    DFT-QUANTITIES:  Quantities from log files relating to diffusion trees.

    The quantities below relating to diffustion tree models can be
    obtained from log files (eg, for use in dft-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 diffusion
    tree models, since the standard Markov chain operations are not
    supported.

    The quantities specific to diffusion tree models are listed below.  If
    "n" is present after the letter, it represents a numeric modifier,
    optional with default 1 when in square brackets.

        tn   Array of n'th target values for training cases (numbered from 1).
             NOTE:  One cannot omit n, since if it's missing, it's the 't'
             quantity described in quantities.doc.

        o[n] Array giving for each training case (numbered from 1) the latent
             value associated with variable n (numbered from 1).  Available
             only if latent vectors are stored.

        V[n] As an array, the variances of the n'th diffusion tree (from 1)
             for each variable (numbered from 1).  As a scalar, the top-level
             variance hyperparameter that controls these variances.

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

        c[n] Array giving the parameters for the divergence function for the
             n'th diffusion tree (from 1).  At present, only parameters c@0,
             c@1, and c@2 exist.

        N    As an array, the noise variances for each target variable
             (numbered from 1).  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.

        dn   As an array, the divergence times for internal nodes of the n'th
             diffusion tree (numbered from 1), sorted by increasing divergence
             time.  The lower bound given for portion of the array desired is
             ignored; a lower bound of 1 is always used.  For example, "d1@1:10",
             "d1@:10", "d1@10", and "d1@5:10" all give the ten earliest divergence
             times for tree 1.  As a scalar, the average divergence time over all
             internal nodes.  NOTE:  The tree number, n, cannot be omitted, since
             if it's missing, it's the 'd' quantity described in mc-quantities.doc.

        Dn   As an array, the depths for the training cases (numbered from 1)
             in tree n.  The depth is the number of links to successive parents
             that need to be followed to reach the root.  (The depth will be zero
             if there is only one training case, and otherwise will be at least
             one, and no greater than the number of training cases minus one.)  '
             As a scalar, the average depth over training cases.  NOTE:  The
             tree number, n, cannot be omitted, since if it's missing, it's the
             'D' quantity described in mc-quantities.doc.

        a... Divergence time of last common ancestor of two training cases in
             a tree.  The numeric modifier following "a" is interpreted in
             terms of its decimal digits.  The first non-zero digit should be
             the number of the tree (from 1).  This should be followed by the
             numbers of the training cases (from 1), which must have the SAME
             number of digits.  For instance, "a10213" is the divergence time
             of the last common ancestor of training cases 2 and 13 in tree
             number 1.

        A... An indicator (0/1) of whether or not two training cases are more
             closely related in a tree than they are to a third training case.
             The numeric modifier following "c" is interpreted in terms of its
             decimal digits.  The first non-zero digit should be the number of
             the tree (from 1).  This should be followed by the numbers of the
             three training cases (from 1), which must have the SAME number of
             digits.  For instance, "A2555008077" has the value 1 if in tree
             number 2, training case 555 is more closely related to training
             case 8 than either of them are to training case 77; otherwise, it
             has the value 0.  The three training cases must be distinct.

    Note that the numbering of training cases starting from 1 is different
    from some other modules in this software.  This is so these numbers
    can be combined with zero for the root node and with negative numbers
    for other non-terminal nodes.

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