Related papers: Optimal Monte Carlo Methods for $L^2$-Approximatio…
Statisticians often use Monte Carlo methods to approximate probability distributions, primarily with Markov chain Monte Carlo and importance sampling. Sequential Monte Carlo samplers are a class of algorithms that combine both techniques to…
Multifidelity Monte Carlo methods often rely on a preprocessing phase consisting of standard Monte Carlo sampling to estimate correlation coefficients between models of different fidelity to determine the weights and number of samples for…
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 consider the problem of adaptive stratified sampling for Monte Carlo integration of a differentiable function given a finite number of evaluations to the function. We construct a sampling scheme that samples more often in regions where…
We propose a methodology for computing single and multi-asset European option prices, and more generally expectations of scalar functions of (multivariate) random variables. This new approach combines the ability of Monte Carlo simulation…
Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection…
Quasi-Monte Carlo sampling can attain far better accuracy than plain Monte Carlo sampling. However, with plain Monte Carlo sampling it is much easier to estimate the attained accuracy. This article describes methods old and new to quantify…
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 introduces a Monte Carlo method for maximum likelihood inference in the context of discretely observed diffusion processes. The method gives unbiased and a.s.\@ continuous estimators of the likelihood function for a family of…
In this paper, we present the Monte-Carlo Compressive Optimization algorithm, a new method to solve a combinatorial optimization problem that is assumed compressible. The method relies on random queries to the objective function in order to…
The behavior of a Lattice Monte Carlo algorithm (if it is designed correctly) must approach that of the continuum system that it is designed to simulate as the time step and the mesh step tend to zero. However, we show for an algorithm for…
We propose a modified power method for computing the subdominant eigenvalue $\lambda_2$ of a matrix or continuous operator. Here we focus on defining simple Monte Carlo methods for its application. The methods presented use random walkers…
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…
This manuscript presents a framework for using multilevel quadrature formulae to compute the solution of optimal control problems constrained by random partial differential equations. Our approach consists in solving a sequence of optimal…
We study approximation of the embedding $\ell_p^m \hookrightarrow \ell_q^m$, $1 \leq p < q \leq \infty$, based on randomized algorithms that use up to $n$ arbitrary linear functionals as information on a problem instance where $n \ll m$. By…
We present novel Monte Carlo (MC) and multilevel Monte Carlo (MLMC) methods to determine the unbiased covariance of random variables using h-statistics. The advantage of this procedure lies in the unbiased construction of the estimator's…
The two-dimensional Hubbard model is studied using the variational quantum Monte Carlo technique with Gutzwiller-type variational wave functions. In addition to the simple one-site correlated Gutzwiller wave function, we use a form with…
In this paper we address the widely-experienced difficulty in tuning Hamiltonian-based Monte Carlo samplers. We develop an algorithm that allows for the adaptation of Hamiltonian and Riemann manifold Hamiltonian Monte Carlo samplers using…
Owing to their favorable scaling with dimensionality, Monte Carlo (MC) methods have become the tool of choice for numerical integration across the quantitative sciences. Almost invariably, efficient MC integration schemes are strictly…
We consider the problem of numerical approximation of integrals of random fields over a unit hypercube. We use a stratified Monte Carlo quadrature and measure the approximation performance by the mean squared error. The quadrature is…