    MIX-QUANTITIES:  Quantities from log files relating to mixture models.

    The quantities below relating to mixture models can be obtained from
    log files (eg, for use in mix-plt).  The generic quantities documented
    in quantities.doc are also available.  The Markov chain quantities
    documented in mc-quantities.doc are defined as well, but at present
    most of them are not meaningful for mixture models, since the standard
    Markov chain operations are not supported.

    The quantities specific to mixture models are as follows (if "n" is
    present after the letter, it represents a numeric modifier):

        tn   Array of n'th target values for training cases.

        u    An array containing the mean offset for each target value.

        un   An array containing the offset parameters for component n,
             numbered (starting at 1) in order of decreasing frequency
             in the training set.  If n is greater than the number of
             components currently represented in the training set, the
             value of un is the same as the mean offset (quantity u).

        V    As an array, the variances of offsets for each target value.
             As a scalar, the top-level variance hyperparameter that
             controls these variances.

        v    Same as for V, but expressed in terms of standard deviations
             rather than variances.

        N    As an array, the hyperparameters controlling the variances
             for each of the (real) target values in the components of the
             mixture. As a scalar, the top-level variance hyperparameter
             that controls these variances.  Valid only when the targets
             are real-valued.

        n    Same as for N, but expressed in terms of standard deviations
             rather than variances.

        Nn   Array of noise variances for the n'th component, or array of
             noise-variance hyperparameters if n is greater than the number
             of components currently active in the training set.

        nn   As for Nn, but in terms of standard deviations.

        Cn   The fraction of training cases that are associated with the
             first n mixture components.  The components are ordered according
             to the number of training cases with which they are associated
             (most frequent first).

        cn   The frequency of the n'th most common mixture component among the
             training cases.  The components are ordered according to the number
             of training cases with which they are associated (most frequent
             first).  The value is zero if there are fewer than n active
             components at present.

        a[n] The number of components needed to account for all but n% of the
             training cases.  The default is n=0 - ie, just "a" is the total
             number of currently active components.

        on   Array giving for each training case (numbered from 0) the offset
             parameter for the n'th target value for the component associated
             with this training case.

        h    Array giving for each training case (numbered from 0) the number
             of training cases currently associated with the component associated
             with this training case (counting this case itself, so the minimum
             value is 1, and the maximum is the number of training cases).

                Copyright (c) 1995-2003 by Radford M. Neal