Related papers: Guaranteed Monte Carlo Methods for Bernoulli Rando…
A method based on multicanonical Monte Carlo is applied to the calculation of large deviations in the largest eigenvalue of random matrices. The method is successfully tested with the Gaussian orthogonal ensemble (GOE), sparse random…
Given a stream of Bernoulli random variables, consider the problem of estimating the mean of the random variable within a specified relative error with a specified probability of failure. Until now, the Gamma Bernoulli Approximation Scheme…
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…
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,…
Complex scientific models where the likelihood cannot be evaluated present a challenge for statistical inference. Over the past two decades, a wide range of algorithms have been proposed for learning parameters in computationally feasible…
As increasingly complex hypothesis-testing scenarios are considered in many scientific fields, analytic derivation of null distributions is often out of reach. To the rescue comes Monte Carlo testing, which may appear deceptively simple: as…
Monte Carlo method is a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. They are often used in physical and mathematical problems and are most useful when it is difficult or…
The Monte Carlo algorithm is increasingly utilized, with its central step involving computer-based random sampling from stochastic models. While both Markov Chain Monte Carlo (MCMC) and Reject Monte Carlo serve as sampling methods, the…
The order of convergence of the Monte Carlo method is 1/2 which means that we need quadruple samples to decrease the error in half in the numerical simulation. Multilevel Monte Carlo methods reach the same order of error by spending less…
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…
Monte Carlo integration is a commonly used technique to compute intractable integrals and is typically thought to perform poorly for very high-dimensional integrals. To show that this is not always the case, we examine Monte Carlo…
We shall show in this paper that there are experiments which are Bernoulli trials with success probability p > 0.5, and which have the curious feature that it is possible to correctly predict the outcome with probability > p.
To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the…
We describe an embarrassingly parallel, anytime Monte Carlo method for likelihood-free models. The algorithm starts with the view that the stochasticity of the pseudo-samples generated by the simulator can be controlled externally by a…
Monte Carlo experiments produce samples in order to estimate features of a given distribution. However, simultaneous estimation of means and quantiles has received little attention, despite being common practice. In this setting we…
Importance sampling Monte-Carlo methods are widely used for the approximation of expectations with respect to partially known probability measures. In this paper we study a deterministic version of such an estimator based on quasi-Monte…
Monte Carlo methods to evaluate and maximize the likelihood function enable the construction of confidence intervals and hypothesis tests, facilitating scientific investigation using models for which the likelihood function is intractable.…
Monte Carlo is a versatile and frequently used tool in statistical physics and beyond. Correspondingly, the number of algorithms and variants reported in the literature is vast, and an overview is not easy to achieve. In this pedagogical…
In this paper, a Monte Carlo based approach for the quantification of the importance of the scattering input parameters with respect to the failure probability is presented. Using the basic idea of the alpha-factors of the First Order…
Monte Carlo methods represent the "de facto" standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use…