    MC-AIS:  Monitor annealed importance sampling (AIS) runs.

    MC-ais reads logs files containing data from Annealed Importance
    Sampling (AIS) runs, and produces various indicators of how well AIS
    is performing.

    Usage:

        mc-ais values { log-file [ range ] }

    Reads data from the log files given, in the indicated ranges (default
    is the whole files), and computes from this data various values for
    each temperature in the tempering schedule, and writes them to
    standard output.  The values computed are given by the first argument,
    which should consist of one or more letters form the following list:

        I   index in tempering schedule
        i   inverse temperature at this index
        T   temperature at this index

        m   mean of the importance weights at this index
        M   log of the mean of the importance weights
        F   minus the log of the mean of the importance weights

        v   variance of the normalized importance weights at this index
        V   variance of the logs of the importance weights at this index
        W   log (1 + variance of the normalized importance weights at this index)
        a   adjusted sample size at this index

    The values requested are written to standard output.  Each line of
    output pertains to one index in the tempering schedule, and contains
    the values for that index, in the order requested.

    The mean of the importance weights converges to the ratio of the
    normalizing constants for the distribution at the given index and for
    the distribution at inverse temperature zero.  The normalized
    importance weights are obtained by dividing by the mean weight.  The
    adjusted sample size is the number of points for which data exists
    divided by one plus the variance of the normalized importance weights.
    It is a rough indicator of the effective size of the sample available
    for computing expectations.

    If the distribution of the logs of the weights is Gaussian, maximum
    sampling efficiency is achieved when the tempering schedule is such
    that the variance of the log weights (V) goes up linearly with the
    tempering index (I), ending at the value of about one, corresponding
    to the variance for the normalized weights being e-1 (about 1.7).

    The distribution of the log weights will not be Gaussian when there
    are isolated modes, however, or when there are occasional very bad
    runs.  Because of this, it may be better to monitoring W than V, as it
    will not be affected by a few really bad runs.  (When the logs of the
    weights are Gaussian, W and V should be the same.)  A general rule of
    thumb is therefore to modify the tempering schedule so that the
    command "mc-ais IW logfile" shows W increasing approximately linearly
    with tempering index (I) up to a final value of about one.

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