INTEGRABLE EXPANSIONS FOR POSTERIOR DISTRIBUTIONS FOR MULTIPARAMETER EXPONENTIAL FAMILIES WITH APPLICATIONS TO SEQUENTIAL CONFIDENCE LEVELS
Ruby C. Weng, Michael B. Woodroofe · 2000
Integrable expansions for posterior distributions are obtained for sequen- tial samples from a multiparameter exponential family. A data dependent trans- formation is used to convert the likelihood function to the form of a standard multivariate normal density. Then a version of Stein's Identity is applied. This leaves an expression from which an asymptotic expansion is easily obtained. The results are applied to find confidence intervals for the ratio of two Poisson means after a sequential test and compare well with simulations.