Related papers: Monte Carlo Estimation for Imprecise Probabilities…
We present a general approach to greatly increase at little cost the efficiency of Monte Carlo algorithms. To each observable to be computed we associate a renormalized observable (improved estimator) having the same average but a different…
Adaptive Monte Carlo methods are recent variance reduction techniques. In this work, we propose a mathematical setting which greatly relaxes the assumptions needed by for the adaptive importance sampling techniques presented by Vazquez-Abad…
A method for the multifidelity Monte Carlo (MFMC) estimation of statistical quantities is proposed which is applicable to computational budgets of any size. Based on a sequence of optimization problems each with a globally minimizing…
Simple Monte Carlo is a versatile computational method with a convergence rate of $O(n^{-1/2})$. It can be used to estimate the means of random variables whose distributions are unknown. Bernoulli random variables, $Y$, are widely used to…
We present two Monte Carlo sampling algorithms for probabilistic inference that guarantee polynomial-time convergence for a larger class of network than current sampling algorithms provide. These new methods are variants of the known…
Computing the variance of a conditional expectation has often been of importance in uncertainty quantification. Sun et al. has introduced an unbiased nested Monte Carlo estimator, which they call $1\frac{1}{2}$-level simulation since the…
In Monte Carlo calculations of expectation values in lattice quantum field theories, the stochastic variance of the sampling procedure that is used defines the precision of the calculation for a fixed number of samples. If the variance of…
Probabilistic prediction of sequences from images and other high-dimensional data is a key challenge, particularly in risk-sensitive applications. In these settings, it is often desirable to quantify the uncertainty associated with the…
Monte Carlo approximations for random linear elliptic PDE constrained optimization problems are studied. We use empirical process theory to obtain best possible mean convergence rates $O(n^{-\frac{1}{2}})$ for optimal values and solutions,…
The performance of the Monte Carlo sampling methods relies on the crucial choice of a proposal density. The notion of optimality is fundamental to design suitable adaptive procedures of the proposal density within Monte Carlo schemes. This…
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…
In this article, we consider computing expectations w.r.t. probability measures which are subject to discretization error. Examples include partially observed diffusion processes or inverse problems, where one may have to discretize time…
While the Quasi-Monte Carlo method of numerical integration achieves smaller integration error than standard Monte Carlo, its use in particle physics phenomenology has been hindered by the abscence of a reliable way to estimate that error.…
We propose a novel method for the elimination of negative Monte Carlo event weights. The method is process-agnostic, independent of any analysis, and preserves all physical observables. We demonstrate the overall performance and systematic…
Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions…
This paper examines the use of Monte Carlo simulations to understand statistical concepts in A/B testing and Randomized Controlled Trials (RCTs). We discuss the applicability of simulations in understanding false positive rates and estimate…
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…
We present general principles for the design and analysis of unbiased Monte Carlo estimators in a wide range of settings. Our estimators posses finite work-normalized variance under mild regularity conditions. We apply our estimators to…
In applications of imprecise probability, analysts must compute lower (or upper) expectations, defined as the infimum of an expectation over a set of parameter values. Monte Carlo methods consistently approximate expectations at fixed…
Monte Carlo methods are used to approximate the means, $\mu$, of random variables $Y$, whose distributions are not known explicitly. The key idea is that the average of a random sample, $Y_1, ..., Y_n$, tends to $\mu$ as $n$ tends to…