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In this paper we develop a very efficient approach to the Monte Carlo estimation of the expected value of partial perfect information (EVPPI) that measures the average benefit of knowing the value of a subset of uncertain parameters…

Numerical Analysis · Mathematics 2019-12-09 Michael B. Giles , Takashi Goda

This paper covers a massive acceleration of Monte-Carlo based pricing method for financial products and financial derivatives. The method is applicable in risk management settings, where a financial product has to be priced under a number…

Computational Engineering, Finance, and Science · Computer Science 2008-09-30 Stefan Dirnstorfer , Andreas J. Grau

Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition…

Quantum Physics · Physics 2017-07-12 Ashley Montanaro

Finding effective ways to exploit parallel computing to accelerate Markov chain Monte Carlo methods is an important problem in Bayesian computation and related disciplines. In this paper, we consider the zeroth-order setting where the…

Computation · Statistics 2026-01-28 Francesco Pozza , Giacomo Zanella

Our focus is on the design and analysis of efficient Monte Carlo methods for computing tail probabilities for the suprema of Gaussian random fields, along with conditional expectations of functionals of the fields given the existence of…

Probability · Mathematics 2012-10-09 Robert J. Adler , Jose H. Blanchet , Jingchen Liu

Sequential Monte Carlo (SMC) methods are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. We propose a new SMC algorithm to compute the expectation of additive functionals recursively.…

Methodology · Statistics 2010-12-27 Pierre Del Moral , Arnaud Doucet , Sumeetpal Singh

Control variates are variance reduction techniques for Monte Carlo estimators. They play a critical role in improving Monte Carlo estimators in scientific and machine learning applications that involve computationally expensive integrals.…

Methodology · Statistics 2026-02-27 Kaiyu Li , Yiming Yang , Xiaoyuan Cheng , Yi He , Zhuo Sun

We construct Monte Carlo methods for the $L^2$-approximation in Hilbert spaces of multivariate functions sampling no more than $n$ function values of the target function. Their errors catch up with the rate of convergence and the…

Numerical Analysis · Mathematics 2018-03-16 David Krieg

We introduce a novel Multi-Order Monte Carlo approach for uncertainty quantification in the context of multiscale time-dependent partial differential equations. The new framework leverages Implicit-Explicit Runge-Kutta time integrators to…

Numerical Analysis · Mathematics 2026-04-08 Giulia Bertaglia , Walter Boscheri , Lorenzo Pareschi

We propose a novel $hp$-multilevel Monte Carlo method for the quantification of uncertainties in the compressible Navier-Stokes equations, using the Discontinuous Galerkin method as deterministic solver. The multilevel approach exploits…

Numerical Analysis · Mathematics 2020-08-25 A. Beck , J. Dürrwächter , T. Kuhn , F. Meyer , C. -D. Munz , C. Rohde

Within ab initio Quantum Monte Carlo simulations, the leading numerical cost for large systems is the computation of the values of the Slater determinants in the trial wavefunction. Each Monte Carlo step requires finding the determinant of…

Computational Physics · Physics 2017-11-22 T. McDaniel , E. F. D'Azevedo , Y. W. Li , K. Wong , P. R. C. Kent

Recently, Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) methods have been proposed for scaling up Monte Carlo computations to large data problems. Whilst these approaches have proven useful in many applications, vanilla SG-MCMC…

Machine Learning · Statistics 2016-12-13 Umut Şimşekli , Roland Badeau , A. Taylan Cemgil , Gaël Richard

This manuscript presents a framework for using multilevel quadrature formulae to compute the solution of optimal control problems constrained by random partial differential equations. Our approach consists in solving a sequence of optimal…

Numerical Analysis · Mathematics 2025-05-19 Fabio Nobile , Tommaso Vanzan

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…

Computation · Statistics 2017-10-30 Ajay Jasra , Kengo Kamatani , Kody Law , Yan Zhou

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…

Methodology · Statistics 2018-12-31 Matias Quiroz , Robert Kohn , Mattias Villani , Minh-Ngoc Tran

The recently-introduced self-learning Monte Carlo method is a general-purpose numerical method that speeds up Monte Carlo simulations by training an effective model to propose uncorrelated configurations in the Markov chain. We implement…

Strongly Correlated Electrons · Physics 2017-10-11 Yuki Nagai , Huitao Shen , Yang Qi , Junwei Liu , Liang Fu

In this article we consider recursive approximations of the smoothing distribution associated to partially observed stochastic differential equations (SDEs), which are observed discretely in time. Such models appear in a wide variety of…

Methodology · Statistics 2018-05-15 Jeremie Houssineau , Ajay Jasra , Sumeetpal S. Singh

In this paper we propose an efficient stochastic optimization algorithm to search for Bayesian experimental designs such that the expected information gain is maximized. The gradient of the expected information gain with respect to…

Computation · Statistics 2022-02-03 Takashi Goda , Tomohiko Hironaka , Wataru Kitade , Adam Foster

In this article, we propose a space-time Multi-Index Monte Carlo (MIMC) estimator for a one-dimensional parabolic stochastic partial differential equation (SPDE) of Zakai type. We compare the complexity with the Multilevel Monte Carlo…

Numerical Analysis · Mathematics 2016-12-09 Zhenru Wang , Christoph Reisinger

In this work, we present, analyze, and implement a class of Multi-Level Markov chain Monte Carlo (ML-MCMC) algorithms based on independent Metropolis-Hastings proposals for Bayesian inverse problems. In this context, the likelihood function…

Numerical Analysis · Mathematics 2021-05-06 Juan Pablo Madrigal-Cianci , Fabio Nobile , Raul Tempone