Minimum message length analysis of the behrens-fisher problem

Given two sequences of Gaussian data, the Behrens-Fisher problem is to infer whether there exists a difference between the two corresponding population means if the population variances are unknown. This paper examines the Behrens-Fisher-type problem within the minimum message length framework of inductive inference. Using a special bounding on a uniform prior over the population means, a simple Bayesian hypothesis test is derived that does not require computationally expensive numerical integration of the posterior distribution. The minimum message length procedure is then compared against well-known methods on the Behrens-Fisher hypothesis testing problem and the estimation of the common mean problem showing excellent performance in both cases. Extensions to the generalised Behrens-Fisher problem and the multivariate Behrens-Fisher problem are also discussed.