  We present a Nested Markov chain Monte Carlo (NMC) scheme for building
equilibrium averages based on accurate potentials such as density functional
theory. Metropolis sampling of a reference system, defined by an inexpensive
but approximate potential, was used to substantially decorrelate configurations
at which the potential of interest was evaluated, thereby dramatically reducing
the number needed to build ensemble averages at a given level of precision. The
efficiency of this procedure was maximized on-the-fly through variation of the
reference system thermodynamic state (characterized here by its inverse
temperature $\beta^0$), which was otherwise unconstrained. Local density
approximation (LDA) results are presented for shocked states of argon at
pressures from 4 to 60 GPa, where - depending on the quality of the reference
system potential - acceptance probabilities were enhanced by factors of 1.2-28
relative to unoptimized NMC. The optimization procedure compensated strongly
for reference potential shortcomings, as evidenced by significantly higher
speedups when using a reference potential of lower quality. The efficiency of
optimized NMC is shown to be competitive with that of standard ab initio
molecular dynamics in the canonical ensemble.
