MC-TEMP-SCHED:  Specify temperature schedule for tempering methods.

The mc-temp-sched command is used to specify a "tempering" or
"annealing" schedule, which defines a sequence of distributions in
which a "temperature" parameter changes.  The schedule is used when
sampling using simulated tempering, tempered transitions, and annealed
importance sampling.  The usual distribution is obtained when the
"temperature" is one.  The effect of a temperature other than one
depends on the particular application.  Some applications may ignore
the temperature.

Usage:

    mc-temp-sched log-file { inv-temp[@bias][:[+]n] }

or:

    mc-temp-sched log-file -
  
or:

    mc-temp-sched log-file 

The first two forms append a tempering schedule to a log file, which
must already exist, but not have iterations stored yet.  For the
second form, the schedule stored in the log file is displayed.

A schedule consists of one or more inverse "temperatures", in the
interval [0,1), which are normally monotonically increasing.  An
inverse temperature can be specified directly, or in the form "/temp",
with "temp" being the non-inverse temperature.  A final temperature of
1 is automatically added at the end of the list.  The second form of
the command above, with a single argument of "-" after the log file,
specifies a schedule consisting only of this final temperature.

With each temperature may optionally be associated a "bias", which is
added to the energy of states at that temperature when simulated
tempering is done.  The default bias is zero, as is that for the final
temperature of one.

An argument with a colon represents a set of n temperatures/biases
starting with that given and continuing up to but not including the
next temperature specified (or up to a temperature of one if the
argument is the last).  The biases are interpolated arithmetically.
If the number of temperatures immediately follows the colon, the
temperatures are interpolated geometrically; If a "+" follows the
colon, they are interpolated arithmetically.  For example, the two
arguments "/16@20:2" and "/4@10" give the same results as the three
arguments "/16@20 /8@15 /4@10", and the single argument "0:+4" is the
same as the four arguments "0 0.25 0.5 0.75".

When the tempering schedule is displayed, the schedule is listed in
detail (expanding any specified series), with both the inverse and
the non-inverse forms of the temperature.

            Copyright (c) 1995, 1998 by Radford M. Neal