Related papers: Accuracy and convergence of the backward Monte-Car…
We discuss a backward Monte-Carlo technique for muon transport problem, with emphasis on its application in muography. Backward Monte-Carlo allows exclusive sampling of a final state by reversing the simulation flow. In practice it can be…
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…
The standard Kernel Quadrature method for numerical integration with random point sets (also called Bayesian Monte Carlo) is known to converge in root mean square error at a rate determined by the ratio $s/d$, where $s$ and $d$ encode the…
To improve the efficiency of Monte Carlo estimation, practitioners are turning to biased Markov chain Monte Carlo procedures that trade off asymptotic exactness for computational speed. The reasoning is sound: a reduction in variance due to…
We show that repulsive random variables can yield Monte Carlo methods with faster convergence rates than the typical $N^{-1/2}$, where $N$ is the number of integrand evaluations. More precisely, we propose stochastic numerical quadratures…
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…
Classical algorithms in numerical analysis for numerical integration (quadrature/cubature) follow the principle of approximate and integrate: the integrand is approximated by a simple function (e.g. a polynomial), which is then integrated…
High-dimensional data are routinely collected in many areas. We are particularly interested in Bayesian classification models in which one or more variables are imbalanced. Current Markov chain Monte Carlo algorithms for posterior…
In the Monte Carlo (MC) method statistical noise is usually present. Statistical noise may become dominant in the calculation of a distribution, usually by iteration, but is less Important in calculating integrals. The subject of the…
The order of convergence of the Monte Carlo method is 1/2 which means that we need quadruple samples to decrease the error in half in the numerical simulation. Multilevel Monte Carlo methods reach the same order of error by spending less…
The Diffusion Monte Carlo method is devoted to the computation of electronic ground-state energies of molecules. In this paper, we focus on implementations of this method which consist in exploring the configuration space with a {\bf fixed}…
Monte Carlo methods approximate integrals by sample averages of integrand values. The error of Monte Carlo methods may be expressed as a trio identity: the product of the variation of the integrand, the discrepancy of the sampling measure,…
We present Bayesian techniques for solving inverse problems which involve mean-square convergent random approximations of the forward map. Noisy approximations of the forward map arise in several fields, such as multiscale problems and…
We review the method of stochastic error correction which eliminates the truncation error associated with any subspace diagonalization. Monte Carlo sampling is used to compute the contribution of the remaining basis vectors not included in…
Monte Carlo is a versatile and frequently used tool in statistical physics and beyond. Correspondingly, the number of algorithms and variants reported in the literature is vast, and an overview is not easy to achieve. In this pedagogical…
The trace of a matrix function f(A), most notably of the matrix inverse, can be estimated stochastically using samples< x,f(A)x> if the components of the random vectors x obey an appropriate probability distribution. However such a…
The Monte Carlo method is a powerful tool for performing radiative equilibrium calculations, even in complex geometries. The main drawback of the standard Monte Carlo radiative equilibrium methods is that they require iteration, which makes…
This work deals with the numerical approximation of backward stochastic differential equations (BSDEs). We propose a new algorithm which is based on the regression-later approach and the least squares Monte Carlo method. We give some…
We explain in detail how to estimate mean values and assess statistical errors for arbitrary functions of elementary observables in Monte Carlo simulations. The method is to estimate and sum the relevant autocorrelation functions, which is…
We modify the reweighting factor of the projector used in diffusion Monte Carlo to reduce the time-step error of the total energy. Further, we present a reweighting scheme that has the desirable feature that it is exactly size-consistent,…