A Posterior Density for the Difference Between Two Binominal Proportions and the Highest Posterior Density Credible Interval

@article{Kawasaki2010APD,
  title={A Posterior Density for the Difference Between Two Binominal Proportions and the Highest Posterior Density Credible Interval},
  author={Youhei Kawasaki and E. Miyaoka},
  journal={Journal of the Japan Statistical Society. Japanese issue},
  year={2010},
  volume={40},
  pages={265-275}
}
The statistical inference concerning the difference between two independent binominal proportions has often been discussed in medical and statistical literature. This discussion is far more often based on the frequency theory of statistical inference than on the Bayesian theory. In this article, we propose the expression of the posterior probability density function (pdf) for the difference between two independent binominal proportions. In addition, we calculate the exact Highest Posterior… Expand

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References

SHOWING 1-10 OF 33 REFERENCES
Test-based exact confidence intervals for the difference of two binomial proportions.
TLDR
Test-based methods of constructing exact confidence intervals for the difference in two binomial proportions are proposed and it is shown that a large improvement can be achieved by using the standardized Z test with a constrained maximum likelihood estimate of the variance. Expand
Frequentist performance of Bayesian confidence intervals for comparing proportions in 2 x 2 contingency tables.
TLDR
This article investigates the performance, in a frequentist sense, of Bayesian confidence intervals for the difference of proportions, relative risk, and odds ratio in 2 x 2 contingency tables and recommends tail intervals over highest posterior density (HPD) intervals, for invariance reasons. Expand
Interval estimation for the difference between independent proportions: comparison of eleven methods.
  • R. Newcombe
  • Mathematics, Medicine
  • Statistics in medicine
  • 1998
TLDR
Two new approaches which also avoid aberrations are developed and evaluated, and a tail area profile likelihood based method produces the best coverage properties, but is difficult to calculate for large denominators. Expand
Approximate confidence intervals for one proportion and difference of two proportions
Constructing a confidence interval for a binomial proportion or the difference of two proportions is a routine exercise in daily data analysis. The best-known method is the Wald interval based on theExpand
Unconditional Confidence Interval for the Difference between Two Proportions
Summary In applied statistics it is customary to have to obtain a one- or two-tail confidence interval for the difference d ¼ p2 � p1 between two independent binomial proportions. Traditionally, oneExpand
On small-sample confidence intervals for parameters in discrete distributions.
TLDR
This paper illustrates for a variety of discrete problems, including interval estimation of a binomial parameter, the difference and the ratio of two binomial parameters for independent samples, and the odds ratio. Expand
Bayesian analysis of a 2×2 contingency table with dependent proportions and exact sample size
Abstract In the analysis of a 2×2 contingency table with dependent proportions, several measures used are based on the two conditional probabilities, π1| 1 and π1| 2, and the marginal probabilities,Expand
Simple and Effective Confidence Intervals for Proportions and Differences of Proportions Result from Adding Two Successes and Two Failures
Abstract The standard confidence intervals for proportions and their differences used in introductory statistics courses have poor performance, the actual coverage probability often being much lowerExpand
Confidence intervals for two sample binomial distribution
This paper considers confidence intervals for the difference of two binomial proportions. Some currently used approaches are discussed. A new approach is proposed. Under several generally usedExpand
Exact tests for equality of two proportions: Fisher × Bayes
Yates (1984) using theoretical and philosophical arguments claims to have proved that the Fisher exact test for comparing the proportions of two binomial experiments is the best exact test. TheExpand
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