A Credibility Interval for the Probability that a New Observation Belongs to One of Two Multivariate Normal Populations
Robert A. Rigby · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1982
Summary The moments of the logarithm of the likelihood ratio of a new observation, drawn from one of two multivariate normal populations, are obtained from the posterior moment generating function. The distribution of the logarithm of the likelihood ratio is approximated using Pearson curves. The distribution of the probability p that a new observation belongs to one of the two populations can be obtained by transformation. The relationship between the expected value of this distribution and the “predictive” estimate of p is shown.