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We propose a modification, based on the RESTART (repetitive simulation trials after reaching thresholds) and DPR (dynamics probability redistribution) rare event simulation algorithms, of the standard diffusion Monte Carlo (DMC) algorithm.…
We present an implementation of Quantum Computing for a Markov Chain Monte Carlo method with an application to cosmological functions, to derive posterior distributions from cosmological probes. The algorithm proposes new steps in the…
In dynamic Monte Carlo simulations, using for example the Metropolis dynamic, it is often required to simulate for long times and to simulate large systems. We present an overview of advanced algorithms to simulate for larger times and to…
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…
Closed-form stochastic filtering equations can be derived in a general setting where probability distributions are replaced by some specific outer measures. In this article, we study how the principles of the sequential Monte Carlo method…
A classical Monte Carlo algorithm based on the quasi-classical approximation is applied to the pseudospin Hamiltonian of the model cuprate. The model takes into account both local and non-local correlations, Heisenberg spin-exchange…
Monte Carlo experiments produce samples in order to estimate features of a given distribution. However, simultaneous estimation of means and quantiles has received little attention, despite being common practice. In this setting we…
A brief introduction to the technique of Monte Carlo simulations in statistical physics is presented. The topics covered include statistical ensembles random and pseudo random numbers, random sampling techniques, importance sampling, Markov…
We study the numerical solution of nonlinear partially observed optimal stopping problems. The system state is taken to be a multi-dimensional diffusion and drives the drift of the observation process, which is another multi-dimensional…
Real-world distributed systems and networks are often unreliable and subject to random failures of its components. Such a stochastic behavior affects adversely the complexity of optimization tasks performed routinely upon such systems, in…
This series of six lectures is an introduction to using the Monte Carlo method to carry out nonperturbative studies in quantum field theories. Path integrals in quantum field theory are reviewed, and their evaluation by the Monte Carlo…
We present a new class of interacting Markov chain Monte Carlo algorithms for solving numerically discrete-time measure-valued equations. The associated stochastic processes belong to the class of self-interacting Markov chains. In contrast…
We study a version of the proximal gradient algorithm for which the gradient is intractable and is approximated by Monte Carlo methods (and in particular Markov Chain Monte Carlo). We derive conditions on the step size and the Monte Carlo…
Sequential Monte Carlo (SMC) methods are a class of techniques to sample approximately from any sequence of probability distributions using a combination of importance sampling and resampling steps. This paper is concerned with the…
Probabilistic models are conceptually powerful tools for finding structure in data, but their practical effectiveness is often limited by our ability to perform inference in them. Exact inference is frequently intractable, so approximate…
Sequential Monte Carlo (SMC) methods, also known as particle filters, constitute a class of algorithms used to approximate expectations with respect to a sequence of probability distributions as well as the normalising constants of those…
We present several Monte Carlo strategies for simulating discrete-time Markov chains with continuous multi-dimensional state space; we focus on stratified techniques. We first analyze the variance of the calculation of the measure of a…
In many problems, complex non-Gaussian and/or nonlinear models are required to accurately describe a physical system of interest. In such cases, Monte Carlo algorithms are remarkably flexible and extremely powerful approaches to solve such…
This paper provides a framework in which multilevel Monte Carlo and continuous level Monte Carlo can be compared. In continuous level Monte Carlo the level of refinement is determined by an exponentially distributed random variable, which…
In this paper we propose to evaluate and compare Markov chain Monte Carlo (MCMC) methods to estimate the parameters in a generalized extreme value model. We employed the Bayesian approach using traditional Metropolis-Hastings methods,…