    MC:  Programs and modules supporting Markov chain Monte Carlo methods.

    The 'mc' programs and modules support Monte Carlo methods based on
    sampling using Markov Chains.  The state space, desired distribution,
    and perhaps some special sampling procedures are defined by an
    application module linked with the generic 'mc' modules.  Successive
    states are stored in a log file, for use by programs that make Monte
    Carlo estimates.

    Users of applications that use the 'mc' modules needn't know the
    details of how it works.  The following documentation is for
    programmers wishing to use these modules in a new application.

    The full state space sampled from consists of up to four components:

        1) A set of "position" components, defined by the application, and
           stored in whatever records it pleases.

        2) A set of auxiliary components, also defined by the application,
           and stored in whatever records it pleases.

        3) A set of "momentum" components, in one-to-one correspondence
           with the position components.  These are added by this module,
           and stored in a record of type 'p'.

        4) A current inverse temperature, and associated change direction,
           if simulated tempering is being done.  These are added by this
           module, and stored in a record of type 'b'.

    The auxiliary components are updated only by the application module.
    The position, momentum, and inverse temperature components are updated
    by operations defined in this module, based on an "energy" function
    provided by the application.  The application module can directly
    update position coordinates as well.

    Sampling is an iterative procedure, each iteration being one transition
    of a Markov chain.  An iteration consists of one or more of the
    following operations, each of which has an identifying letter, and
    each of which corresponds to a specification documented with mc-spec:

        B  heatbath               b  rand-dir
        N  negate                 n  neg-dir
        M  metropolis             s  sim-temp
        m  met-1                  r  radial-heatbath

        D  dynamic                A  (application-specific operation)
        P  permuted-dynamic       R  repeat
        H  hybrid                 E  end
        T  tempered-hybrid        p  plot

        S  slice-1                t  temp-trans
        O  slice-over             a  ais
        i  slice-inside
        o  slice-outside

    The sequence of operations to use is specified by the user, and is
    stored in the log file as a record of type 'o'.  Some of the
    operations involve computing dynamical trajectories.  The method to be
    used to do this is also specified by the user, and is stored in the
    log file as a record of type 't'.  Tempering schemes use a temperature
    schedule stored in a record of type 'm'.  In all these cases, the last
    such record stored in the log file is used.

    Records of type 'i' containing information on an iteration are
    periodically written to the log file, along with the current state.
    The momentum part of the state is written as a record of type 'p'.
    The position and auxiliary parts of the state are written as defined
    by the application.

    The state of the random number generator after each iteration is
    stored in records of type 'r', the first of which may be written at
    index -1 using the 'rand-seed' program.

                Copyright (c) 1995-2004 by Radford M. Neal