Media Count : 31

Abstract : Sample y1,y2,...,yn of observations from some specified parent distribution, together with some prior information on one or more parameters of interest of the distribution. Then by applying Bayes theorem we can obtain the overall distribution (or the marginal distribution) if nuisance parameters are involved of parameters of interest, and can make inferences about these parameters. A natural question to ask is how inferences might be affected by a change in the prior distribution, i.e. by the availability of more, or less, information on the parameters. It would be convenient to have a quantity which could be used to indicate the value of more or less prior information. It is suggested, in this paper, for the one parameter case, the use of the ratio the expected values of the posterior variance of the parameter, expectation being taken over the future distribution of the sampling statistics which occur in the posterior variance. We illustrate the use of this ratio for a number of well-known distributions. (Author)

Descriptors :   (*STATISTICAL DISTRIBUTIONS, SAMPLING), DISTRIBUTION FUNCTIONS, BINOMIALS, DETERMINANTS(MATHEMATICS), MATRICES(MATHEMATICS), DISTRIBUTION THEORY

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE