Optimal Monte Carlo method in estimating areas

Optimal Monte Carlo updating.

Based on Peskun's theorem it is shown that optimal transition matrices in Markov chain Monte Carlo should have zero diagonal elements except for the diagonal element corresponding to the largest weight. We will compare the statistical efficiency of this sampler to existing algorithms, such as heat-bath updating and the Metropolis algorithm. We provide numerical results for the Potts model as an...

Optimal implementation of the Shadow Hybrid Monte Carlo method

Abstract. keywords: Sampling methods; Hybrid Monte Carlo; Symplectic integrator; Shadow Hamiltonian; Conformational sampling.

The Monte-Carlo Method

The Monte Carlo Method

The Monte Carlo method is often referred to as a ‘computer experiment’. One might think of this as a way of conveying the fact that the output of simulations is not an equation, as in conventional theory. Instead, numbers appear on the computer screen in somewhat the same way that numbers appear on a measuring device in the laboratory. Thus there is the implication that somehow simulations are ...

Monte Carlo Simulation Method

Quantum Monte Carlo (QMC) methods such as Variational Monte Carlo, Diffusion Monte Carlo or Path Integral Monte Carlo are the most accurate and general methods for computing total electronic energies. We will review methods we have developed to perform QMC for the electrons coupled to another MC simulation for the ions. In this method, one estimates the Born-Oppenheimer energy E(Z) where Z repr...