A Bayesian solution to the Behrens-Fisher problem using Monte Carlo simulation techniques

Although it is difficult to derive the exact posterior distribution of a test statistic in the case of the Behrens-Fisher problem, the exact moments can be obtained in certain cases. By calculating the first four moments of the test statistic and by comparing Pearson curves to Monte Carlo simulation experiments, it is shown that good approximations of the true distribution can be obtained. Since there is no unique way to test hypotheses from a Bayesian point of view, Broemeling et al. (1990) proposed an approximate chi-square credibility region. In this note a ""more exact"" credibility region is derived. As mentioned, this is obtained by either using Pearson curves or Monte Carlo simulations. The theory and results are extended to the multivariate case.