Journal Article10.2307/2348441
Sample Size Determination in Bayesian Statistics—A Commentary
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TL;DR: The most complete treatment to date on classical sample size methodology seems to be Desu and Rhagavarao (1990) where the Bayesian approach is barely mentioned as mentioned in this paper.
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Abstract: I wish to thank the Editor of The Statistician for inviting me to write this commentary which addresses not only the specific results obtained by Joseph et al. (1995) but also some related results presented by other researchers. Joseph et al. (1995) have written quite an interesting paper on sample size in a Bayesian context, which contributes significantly to the on-going discussion on this topic. As mentioned by Adcock (1992) the determination of sample size is an important question for the applied statistician. Although this question has been of interest for a long time in classical frequentist statistics, it seems to have attracted the attention of Bayesians only quite recently; the reasons could be those mentioned by Pham-Gia and Turkkan (1992). The most complete treatment to date on classical sample size methodology seems to be Desu and Rhagavarao (1990) where the Bayesian approach is barely mentioned. A list of useful sample size tables can also be found in that work.
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Determination of exact sample size in the Bayesian estimation of the difference of two proportions
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Abstract: Using generalized hypergeometric functions in several variables in a Bayesian context, we compute the exact minimum double-sample size (n 1 , n 2 ) required in the Bernoulli sampling of two independent populations, so that the expected length (or the maximum length) of the highest posterior density credible interval of P = P 1 - P 2 is less than a preset quantity, where P 1 and P 2 are two independent proportions. This precise and computer-intensive approach permits the treatment of this Bayesian sample size determination problem under very general hypotheses and also provides a relationship between the minimal values of n 1 and n 2 . Similar results are derived in an applied Bayesian decision theory context, with a quadratic loss function, and the criteria used are now the posterior risk, the Bayes risk and the expected value of sample information.
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A Bayesian Approach on Sample Size Calculation for Comparing Means
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References
Unimodality, convexity, and applications
TL;DR: Unimodality of Discrete Distributions as mentioned in this paper is a generalization of the notion of infinite-divergences in the context of univariate unimodal distributions.
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Sample Size for Estimating Multinomial Proportions
TL;DR: In this article, a procedure and a table for selecting sample size for simultaneously estimating the parameters of a multinomial distribution is presented, analogous to the case in which a binomial parameter equals one-half.
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Sample Size Calculations for Binomial Proportions Via Highest Posterior Density Intervals
TL;DR: In this article, three different Bayesian approaches to sample size calculations based on highest posterior density (HPD) intervals are discussed and illustrated in the context of a binomial experiment.
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Bayesian analysis of the difference of two proportions
TL;DR: In this paper, the expression of the prior distribution of p1-P2, where P1 and P2 and independent proportions with a beta prior each, was derived, showing the closure of the beta-difference family for independent dual Bernoulli samples.
83
Bayesian Sample Size Calculations and Prior Beliefs About Child Sexual Abuse
J. L. Hutton,R. G. Owens +1 more
TL;DR: In this article, a Bayesian approach is used to estimate the sample size required to estimate a parameter, which is then determined by requiring the posterior distribution to have particular properties, such as the desired properties of the posterior distributions for the parameter of interest.
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