Related papers: Quasi-Monte Carlo Methods: What, Why, and How?
This article provides a high-level overview of some recent works on the application of quasi-Monte Carlo (QMC) methods to PDEs with random coefficients. It is based on an in-depth survey of a similar title by the same authors, with an…
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…
The Monte Carlo (MC) method is the most common technique used for uncertainty quantification, due to its simplicity and good statistical results. However, its computational cost is extremely high, and, in many cases, prohibitive.…
We discuss the problem of defining an estimate for the error in quasi-Monte Carlo integration. The key issue is the definition of an ensemble of quasi-random point sets that, on the one hand, includes a sufficiency of equivalent point sets,…
Many machine learning problems optimize an objective that must be measured with noise. The primary method is a first order stochastic gradient descent using one or more Monte Carlo (MC) samples at each step. There are settings where…
The mean of a random variable can be understood as a linear functional on the space of probability distributions. Quantum computing is known to provide a quadratic speedup over classical Monte Carlo methods for mean estimation. In this…
In Quasi-Monte Carlo integration, the integration error is believed to be generally smaller than in classical Monte Carlo with the same number of integration points. Using an appropriate definition of an ensemble of quasi-randompoint sets,…
This is basically a review of the field of Quasi-Monte Carlo intended for computational physicists and other potential users of quasi-random numbers. As such, much of the material is not new, but is presented here in a style hopefully more…
The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…
Estimating the unknown density from which a given independent sample originates is more difficult than estimating the mean, in the sense that for the best popular non-parametric density estimators, the mean integrated square error converges…
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…
The present work addresses the question how sampling algorithms for commonly applied copula models can be adapted to account for quasi-random numbers. Besides sampling methods such as the conditional distribution method (based on a…
Computing systems interacting with real-world processes must safely and reliably process uncertain data. The Monte Carlo method is a popular approach for computing with such uncertain values. This article introduces a framework for…
We give a cross-disciplinary survey on ``population'' Monte Carlo algorithms. In these algorithms, a set of ``walkers'' or ``particles'' is used as a representation of a high-dimensional vector. The computation is carried out by a random…
Quasi-Monte Carlo (qMC) methods are a powerful alternative to classical Monte-Carlo (MC) integration. Under certain conditions, they can approximate the desired integral at a faster rate than the usual Central Limit Theorem, resulting in…
Sequential Monte Carlo samplers represent a compelling approach to posterior inference in Bayesian models, due to being parallelisable and providing an unbiased estimate of the posterior normalising constant. In this work, we significantly…
Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…
In this paper, we analyse a method for approximating the distribution function and density of a random variable that depends in a non-trivial way on a possibly high number of independent random variables, each with support on the whole real…
Consider a central problem in randomized approximation schemes that use a Monte Carlo approach. Given a sequence of independent, identically distributed random variables $X_1,X_2,\ldots$ with mean $\mu$ and standard deviation at most $c…
Monte Carlo sampling is a powerful toolbox of algorithmic techniques widely used for a number of applications wherein some noisy quantity, or summary statistic thereof, is sought to be estimated. In this paper, we survey the literature for…