Related papers: Fast Monte-Carlo
Markov chain Monte Carlo (MCMC) methods to sample from a probability distribution $\pi$ defined on a space $(\Theta,\mathcal{T})$ consist of the simulation of realisations of Markov chains $\{\theta_{n},n\geq1\}$ of invariant distribution…
A Monte Carlo method for computing the action of a matrix exponential for a certain class of matrices on a vector is proposed. The method is based on generating random paths, which evolve through the indices of the matrix, governed by a…
We study the problem of sampling from a distribution $\target$ using the Langevin Monte Carlo algorithm and provide rate of convergences for this algorithm in terms of Wasserstein distance of order $2$. Our result holds as long as the…
Pseudo-marginal Markov chain Monte Carlo methods for sampling from intractable distributions have gained recent interest and have been theoretically studied in considerable depth. Their main appeal is that they are exact, in the sense that…
We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to…
We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the cumulative distribution function of a quantity of interest in problems with random input parameters or initial conditions. Our approach…
We propose a new Monte Carlo method for efficiently sampling trajectories with fixed initial and final conditions in a system with discrete degrees of freedom. The method can be applied to any stochastic process with local interactions,…
This paper introduces the Sequential Monte Carlo Transformer, an original approach that naturally captures the observations distribution in a transformer architecture. The keys, queries, values and attention vectors of the network are…
We address the problem of approximating the posterior probability distribution of the fixed parameters of a state-space dynamical system using a sequential Monte Carlo method. The proposed approach relies on a nested structure that employs…
Markov chain Monte Carlo (MCMC) is a simulation method commonly used for estimating expectations with respect to a given distribution. We consider estimating the covariance matrix of the asymptotic multivariate normal distribution of a…
We develop a new Monte Carlo method that solves hyperbolic transport equations with stiff terms, characterized by a (small) scaling parameter. In particular, we focus on systems which lead to a reduced problem of parabolic type in the limit…
In many situations it is important to be able to propose $N$ independent realizations of a given distribution law. We propose a strategy for making $N$ parallel Monte Carlo Markov Chains (MCMC) interact in order to get an approximation of…
Monte Carlo is a simple and flexible tool that is widely used in computational finance. In this context, it is common for the quantity of interest to be the expected value of a random variable defined via a stochastic differential equation.…
Markov Chain Monte Carlo (MCMC) methods have become a cornerstone of many modern scientific analyses by providing a straightforward approach to numerically estimate uncertainties in the parameters of a model using a sequence of random…
We introduce Path-ZVA: an efficient simulation technique for estimating the probability of reaching a rare goal state before a regeneration state in a (discrete-time) Markov chain. Standard Monte Carlo simulation techniques do not work well…
We study the problem of generating a sample from the stationary distribution of a Markov chain, given a method to simulate the chain. We give an approximation algorithm for the case of a random walk on a regular graph with n vertices that…
Active subspaces can effectively reduce the dimension of high-dimensional parameter studies enabling otherwise infeasible experiments with expensive simulations. The key components of active subspace methods are the eigenvectors of a…
Markov chain Monte Carlo methods have become standard tools in statistics to sample from complex probability measures. Many available techniques rely on discrete-time reversible Markov chains whose transition kernels build up over the…
We propose extensions and improvements of the statistical analysis of distributed multipoles (SADM) algorithm put forth by Chipot et al. in [6] for the derivation of distributed atomic multipoles from the quantum-mechanical electrostatic…
We propose a new time quantifiable Monte Carlo (MC) method to simulate the thermally induced magnetization reversal for an isolated single domain particle system. The MC method involves the determination of density of states, and the use of…