Related papers: Monte Carlo: Basics

This paper introduces a class of Monte Carlo algorithms which are based upon the simulation of a Markov process whose quasi-stationary distribution coincides with a distribution of interest. This differs fundamentally from, say, current…

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…

In the present paper we consider the initial data, external force, viscosity coefficients, and heat conductivity coefficient as random data for the compressible Navier--Stokes--Fourier system. The Monte Carlo method, which is frequently…

The naive importance sampling estimator, based on samples from a single importance density, can be numerically unstable. Instead, we consider generalized importance sampling estimators where samples from more than one probability…

Quantiles and expected shortfalls are usually used to measure risks of stochastic systems, which are often estimated by Monte Carlo methods. This paper focuses on the use of quasi-Monte Carlo (QMC) method, whose convergence rate is…

In this survey paper we discuss some tools and methods which are of use in quasi-Monte Carlo (QMC) theory. We group them in chapters on Numerical Analysis, Harmonic Analysis, Algebra and Number Theory, and Probability Theory. We do not…

We introduce a new class of Monte Carlo based approximations of expectations of random variables such that their laws are only available via certain discretizations. Sampling from the discretized versions of these laws can typically…

Present quantum Monte Carlo codes use statistical techniques adapted to find the amplitude of a quantum system or the associated eigenvalues. Thus, they do not use a true physical random source. It is demonstrated that, in fact, quantum…

Many questions in quantitative finance, uncertainty quantification, and other disciplines are answered by computing the population mean, $\mu := \mathbb{E}(Y)$, where instances of $Y:=f(\boldsymbol{X})$ may be generated by numerical…

We introduce a multiscale Monte Carlo algorithm to simulate dense simple fluids. The probability of an update follows a power law distribution in its length scale. The collective motion of clusters of particles requires generalization of…

This is the documentation for generating random samples from the quantum state space in accordance with a specified distribution, associated with this webpage: http://tinyurl.com/QSampling . Ready-made samples (each with at least a million…

I discuss optimized data analysis and Monte Carlo methods. Reweighting methods are discussed through examples, like Lee-Yang zeroes in the Ising model and the absence of deconfinement in QCD. I discuss reweighted data analysis and…

Boson sampling is a promising candidate for quantum supremacy. It requires to sample from a complicated distribution, and is trusted to be intractable on classical computers. Among the various classical sampling methods, the Markov chain…

The preferential sampling of locations chosen to observe a spatio-temporal process has been identified as a major problem across multiple fields. Predictions of the process can be severely biased when standard statistical methodologies are…

Monte Carlo techniques have been widely employed in statistical physics as well as in quantum theory in the Lagrangian formulation. However, in some areas of application to quantum theories computational progress has been slow. Here we…

In this paper, we examine the Sample Average Approximation (SAA) procedure within a framework where the Monte Carlo estimator of the expectation is biased. We also introduce Multilevel Monte Carlo (MLMC) in the SAA setup to enhance the…

We discuss the application of multilevel Monte Carlo methods to elliptic partial differential equations with random coefficients. Such problems arise, for example, in uncertainty quantification in subsurface flow modeling. We give a brief…

We consider a statistical test whose p-value can only be approximated using Monte Carlo simulations. We are interested in deciding whether the p-value for an observed data set lies above or below a given threshold such as 5%. We want to…

In these lectures, given in '96 summer schools in Beg-Rohu (France) and Budapest, I discuss the fundamental principles of thermodynamic and dynamic Monte Carlo methods in a simple light-weight fashion. The keywords are MARKOV CHAINS,…

For long term investments, model portfolios are defined at the level of indexes, a setup known as Strategic Asset Allocation (SAA). The possible outcomes at a scale of a few decades can be obtained by Monte Carlo simulations, resulting in a…