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
235-253
Sahu, S.K.
33f1386d-6d73-4b60-a796-d626721f72bf
Smith, T.M.F.
61602253-c2d6-43a1-862b-291379e75318
2006
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), .
(doi:10.1111/j.1467-985X.2006.00408.x).
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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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
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Local EPrints ID: 30160
URI: http://eprints.soton.ac.uk/id/eprint/30160
ISSN: 0964-1998
PURE UUID: d6477765-ed4a-4f54-a0f5-169da37023af
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Date deposited: 11 May 2006
Last modified: 16 Mar 2024 03:15
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Author:
T.M.F. Smith
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