English
Related papers

Related papers: Multilevel Surrogate-based Control Variates

200 papers

Adaptive Monte Carlo methods are very efficient techniques designed to tune simulation estimators on-line. In this work, we present an alternative to stochastic approximation to tune the optimal change of measure in the context of…

Probability · Mathematics 2009-10-23 Benjamin Jourdain , Jérôme Lelong

A new methodology is presented for the construction of control variates to reduce the variance of additive functionals of Markov Chain Monte Carlo (MCMC) samplers. Our control variates are definedthrough the minimization of the asymptotic…

Methodology · Statistics 2019-07-09 Nicolas Brosse , Alain Durmus , Sean Meyn , Eric Moulines , Anand Radhakrishnan

We propose a multi-fidelity neural network surrogate sampling method for the uncertainty quantification of physical/biological systems described by ordinary or partial differential equations. We first generate a set of low/high-fidelity…

Numerical Analysis · Mathematics 2020-05-07 Mohammad Motamed

In this paper, we consider the implementation of multi-level Monte Carlo method to a stochastic optimal control problem with log-normal coefficients and its surrogate model problem. From the perspective of two optimization problems, i.e.,…

Optimization and Control · Mathematics 2016-01-19 Qi Sun , Ju Ming

The subsurface flow is usually subject to uncertain porous media structures. In most cases, however, we only have partial knowledge about the porous media properties. A common approach is to model the uncertain parameters of porous media as…

Numerical Analysis · Mathematics 2019-10-11 Yang Liu , Jingfa Li , Shuyu Sun , Bo Yu

Markov Chain Monte Carlo (MCMC) is a popular class of statistical methods for simulating autocorrelated draws from target distributions, including posterior distributions in Bayesian analysis. An important consideration in using simulated…

Methodology · Statistics 2017-06-16 Benjamin E. Deonovic , Brian J. Smith

In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar parameter. The distribution of this performance parameter is important in many uncertainty quantification problems, ranging…

Methodology · Statistics 2022-10-03 Robert Millar , Jinglai Li , Hui Li

Markov chain Monte Carlo (MCMC) simulation methods are widely used to assess parametric uncertainties of hydrologic models conditioned on measurements of observable state variables. However, when the model is CPU-intensive and…

Optimization and Control · Mathematics 2018-06-18 Jiangjiang Zhang , Jun Man , Guang Lin , Laosheng Wu , Lingzao Zeng

Stochastic PDE eigenvalue problems are useful models for quantifying the uncertainty in several applications from the physical sciences and engineering, e.g., structural vibration analysis, the criticality of a nuclear reactor or photonic…

Numerical Analysis · Mathematics 2022-10-07 Alexander D. Gilbert , Robert Scheichl

Bayesian formulations of inverse problems are attractive for their ability to incorporate prior knowledge and update probabilistic models as new data become available. Markov chain Monte Carlo (MCMC) methods sample posterior probability…

Geophysics · Physics 2025-05-07 Giovanni Angelo Meles , Stefano Marelli , Niklas Linde

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…

Computation · Statistics 2025-07-08 Arka Banerjee , Dootika Vats

In this article we develop a multi-grid multi-level Monte Carlo (MGMLMC) method for the stochastic Stokes-Darcy interface model with random hydraulic conductivity both in the porous media domain and on the interface. Because the randomness…

Numerical Analysis · Mathematics 2019-03-07 Zhipeng Yang , Xiaoming He , Li Zhang , Ju Ming

Inspired by the latest developments in multilevel Monte Carlo (MLMC) methods and randomised sketching for linear algebra problems we propose a MLMC estimator for real-time processing of matrix structured random data. Our algorithm is…

Numerical Analysis · Mathematics 2020-04-30 Yue Wu , Nick Polydorides

Markov Chain Monte Carlo (MCMC) sampling is computationally expensive, especially for complex models. Alternative methods make simplifying assumptions about the posterior to reduce computational burden, but their impact on predictive…

Computation · Statistics 2025-10-27 Florian D. van Leeuwen , Sara van Erp

In this paper, we provide bounds on the asymptotic variance for a class of sequential Monte Carlo (SMC) samplers designed for approximating multimodal distributions. Such methods combine standard SMC methods and Markov chain Monte Carlo…

Probability · Mathematics 2018-01-25 Daniel Paulin , Ajay Jasra , Alexandre Thiery

Variational Bayes (VB) is a popular tool for Bayesian inference in statistical modeling. Recently, some VB algorithms are proposed to handle intractable likelihoods with applications such as approximate Bayesian computation. In this paper,…

Numerical Analysis · Mathematics 2021-09-28 Zhijian He , Zhenghang Xu , Xiaoqun Wang

We consider the problem of estimating a nested structure of two expectations taking the form $U_0 = E[\max\{U_1(Y), \pi(Y)\}]$, where $U_1(Y) = E[X\ |\ Y]$. Terms of this form arise in financial risk estimation and option pricing. When…

Computational Finance · Quantitative Finance 2023-08-16 Abdul-Lateef Haji-Ali , Jonathan Spence

Standard approaches for uncertainty quantification in cardiovascular modeling pose challenges due to the large number of uncertain inputs and the significant computational cost of realistic three-dimensional simulations. We propose an…

Quantitative Methods · Quantitative Biology 2020-04-20 Casey M. Fleeter , Gianluca Geraci , Daniele E. Schiavazzi , Andrew M. Kahn , Alison L. Marsden

Markov chain Monte Carlo (MCMC) is a sampling-based method for estimating features of probability distributions. MCMC methods produce a serially correlated, yet representative, sample from the desired distribution. As such it can be…

Computation · Statistics 2019-12-10 Dootika Vats , Nathan Robertson , James M Flegal , Galin L Jones

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…

Numerical Analysis · Mathematics 2022-11-22 Ionut-Gabriel Farcas , Benjamin Peherstorfer , Tobias Neckel , Frank Jenko , Hans-Joachim Bungartz