Abstract: Integrable expansions for posterior distributions are obtained for sequential samples from a multiparameter exponential family. A data dependent transformation 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.
Key words and phrases: Asymptotic expansions, multiparameter exponential family, sequential confidence levels, Stein's Identity, very weak expansion.