Related papers: High-dimensional and higher-order multifidelity Mo…

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…

Random-effects meta-analyses have been widely applied in evidence synthesis for various types of medical studies. However, standard inference methods (e.g. restricted maximum likelihood estimation) usually underestimate statistical errors…

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…

In this paper we address the problem of the prohibitively large computational cost of existing Markov chain Monte Carlo methods for large--scale applications with high dimensional parameter spaces, e.g. in uncertainty quantification in…

The main focus of the analysts who deal with clustered data is usually not on the clustering variables, and hence the group-specific parameters are treated as nuisance. If a fixed effects formulation is preferred and the total number of…

The celebrated Monte Carlo method estimates an expensive-to-compute quantity by random sampling. Bandit-based Monte Carlo optimization is a general technique for computing the minimum of many such expensive-to-compute quantities by adaptive…

We present a novel approach which aims at high-performance uncertainty quantification for cardiac electrophysiology simulations. Employing the monodomain equation to model the transmembrane potential inside the cardiac cells, we evaluate…

We analyse a multilevel Monte Carlo method for the approximation of distribution functions of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide an…

The combination of continuum Many-Body Quantum physics and Monte Carlo methods provide a powerful and well established approach to first principles calculations for large systems. Replacing the exact solution of the problem with a…

In many problems, complex non-Gaussian and/or nonlinear models are required to accurately describe a physical system of interest. In such cases, Monte Carlo algorithms are remarkably flexible and extremely powerful approaches to solve such…

Metrics of model goodness-of-fit, model comparison, and model parameter estimation are the main categories of statistical problems in science. Bayesian and frequentist methods that address these questions often rely on a likelihood…

High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…

For real symmetric matrices that are accessible only through matrix vector products, we present Monte Carlo estimators for computing the diagonal elements. Our probabilistic bounds for normwise absolute and relative errors apply to Monte…

Machine learning (ML) methods, which fit to data the parameters of a given parameterized model class, have garnered significant interest as potential methods for learning surrogate models for complex engineering systems for which…

Bayesian parameter inference for complex stochastic simulators is challenging due to intractable likelihood functions. Existing simulation-based inference methods often require large number of simulations and become costly to use in…

In this article we consider computing expectations w.r.t.~probability laws associated to a certain class of stochastic systems. In order to achieve such a task, one must not only resort to numerical approximation of the expectation, but…

This paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non-Gaussian uncertainties. It combines state-of-the-art techniques in advanced Monte Carlo sampling…

Estimating Monte Carlo error is critical to valid simulation results in Markov chain Monte Carlo (MCMC) and initial sequence estimators were one of the first methods introduced for this. Over the last few years, focus has been on…

We consider the problem of sequentially choosing between a set of unbiased Monte Carlo estimators to minimize the mean-squared-error (MSE) of a final combined estimate. By reducing this task to a stochastic multi-armed bandit problem, we…

We develop a multilevel Monte Carlo (MLMC) framework for uncertainty quantification with Monte Carlo dropout. Treating dropout masks as a source of epistemic randomness, we define a fidelity hierarchy by the number of stochastic forward…