We propose new control variates for variance reduction in the Metropolis–Hastings algorithm. We use variates that are functions of both the current state of the Markov chain and the proposed new state. This enable us to specify control variates which have known mean values for general target and proposal distributions. We develop the ideas for both the standard Metropolis–Hastings algorithm and...

Abstract. I show how Markov chain sampling with the Metropolis-Hastings algorithm can be modified so as to take bigger steps when the distribution being sampled from has the characteristic that its density can be quickly recomputed for a new point if this point differs from a previous point only with respect to a subset of “fast” variables. I show empirically that when using this method, the ef...

We show how to use subgroups of the symmetry group of a reversible Markov chain to give useful bounds on eigenvalues and their multiplicity. We supplement classical representation theoretic tools involving a group commuting with a self-adjoint operator with criteria for an eigenvector to descend to an orbit graph. As examples, we show that the Metropolis construction can dominate a max-degree c...

II. Classical and Path Integral Monte Carlo (Filinov, Bonitz; Nov. 10,12,14, 17) a) Introduction to classical Metropolis Monte Carlo b) Quantum Statistics, Density matrix c) Feynman’s path integral. Mapping onto an effective classical system d) Spin statistics, exchange, Fermion sign problem e) Generalized Metropolis algorithm for quantum systems, PIMC f) High-temperature N-particle density mat...

We show that addition of Metropolis single spin flips to the Wolff cluster-flipping Monte Carlo procedure leads to a dramatic increase in performance for the spin-1/2 Ising model. We also show that adding Wolff cluster flipping to the Metropolis or heat bath algorithms in systems where just cluster flipping is not immediately obvious (such as the spin-3/2 Ising model) can substantially reduce t...