Let the GM approximation to the distribution be given by

By Bayes rule,

where is the conditional density for given assuming that and are from that certain Gaussian sub-class . Fortunately, there is a closed-form equation for [55]. is Gaussian with mean

and covariance

Note that the conditional distribution is a Gaussian Mixture in its own right, with mode weights modified by which tends to ``select" the modes closest to . To reduce the number of modes in the conditioning process, one could easily remove those modes with a low value of (suggested by R. L. Streit).

This conditional distribution can be used for data visualization or, to easily calculate the conditional mean estimate, which is a by-product of equations (13.5),(13.6),(13.7):

Baggenstoss 2017-05-19