BVG-MC:  Do Markov chain simulation to sample from a bivariate Gaussian.

The bvg-mc program is the specialization of xxx-mc to the task of
sampling from a bivariate Gaussian.  See xxx-mc.doc for the generic
features of this program.

The following applications-specific sampling procedures are implemented:

    gibbs          Does a Gibbs sampling update for all replications 
                   of the bivariate Gaussian.  A update consists of 
                   sampling first from the conditional distribution for 
                   the first component, and then from the conditional 
                   distribution for the second component.

    gibbs0 alpha   Does an Adler-style overrelaxed update for the first 
                   component (separately for all replications).  The 
                   new value of the offset of the component from its
                   conditional mean is alpha times the old offset plus
                   Gaussian noise of variance 1-alpha^2 times the
                   conditional variance.

    gibbs1 alpha   Does an Adler-style overrelaxed update for the second
                   component.

To do Adler-style successive overrelaxation, gibbs0 and gibbs1 should
be done alternately.

The inverse temperature used in tempering methods is interpreted in
the standard way, as a power to raise the (unnormalized) probability
density to, or equivalently, a factor to multiply the energy by.

The default dynamical stepsizes are all set to one, except that they
are appropriately scaled during tempering.

            Copyright (c) 1995 by Radford M. Neal