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Many scientific and engineering problems require to perform Bayesian inferences in function spaces, in which the unknowns are of infinite dimension. In such problems, many standard Markov Chain Monte Carlo (MCMC) algorithms become arbitrary…

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…

Along with Markov chain Monte Carlo (MCMC) methods, variational inference (VI) has emerged as a central computational approach to large-scale Bayesian inference. Rather than sampling from the true posterior $\pi$, VI aims at producing a…

Variational Monte Carlo (VMC) is a powerful and fast-growing method for optimizing and evolving parameterized many-body wave functions, especially with modern neural-network quantum states. In practice, however, the stochastic estimators…

Bayesian hierarchical linear models provide a natural framework to analyze nested and clustered data. Classical estimation with Markov chain Monte Carlo produces well calibrated posterior distributions but becomes computationally expensive…

We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to…

We show that for any multiple-try Metropolis algorithm, one can always accept the proposal and evaluate the importance weight that is needed to correct for the bias without extra computational cost. This results in a general, convenient,…

Fast inference of numerical model parameters from data is an important prerequisite to generate predictive models for a wide range of applications. Use of sampling-based approaches such as Markov chain Monte Carlo may become intractable…

This paper surveys some well-established approaches on the approximation of Bayes factors used in Bayesian model choice, mostly as covered in Chen et al. (2000). Our focus here is on methods that are based on importance sampling strategies…

Surrogate models - also called emulators - are widely used to facilitate Bayesian inference in settings where computational costs preclude the use of standard posterior inference algorithms. Their deployment is now standard practice across…

Hamiltonian Monte Carlo (HMC) is a powerful algorithm to sample latent variables from Bayesian models. The advent of probabilistic programming languages (PPLs) frees users from writing inference algorithms and lets users focus on modeling.…

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…

Factors models are routinely used to analyze high-dimensional data in both single-study and multi-study settings. Bayesian inference for such models relies on Markov Chain Monte Carlo (MCMC) methods which scale poorly as the number of…

Importance sampling is a promising variance reduction technique for Monte Carlo simulation based derivative pricing. Existing importance sampling methods are based on a parametric choice of the proposal. This article proposes an algorithm…

Multilevel Monte Carlo (MLMC) is a flexible and effective variance reduction technique for accelerating reliability assessments of complex power system. Recently, data-driven surrogate models have been proposed as lower-level models in the…

This article proposes an artificial data generating algorithm that is simple and easy to customize. The fundamental concept is to perform random permutation of Monte Carlo generated random numbers which conform to the unconditional…

We present a probabilistic deep learning methodology that enables the construction of predictive data-driven surrogates for stochastic systems. Leveraging recent advances in variational inference with implicit distributions, we put forth a…

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…

Approximate Bayesian computation (ABC) is now an established technique for statistical inference used in cases where the likelihood function is computationally expensive or not available. It relies on the use of a~model that is specified in…

Importance sampling (IS) is commonly used for cross validation (CV) in Bayesian models, because it only involves reweighting existing posterior draws without needing to re-estimate the model by re-running Markov chain Monte Carlo (MCMC).…