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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…
Adaptive Monte Carlo schemes developed over the last years usually seek to ensure ergodicity of the sampling process in line with MCMC tradition. This poses constraints on what is possible in terms of adaptation. In the general case…
We are concerned with the numerical resolution of backward stochastic differential equations. We propose a new numerical scheme based on iterative regressions on function bases, which coefficients are evaluated using Monte Carlo…
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…
Many inverse problems in nuclear fusion and high-energy astrophysics research, such as the optimization of tokamak reactor geometries or the inference of black hole parameters from interferometric images, necessitate high-dimensional…
Quasi-Monte Carlo (QMC) methods are being adopted in statistical applications due to the increasingly challenging nature of numerical integrals that are now routinely encountered. For integrands with $d$-dimensions and derivatives of order…
We consider Monte-Carlo discretizations of partial differential equations based on a combination of semi-lagrangian schemes and probabilistic representations of the solutions. We study the Monte-Carlo error in a simple case, and show that…
We describe an adaptive importance sampling algorithm for rare events that is based on a dual stochastic control formulation of a path sampling problem. Specifically, we focus on path functionals that have the form of cumulate generating…
A new acceleration algorithm to address the problem of multiple time scales in variational Monte Carlo simulations is presented. After a first attempted move has been rejected, the delayed rejection algorithm attempts a second move with a…
Quantum Monte Carlo is one of the most promising approaches for dealing with large-scale quantum many-body systems. It has played an extremely important role in understanding strongly correlated physics. However, two fundamental problems,…
In this article, we present a review of the recent developments on the topic of Multilevel Monte Carlo (MLMC) algorithm, in the paradigm of applications in financial engineering. We specifically focus on the recent studies conducted in two…
Recently, a diffusion Monte Carlo algorithm was applied to the study of spin dependent interactions in condensed matter. Following some of the ideas presented therein, and applied to a Hamiltonian containing a Rashba-like interaction, a…
The EM algorithm is a powerful tool for maximum likelihood estimation with missing data. In practice, the calculations required for the EM algorithm are often intractable. We review numerous methods to circumvent this intractability, all of…
This paper concerns numerical assessment of Monte Carlo error in particle filters. We show that by keeping track of certain key features of the genealogical structure arising from resampling operations, it is possible to estimate variances…
Importance sampling is a common technique for Monte Carlo approximation, including Monte Carlo approximation of p-values. Here it is shown that a simple correction of the usual importance sampling p-values creates valid p-values, meaning…
This paper analyzes the classical linear regression model with measurement errors in all the variables. First, we provide necessary and sufficient conditions for identification of the coefficients. We show that the coefficients are not…
Frequentist and likelihood methods of inference based on the multivariate skew-normal model encounter several technical difficulties with this model. In spite of the popularity of this class of densities, there are no broadly satisfactory…
Monte Carlo rendering algorithms are widely used to produce photorealistic computer graphics images. However, these algorithms need to sample a substantial amount of rays per pixel to enable proper global illumination and thus require an…
Direct sampling of multi-dimensional systems with quantum Monte Carlo methods allows exact account of many-body effects or particle correlations. The most straightforward approach to solve the Schr\"odinger equation, Diffusion Monte Carlo,…
The safety concern for unmanned systems, namely the concern for the potential casualty caused by system abnormalities, has been a bottleneck for their development, especially in populated areas. Evidently, the collision between the unmanned…