Related papers: Introduction to Monte Carlo Methods
The efficient evaluation of high-dimensional integrals is of importance in both theoretical and practical fields of science, such as data science, statistical physics, and machine learning. However, exact computation methods suffer from the…
We consider generalizations of the classical inverse problem to Bayesien type estimators, where the result is not one optimal parameter but an optimal probability distribution in parameter space. The practical computational tool to compute…
We describe a generalized scheme for the probability-changing cluster (PCC) algorithm, based on the study of the finite-size scaling property of the correlation ratio, the ratio of the correlation functions with different distances. We…
Equilibrium systems evolve according to Detailed Balance (DB). This principe guided development of the Monte-Carlo sampling techniques, of which Metropolis-Hastings (MH) algorithm is the famous representative. It is also known that DB is…
A cluster Monte Carlo method for systems of classical spins with purely dipolar couplings is presented. It is tested and applied for finite arrays of perpendicular Ising dipoles on the triangular lattice. This model is a modification with…
Bayesian methods and their implementations by means of sophisticated Monte Carlo techniques have become very popular in signal processing over the last years. Importance Sampling (IS) is a well-known Monte Carlo technique that approximates…
Detailed mean field and Monte Carlo studies of the dynamic magnetization-reversal transition in the Ising model in its ordered phase under a competing external magnetic field of finite duration have been presented here. Approximate…
We present an efficient algorithm for the inference of stochastic block models in large networks. The algorithm can be used as an optimized Markov chain Monte Carlo (MCMC) method, with a fast mixing time and a much reduced susceptibility to…
A Monte Carlo Renormalization Group algorithm is used on the Ising model to derive critical exponents and the critical temperature. The algorithm is based on a minimum relative entropy iteration developed previously to derive potentials…
We briefly review the principles, mathematical bases, numerical shortcuts and applications of fast random walk (FRW) algorithms. This Monte Carlo technique allows one to simulate individual trajectories of diffusing particles in order to…
Sampling occupies an important position in theories of various scientific fields, and Markov chain Monte Carlo (MCMC) provides the most common technique of sampling. In the progress of MCMC, a huge number of studies have aimed the…
A novel class of non-reversible Markov chain Monte Carlo schemes relying on continuous-time piecewise-deterministic Markov Processes has recently emerged. In these algorithms, the state of the Markov process evolves according to a…
This review paper, written for the second edition of the Handbook of Markov Chain Monte Carlo, provides an introduction to the study of convergence analysis for Markov chain Monte Carlo (MCMC), aimed at researchers new to the field. We…
To sample from a given target distribution, Markov chain Monte Carlo (MCMC) sampling relies on constructing an ergodic Markov chain with the target distribution as its invariant measure. For any MCMC method, an important question is how to…
In this paper we present a dynamical Monte Carlo algorithm which is applicable to systems satisfying a clustering condition: during the dynamical evolution the system is mostly trapped in deep local minima (as happens in glasses, pinning…
We propose a new Monte Carlo technique in which the degeneracy of energy states is obtained with a Markovian process analogous to that of Metropolis used currently in canonical simulations. The obtained histograms are much broader than…
The Monte Carlo algorithm is increasingly utilized, with its central step involving computer-based random sampling from stochastic models. While both Markov Chain Monte Carlo (MCMC) and Reject Monte Carlo serve as sampling methods, the…
The short-time behaviour of the critical dynamics for magnetic systems is investigated with Monte Carlo methods. Without losing the generality, we consider the relaxation process for the two dimensional Ising and Potts model starting from…
Sequential Monte Carlo methods which involve sequential importance sampling and resampling are shown to provide a versatile approach to computing probabilities of rare events. By making use of martingale representations of the sequential…
This paper surveys various results about Markov chains on general (non-countable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the motivation and context for the theory which…