Zaslavsky Boris G
FDA, CBER HFM-219, 1401 Rockville Pike, Rockville, Maryland 20852-1448, USA.
Biometrics. 2013 Mar;69(1):157-63. doi: 10.1111/j.1541-0420.2012.01806.x. Epub 2012 Sep 24.
This article is motivated by an interest in comparing inferences made when using a Bayesian or frequentist statistical approach. The article addresses the study of one-sided superiority and noninferiority Bayesian tests. These tests are stated in terms of the posterior probability that the null hypothesis is true for the binomial distribution and in terms of one-sided credible limits. We restrict our considerations to conjugate beta priors with integer parameters. Under this assumption, the posterior probabilities of tested hypotheses can be transformed into the frequentist probabilities of Bernoulli trials with an adjusted number of events and population sizes. The method resembles a standard frequentist problem formulation. By using an appropriate choice of prior parameters, the posterior probabilities of the null hypothesis can be made smaller or larger than the p-values of frequentist tests.
本文的动机在于比较使用贝叶斯或频率主义统计方法时所做的推断。本文探讨单侧优效性和非劣效性贝叶斯检验的研究。这些检验是根据二项分布中零假设为真的后验概率以及单侧可信区间来表述的。我们将考虑范围限制在具有整数参数的共轭贝塔先验分布。在此假设下，被检验假设的后验概率可以转换为具有调整后事件数和总体规模的伯努利试验的频率主义概率。该方法类似于标准的频率主义问题表述。通过适当选择先验参数，零假设的后验概率可以小于或大于频率主义检验的p值。
