    DIST-EST:  Estimate the expectation of some function of state.

    Dist-est reads data from one or more log files and uses it to estimate
    the expectation of a function of the state variables.  If annealed
    importance sampling was used, the estimate accounts for the differing
    importance weights.

    Usage:

        dist-est formula [ temp-index ] { log-file [ range ] }

    Estimates the expectation of the function of state specified by the
    formula given as the first argument.  This formula may refer to state
    variables, and to other variables defined in the specification given
    to dist-spec.  The expectation is normally with respect to the
    distribution at inverse temperature one, but if Annealed Importance
    Sampling or simulated tempering was done, an index into the tempering
    schedule may be given in order to produce an estimate with respect to
    one of the other distributions in the schedule.

    The data comes from one or more log files, at iterations within the
    specified ranges.  The ranges have the form "[low][:[high]]][%mod]".
    The low bound defaults to one.  If no high bound is given, the range
    extends to the highest index in the log file.  If the "%mod" option is
    present, only iterations within the range whose index is a multiple of
    "mod" are used (e.g. "5:12%3" is equivalent to 6 9 12).  If no range
    is given, the default is "1:".

    The output gives the estimated mean of the function, along with the
    number points used and the standard error for the estimate.  If
    annealed importance sampling was used, the mean of the importance
    weights is also reported, along with the adjusted sample size
    (dividing by one plus the variance of the normalized weights), and the
    effective sample size for the particular function whose expectation is
    being estimated.

    Note: The standard errors reported assume the points were generated
    independently, which will not generally be true unless annealed
    importance sampling was done (with independent starting points).

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