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A Bayesian method of sample size determination with practical applications

A Bayesian method of sample size determination with practical applications
A Bayesian method of sample size determination with practical applications
The problem motivating this article is the determination of sample size in clinical trials under normal likelihoods and at the substantive testing stage of a financial audit where normality is not an appropriate assumption. A combination of analytical and simulation based techniques within the Bayesian framework is proposed. The framework accommodates two different prior distributions: one is the general purpose fitting prior distribution used in Bayesian analysis and the other is the expert subjective prior distribution, the sampling prior which is believed to generate the parameter values which in turn generate the data. We obtain many theoretical results and one key result is that typical non-informative prior distributions lead to very small sample sizes. On the other hand, a very informative prior distribution may either lead to a very small or a very large sample size depending on the location of the centre of the prior distribution and the hypothesized value of the parameter. The methods developed here are quite general and can be applied to other sample size determination (SSD) problems. A number of numerical illustrations which bring out many other aspects of the optimum sample size are given.
auditing, bayesian inference, book values, clinical trials, fitting prior, mixture distribution, rare errors, simulation based approach, sampling prior taints
0964-1998
235-253
Sahu, S.K.
33f1386d-6d73-4b60-a796-d626721f72bf
Smith, T.M.F.
61602253-c2d6-43a1-862b-291379e75318
Sahu, S.K.
33f1386d-6d73-4b60-a796-d626721f72bf
Smith, T.M.F.
61602253-c2d6-43a1-862b-291379e75318

Sahu, S.K. and Smith, T.M.F. (2006) A Bayesian method of sample size determination with practical applications Journal of the Royal Statistical Society: Series A (Statistics in Society), 169, (2), pp. 235-253. (doi:10.1111/j.1467-985X.2006.00408.x).

Record type: Article

Abstract

The problem motivating this article is the determination of sample size in clinical trials under normal likelihoods and at the substantive testing stage of a financial audit where normality is not an appropriate assumption. A combination of analytical and simulation based techniques within the Bayesian framework is proposed. The framework accommodates two different prior distributions: one is the general purpose fitting prior distribution used in Bayesian analysis and the other is the expert subjective prior distribution, the sampling prior which is believed to generate the parameter values which in turn generate the data. We obtain many theoretical results and one key result is that typical non-informative prior distributions lead to very small sample sizes. On the other hand, a very informative prior distribution may either lead to a very small or a very large sample size depending on the location of the centre of the prior distribution and the hypothesized value of the parameter. The methods developed here are quite general and can be applied to other sample size determination (SSD) problems. A number of numerical illustrations which bring out many other aspects of the optimum sample size are given.

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More information

Published date: 2006
Keywords: auditing, bayesian inference, book values, clinical trials, fitting prior, mixture distribution, rare errors, simulation based approach, sampling prior taints
Organisations: Statistics

Identifiers

Local EPrints ID: 30160
URI: http://eprints.soton.ac.uk/id/eprint/30160
ISSN: 0964-1998
PURE UUID: d6477765-ed4a-4f54-a0f5-169da37023af
ORCID for S.K. Sahu: ORCID iD orcid.org/0000-0003-2315-3598

Catalogue record

Date deposited: 11 May 2006
Last modified: 17 Jul 2017 15:55

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