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
    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.  Ideally, for maximum efficiency, the
tempering schedule should be chosen so that the variance of the log
weights goes up linearly with the tempering index, ending at the value
of about one, though this may not be achievable when there are
isolated modes.  The variance of the normalized weights would ideally
be e-1 (about 1.7).

            Copyright (c) 1998 by Radford M. Neal