Related papers: Fast Conservative Monte Carlo Confidence Intervals
A technique for reducing the number of integrals in a Monte Carlo calculation is introduced. For integrations relying on classical or mean-field trajectories with local weighting functions, it is possible to integrate analytically at least…
Monte Carlo and Quasi-Monte Carlo methods present a convenient approach for approximating the expected value of a random variable. Algorithms exist to adaptively sample the random variable until a user defined absolute error tolerance is…
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…
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…
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…
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…
Quasi-Monte Carlo sampling can attain far better accuracy than plain Monte Carlo sampling. However, with plain Monte Carlo sampling it is much easier to estimate the attained accuracy. This article describes methods old and new to quantify…
In a multi-fidelity setting, data are available from two sources, high- and low-fidelity. Low-fidelity data has larger size and can be leveraged to make more efficient inference about quantities of interest, e.g. the mean, for high-fidelity…
Randomization-based inference commonly relies on grid search methods to construct confidence intervals by inverting hypothesis tests over a range of parameter values. While straightforward, this approach is computationally intensive and can…
Classical algorithms in numerical analysis for numerical integration (quadrature/cubature) follow the principle of approximate and integrate: the integrand is approximated by a simple function (e.g. a polynomial), which is then integrated…
We propose confidence regions for the parameters of incomplete models with exact coverage of the true parameter in finite samples. Our confidence region inverts a test, which generalizes Monte Carlo tests to incomplete models. The test…
We show that repulsive random variables can yield Monte Carlo methods with faster convergence rates than the typical $N^{-1/2}$, where $N$ is the number of integrand evaluations. More precisely, we propose stochastic numerical quadratures…
Consider testing multiple hypotheses using tests that can only be evaluated by simulation, such as permutation tests or bootstrap tests. This article introduces MMCTest, a sequential algorithm which gives, with arbitrarily high probability,…
In this note we study the numerical stability problem that may take place when calculating the cumulative distribution function of the {\it Hypoexponential} random variable. This computation is extensively used during the execution of Monte…
One of the most demanding calculations is to generate random samples from a specified probability distribution (usually with an unknown normalizing prefactor) in a high-dimensional configuration space. One often has to resort to using a…
Simulation studies are used to evaluate and compare the properties of statistical methods in controlled experimental settings. In most cases, performing a simulation study requires knowledge of the true value of the parameter, or estimand,…
Multi-fidelity Monte Carlo methods leverage low-fidelity and surrogate models for variance reduction to make tractable uncertainty quantification even when numerically simulating the physical systems of interest with high-fidelity models is…
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…
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,…
Recently, global pulsar timing arrays have released results from searching for a nano-Hertz gravitational wave background signal. Although there has not been any definite evidence of the presence of such a signal in residuals of pulsar…