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Discrepancies play an important role in the study of uniformity properties of point sets. Their probability distributions are a help in the analysis of the efficiency of the Quasi Monte Carlo method of numerical integration, which uses…
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…
High-quality random samples of quantum states are needed for a variety of tasks in quantum information and quantum computation. Searching the high-dimensional quantum state space for a global maximum of an objective function with many local…
An efficient simulation-based methodology is proposed for the rolling window estimation of state space models, called particle rolling Markov chain Monte Carlo (MCMC) with double block sampling. In our method, which is based on Sequential…
Bayesian inference with Markov Chain Monte Carlo (MCMC) is challenging when the likelihood function is irregular and expensive to compute. We explore several sampling algorithms that make use of subset evaluations to reduce computational…
Monte Carlo (MC) algorithms are commonly employed to explore high-dimensional parameter spaces constrained by data. All the statistical information obtained in the output of these analyses is contained in the Markov chains, which one needs…
High statistical precision is critical for Monte Carlo (MC) samples in high energy physics and is degraded by negatively weighted events. This paper investigates a procedure to learn the relationship between the negative and positive weight…
This paper presents a novel approach to estimate the Standard Model backgrounds based on modifying Monte Carlo predictions within their systematic uncertainties. The improved background model is obtained by altering the original predictions…
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…
In this review, we address the use of Monte Carlo methods for approximating definite integrals of the form $Z = \int L(x) d P(x)$, where $L$ is a target function (often a likelihood) and $P$ a finite measure. We present vertical-likelihood…
Demand for high-performance, robust, and safe autonomous systems has grown substantially in recent years. These objectives motivate the desire for efficient safety-theoretic reasoning that can be embedded in core decision-making tasks such…
In predictive modeling with simulation or machine learning, it is critical to accurately assess the quality of estimated values through output analysis. In recent decades output analysis has become enriched with methods that quantify the…
Two-line elements are widely used for space operations to predict the orbit with a moderate accuracy for 2-3 days. Local optimization methods, such as the nonlinear least squares method with differential corrections, can estimate a TLE as…
Many problems in materials science and biology involve particles interacting with strong, short-ranged bonds, that can break and form on experimental timescales. Treating such bonds as constraints can significantly speed up sampling their…
We propose Subsampling MCMC, a Markov Chain Monte Carlo (MCMC) framework where the likelihood function for $n$ observations is estimated from a random subset of $m$ observations. We introduce a highly efficient unbiased estimator of the…
We consider systems of stochastic differential equations with multiple scales and small noise and assume that the coefficients of the equations are ergodic and stationary random fields. Our goal is to construct provably-efficient importance…
Monte Carlo simulations are based on the manipulation of random numbers to evaluate probable outcomes, with applicability in a variety of different fields. By assigning probabilities, which can be determined a priori, to various events, it…
Population Monte Carlo (PMC) sampling methods are powerful tools for approximating distributions of static unknowns given a set of observations. These methods are iterative in nature: at each step they generate samples from a proposal…
Approximate Bayesian computation (ABC) methods can be used to sample from posterior distributions when the likelihood function is unavailable or intractable, as is often the case in biological systems. ABC methods suffer from inefficient…
We present a comprehensive comparison of different Markov Chain Monte Carlo (MCMC) sampling methods, evaluating their performance on both standard test problems and cosmological parameter estimation. Our analysis includes traditional…