Related papers: Monte Carlo methods in statistical physics: Mathem…

I show how to construct Monte Carlo algorithms (programs), prove that they are correct and document them. Complicated algorithms are build using a handful of elementary methods. This construction process is transparently illustrated using…

Monte Carlo techniques play a central role in statistical mechanics approaches for connecting macroscopic thermodynamic and kinetic properties to the electronic structure of a material. This paper describes the implementation of Monte Carlo…

Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection…

We give a cross-disciplinary survey on ``population'' Monte Carlo algorithms. In these algorithms, a set of ``walkers'' or ``particles'' is used as a representation of a high-dimensional vector. The computation is carried out by a random…

A Monte Carlo method to optimize cuts on variables is presented and evaluated. The method gives a much higher signal to noise ratio than does a manual choice of cuts.

Hamiltonian Monte Carlo has proven a remarkable empirical success, but only recently have we begun to develop a rigorous understanding of why it performs so well on difficult problems and how it is best applied in practice. Unfortunately,…

To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the…

In general, the statistical simulation approaches are referred to as the Monte Carlo methods as a whole. The broad class of the Monte Carlo methods involves the Markov chain Monte Carlo (MCMC) techniques that attract the attention of…

Present quantum Monte Carlo codes use statistical techniques adapted to find the amplitude of a quantum system or the associated eigenvalues. Thus, they do not use a true physical random source. It is demonstrated that, in fact, quantum…

With its systematic exploration of probability distributions, Hamiltonian Monte Carlo is a potent Markov Chain Monte Carlo technique; it is an approach, however, ultimately contingent on the choice of a suitable Hamiltonian function. By…

Complex scientific models where the likelihood cannot be evaluated present a challenge for statistical inference. Over the past two decades, a wide range of algorithms have been proposed for learning parameters in computationally feasible…

While recent work towards the development of tight-binding and ab-initio algorithms has focused on molecular dynamics, Monte Carlo methods can often lead to better results with relatively little effort. We present here a multi-step Monte…

The stochastic-gauge representation is a method of mapping the equation of motion for the quantum mechanical density operator onto a set of equivalent stochastic differential equations. One of the stochastic variables is termed the…

We present a method which extends Monte Carlo studies to situations that require a large dynamic range in particle number. The underlying idea is that, in order to calculate the collisional evolution of a system, some particle interactions…

Sampling-based inference has seen a surge of interest in recent years. Hamiltonian Monte Carlo (HMC) has emerged as a powerful algorithm that leverages concepts from Hamiltonian dynamics to efficiently explore complex target distributions.…

We describe and analyze some Monte Carlo methods for manifolds in Euclidean space defined by equality and inequality constraints. First, we give an MCMC sampler for probability distributions defined by un-normalized densities on such…

In order to find the equilibrium geometries of molecules and solids and to perform ab initio molecular dynamics, it is necessary to calculate the forces on the nuclei. We present a correlated sampling method to efficiently calculate…

Robust inference for stochastic dynamical systems is often hampered by sparse sampling and the absence of closed-form likelihoods. We introduce a Monte Carlo path-inference framework that leverages full-path statistics and bridge processes…

We introduce and discuss Monte Carlo methods in quantum field theories. Methods of independent Monte Carlo, such as random sampling and importance sampling, and methods of dependent Monte Carlo, such as Metropolis sampling and Hamiltonian…

Quantum mechanics for many-body systems may be reduced to the evaluation of integrals in 3N dimensions using Monte-Carlo, providing the Quantum Monte Carlo ab initio methods. Here we limit ourselves to expectation values for trial…