Abstract: The main results provide asymptotic expansions for posterior distributions which may be integrated termwise with respect to the marginal distribution of the data. The proof uses a data dependent transformation which converts the likelihood function to exact normality and then applies a version of Stein's Identity to the posterior distributions. Applications to sequential confidence intervals are described briefly.
Key words and phrases: Posterior distributions, parameter transformations, Stein's Identity, martingale convergence theorem, stopping times, sequential confidence intervals.