Related papers: Sampling from a polytope and hard-disk Monte Carlo
Monte Carlo methods are widely used to estimate observables in many-body quantum systems. However, conventional sampling schemes often require a large number of samples to achieve sufficient accuracy. In this work we propose the…
Markov chain Monte Carlo (MCMC) algorithms are indispensable when sampling from a complex, high-dimensional distribution by a conventional method is intractable. Even though MCMC is a powerful tool, it is also hard to control and tune in…
Many problems in materials science and biology involve particles interacting with strong, short-ranged bonds, that can break and form on experimental timescales. Treating such bonds as constraints can significantly speed up sampling their…
The Markov Chain Monte Carlo method is at the heart of efficient approximation schemes for a wide range of problems in combinatorial enumeration and statistical physics. It is therefore very natural and important to determine whether…
We propose locally stable sparse hard-disk packings, as introduced by B\"or\"oczky, as a model for the analysis and benchmarking of Markov-chain Monte Carlo (MCMC) algorithms. We first generate such packings in a square box with periodic…
We propose a hybrid Monte Carlo (HMC) technique applicable to high-dimensional multivariate normal distributions that effectively samples along chaotic trajectories. The method is predicated on the freedom of choice of the HMC momentum…
Using Markov chain Monte Carlo to sample from posterior distributions was the key innovation which made Bayesian data analysis practical. Notoriously, however, MCMC is hard to tune, hard to diagnose, and hard to parallelize. This…
It was recently demonstrated that a simple Monte Carlo (MC) algorithm involving the swap of particle pairs dramatically accelerates the equilibrium sampling of simulated supercooled liquids. We propose two numerical schemes integrating the…
Markov chain Monte Carlo (MCMC) sampling of densities restricted to linearly constrained domains is an important task arising in Bayesian treatment of inverse problems in the natural sciences. While efficient algorithms for uniform polytope…
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…
Monte Carlo simulations are widely used to simulate complex molecular systems, but standard approaches suffer from metastability. Lately, the use of non-local proposal updates in a collective-variable (CV) space has been proposed in several…
We discuss non-reversible Markov-chain Monte Carlo algorithms that, for particle systems, rigorously sample the positional Boltzmann distribution and that have faster than physical dynamics. These algorithms all feature a non-thermal…
This paper addresses the problem of Monte Carlo approximation of posterior probability distributions. In particular, we have considered a recently proposed technique known as population Monte Carlo (PMC), which is based on an iterative…
An improved real-time quantum Monte Carlo procedure is presented and applied to describe the electronic transfer dynamics along molecular chains. The model consists of discrete electronic sites coupled to a thermal environment which is…
In this paper a method based on a Markov chain Monte Carlo (MCMC) algorithm is proposed to compute the probability of a rare event. The conditional distribution of the underlying process given that the rare event occurs has the probability…
We applied a multicanonical algorithm (entropic sampling) to a two-dimensional and a three-dimensional Lennard-Jones system with quasicrystalline and glassy ground states. Focusing on the ability of the algorithm to locate low lying energy…
Monte Carlo algorithms often aim to draw from a distribution $\pi$ by simulating a Markov chain with transition kernel $P$ such that $\pi$ is invariant under $P$. However, there are many situations for which it is impractical or impossible…
Hamiltonian Monte Carlo (HMC) sampling methods provide a mechanism for defining distant proposals with high acceptance probabilities in a Metropolis-Hastings framework, enabling more efficient exploration of the state space than standard…
We review the background of the cluster algorithms in Monte Carlo simulation of statistical physics problems. One of the first such successful algorithm was developed by Swendsen and Wang eight years ago. In contrast to the local…
We introduce a quantum Monte Carlo method to simulate the reversible dynamics of correlated many-body systems. Our method is based on the Laplace transform of the time-evolution operator which, as opposed to most quantum Monte Carlo…