Related papers: A Continuation Multilevel Monte Carlo algorithm

In this paper we present a rigorous cost and error analysis of a multilevel estimator based on randomly shifted Quasi-Monte Carlo (QMC) lattice rules for lognormal diffusion problems. These problems are motivated by uncertainty…

Sequential Monte Carlo (SMC) methods, also known as particle filters, constitute a class of algorithms used to approximate expectations with respect to a sequence of probability distributions as well as the normalising constants of those…

The multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty quantification in PDE models. It combines approximations at different levels of accuracy using a hierarchy of…

We present in this paper a hybrid, Multi-Level Monte Carlo (MLMC) method for solving the neutral particle transport equation. MLMC methods, originally developed to solve parametric integration problems, work by using a cheap, low fidelity…

This work addresses uncertainty quantification of electromagnetic devices determined by the eddy current problem. The multilevel Monte Carlo (MLMC) method is used for the treatment of uncertain parameters while the devices are discretized…

This paper addresses optimization problems constrained by partial differential equations with uncertain coefficients. In particular, the robust control problem and the average control problem are considered for a tracking type cost…

Designing efficient learning algorithms with complexity guarantees for Markov decision processes (MDPs) with large or continuous state and action spaces remains a fundamental challenge. We address this challenge for entropy-regularized MDPs…

Approximate inference in probabilistic graphical models (PGMs) can be grouped into deterministic methods and Monte-Carlo-based methods. The former can often provide accurate and rapid inferences, but are typically associated with biases…

Stochastic gradient Markov chain Monte Carlo (MCMC) algorithms have received much attention in Bayesian computing for big data problems, but they are only applicable to a small class of problems for which the parameter space has a fixed…

Quasi-Monte Carlo (QMC) methods for estimating integrals are attractive since the resulting estimators typically converge at a faster rate than pseudo-random Monte Carlo. However, they can be difficult to set up on arbitrary posterior…

We propose Subsampling MCMC, a Markov Chain Monte Carlo (MCMC) framework where the likelihood function for $n$ observations is estimated from a random subset of $m$ observations. We introduce a highly efficient unbiased estimator of the…

Markov chain Monte Carlo (MCMC) is an established approach for uncertainty quantification and propagation in scientific applications. A key challenge in applying MCMC to scientific domains is computation: the target density of interest is…

In this work, we extend the hybrid Chernoff tau-leap method to the multilevel Monte Carlo (MLMC) setting. Inspired by the work of Anderson and Higham on the tau-leap MLMC method with uniform time steps, we develop a novel algorithm that is…

Stochastic PDE eigenvalue problems often arise in the field of uncertainty quantification, whereby one seeks to quantify the uncertainty in an eigenvalue, or its eigenfunction. In this paper we present an efficient multilevel quasi-Monte…

We introduce Markov chain Monte Carlo (MCMC) algorithms based on numerical approximations of piecewise-deterministic Markov processes obtained with the framework of splitting schemes. We present unadjusted as well as adjusted algorithms,…

Because of their robustness, efficiency and non-intrusiveness, Monte Carlo methods are probably the most popular approach in uncertainty quantification to computing expected values of quantities of interest (QoIs). Multilevel Monte Carlo…

This paper is on Bayesian inference for parametric statistical models that are defined by a stochastic simulator which specifies how data is generated. Exact sampling is then possible but evaluating the likelihood function is typically…

We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. Under such an assumption,…

Uncertainty estimation in deep models is essential in many real-world applications and has benefited from developments over the last several years. Recent evidence suggests that existing solutions dependent on simple Gaussian formulations…

This paper develops a novel weak multilevel Monte-Carlo (MLMC) approximation scheme for L\'evy-driven Stochastic Differential Equations (SDEs). The scheme is based on the state space discretization (via a continuous-time Markov chain…