Related papers: Improved small-sample inference for functions of p…

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…

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…

Estimating failure probabilities of engineering systems is an important problem in many engineering fields. In this work we consider such problems where the failure probability is extremely small (e.g $\leq10^{-10}$). In this case, standard…

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…

It is important to estimate the errors of probabilistic inference algorithms. Existing diagnostics for Markov chain Monte Carlo methods assume inference is asymptotically exact, and are not appropriate for approximate methods like…

Software packages usually report the results of statistical tests using p-values. Users often interpret these by comparing them to standard thresholds, e.g. 0.1%, 1% and 5%, which is sometimes reinforced by a star rating (***, **, *). We…

Variational inference approximates the posterior distribution of a probabilistic model with a parameterized density by maximizing a lower bound for the model evidence. Modern solutions fit a flexible approximation with stochastic gradient…

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…

Drawing a sample from a discrete distribution is one of the building components for Monte Carlo methods. Like other sampling algorithms, discrete sampling suffers from the high computational burden in large-scale inference problems. We…

We develop a theoretical framework for studying numerical estimation of lower previsions, generally applicable to two-level Monte Carlo methods, importance sampling methods, and a wide range of other sampling methods one might devise. We…

We study the complexity of approximating integrals of smooth functions at absolute precision $\varepsilon > 0$ with confidence level $1 - \delta \in (0,1)$. The optimal error rate for multivariate functions from classical isotropic Sobolev…

Large deviation theory has provided important clues for the choice of importance sampling measures for Monte Carlo evaluation of exceedance probabilities. However, Glasserman and Wang [Ann. Appl. Probab. 7 (1997) 731--746] have given…

We describe and analyze a variance reduction approach for Monte Carlo (MC) sampling that accelerates the estimation of statistics of computationally expensive simulation models using an ensemble of models with lower cost. These lower cost…

Continuous level Monte Carlo is an unbiased, continuous version of the celebrated multilevel Monte Carlo method. The approximation level is assumed to be continuous resulting in a stochastic process describing the quantity of interest.…

Importance sampling has been known as a powerful tool to reduce the variance of Monte Carlo estimator for rare event simulation. Based on the criterion of minimizing the variance of Monte Carlo estimator within a parametric family, we…

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…

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,…

Many machine learning problems involve Monte Carlo gradient estimators. As a prominent example, we focus on Monte Carlo variational inference (MCVI) in this paper. The performance of MCVI crucially depends on the variance of its stochastic…

We present a new method for conducting Monte Carlo inference in graphical models which combines explicit search with generalized importance sampling. The idea is to reduce the variance of importance sampling by searching for significant…

We are concerned with a situation in which we would like to test multiple hypotheses with tests whose p-values cannot be computed explicitly but can be approximated using Monte Carlo simulation. This scenario occurs widely in practice. We…