Prior-likelihood factorization and missing data

Marginal posterior distributions, when not available ana­lytically, can be at present numerically inaccessible if the number of parameters for intergration exeeeds 7 to 10. For the normal multivariate regression model, with data absent (missing)in a monotone pattern, some integrations have been accomplished analytically (Guttman and Menzefricke, 1983; Bartlett, 1983; for example).

In this note we show how monotely missing data support an extended prior-likelihood factorization and the needed posterior extended prior-likelihood factorization and the can be obtained directly using standard results.