The multivariate normal mean--sensitivity of its objective Bayesian estimates

摘要

The multivariate Gaussian model is frequently applied in metrology and many other fields. Notably, the recent Supplement 2 to the GUM (an extension of GUM and GUM S1 to multivariate problems) makes extensive use of multivariate normal distributions. Frequently, the mean and the covariance of this distribution have to be estimated from observations. If no additional knowledge is available in these situations, a non-informative prior distribution has to be specified for a Bayesian estimation. Since many paradigms exist according to which a non-informative prior distribution can be chosen, we will identify the influence that selected priors have on the marginal posterior and on the measurement uncertainty of the multivariate normal expectation. Neither the distribution itself nor its parameters are robust to standard choices of non-informative prior distributions for small and medium-sized samples. The length of posterior credible intervals may differ by a factor of two or more.