Care and Handling of Univariate or Multivariate Outliners in Detecting Spuriosity—a Bayesian Approach

The objective of this paper is to present a method of detection of spuriosity using a Bayesian approach. The model used is very specific—all observations are hopefully generated independently from the same normal source, N(μ, σ2), but it is feared that one of these may come from a spurious source, that of N(μ + a, σ2). The posterior of the “shift parameter a” is obtained, and it is shown to be a weighted combination of (Univariate) generalized t-distributions. The weights are very interesting and give much information, as do the separate generalized t-distributions. Examples are given to illustrate the use of the posterior of a, and the weights, etc. The procedure generalizes easily to the multivariate case, i.e., where the observations are hopefully generated independently from N(, ), but the fear exists that one of the observations is spurious from N( + a, ). A brief summary of results for this case is given.