A Bayesian inference of P(lambda(1) %26lt; lambda(2)) for two Poisson parameters

作者：Kawasaki Youhei^*; Miyaoka Etsuo

来源：Journal of Applied Statistics, 2012, 39(10): 2141-2152.

DOI：10.1080/02664763.2012.702264

• gamma distribution
• hypergeometric series
• Poisson distribution
• posterior distribution
• p-value

The statistical inference drawn from the difference between two independent Poisson parameters is often discussed in the medical literature. However, such discussions are usually based on the frequentist viewpoint rather than the Bayesian viewpoint. Here, we propose an index theta = P(lambda(1,post) %26lt; lambda(2,post)), where lambda(1,post) and lambda(2,post) denote Poisson parameters following posterior density. We provide an exact and an approximate expression for calculating theta using the conjugate gamma prior and compare the probabilities obtained using the approximate and the exact expressions. Moreover, we also show a relation between theta and the p-value. We also highlight the significance of theta by applying it to the result of actual clinical trials. Our findings suggest that theta may provide useful information in a clinical trial.

• 出版日期2012