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Related papers: Multilevel Monte Carlo methods

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We present a sequential Monte Carlo sampler algorithm for the Bayesian analysis of generalised linear mixed models (GLMMs). These models support a variety of interesting regression-type analyses, but performing inference is often extremely…

Computation · Statistics 2008-10-08 Y. Fan , D. S. Leslie , M. P. Wand

This paper is a broad and accessible survey of the methods we have at our disposal for Monte Carlo gradient estimation in machine learning and across the statistical sciences: the problem of computing the gradient of an expectation of a…

Machine Learning · Statistics 2020-09-30 Shakir Mohamed , Mihaela Rosca , Michael Figurnov , Andriy Mnih

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

In the framework of uncertainty quantification, we consider a quantity of interest which depends non-smoothly on the high-dimensional parameter representing the uncertainty. We show that, in this situation, the multilevel Monte Carlo…

Numerical Analysis · Mathematics 2017-06-27 Laura Scarabosio

I show how to construct Monte Carlo algorithms (programs), prove that they are correct and document them. Complicated algorithms are build using a handful of elementary methods. This construction process is transparently illustrated using…

Computational Physics · Physics 2007-05-23 S. Jadach

I review the status of the general-purpose Monte Carlo event generators for the LHC, with emphasis on areas of recent physics developments. There has been great progress, especially in multi-jet simulation, but I mention some question marks…

High Energy Physics - Phenomenology · Physics 2010-08-18 Michael H. Seymour

In this article we consider the approximation of expectations w.r.t. probability distributions associated to the solution of partial differential equations (PDEs); this scenario appears routinely in Bayesian inverse problems. In practice,…

Computation · Statistics 2017-02-07 Alexandros Beskos , Ajay Jasra , Kody Law , Raul Tempone , Yan Zhou

We study the use of the multilevel Monte Carlo technique in the context of the calculation of Greeks. The pathwise sensitivity analysis differentiates the path evolution and reduces the payoff's smoothness. This leads to new challenges: the…

Computational Finance · Quantitative Finance 2011-02-08 Sylvestre Burgos , M. B. Giles

In this paper, we examine the Sample Average Approximation (SAA) procedure within a framework where the Monte Carlo estimator of the expectation is biased. We also introduce Multilevel Monte Carlo (MLMC) in the SAA setup to enhance the…

Computational Finance · Quantitative Finance 2024-07-29 Devang Sinha , Siddhartha P. Chakrabarty

We leverage multilevel Monte Carlo (MLMC) to improve the performance of multi-step look-ahead Bayesian optimization (BO) methods that involve nested expectations and maximizations. Often these expectations must be computed by Monte Carlo…

We consider the application of multilevel Monte Carlo methods to steady state Darcy flow in a random porous medium, described mathematically by elliptic partial differential equations with random coefficients. The levels in the multilevel…

Numerical Analysis · Mathematics 2015-06-16 Minho Park , Aretha Teckentrup

This contribution provides a pedagogical introduction to and review of the current status and ongoing progress in the development of Monte Carlo tools for the calculation and simulation of high-Q^2 processes in hadronic collisions.

High Energy Physics - Phenomenology · Physics 2010-10-27 M. L. Mangano

This paper proposes a Sequential Monte Carlo approach for the Bayesian estimation of mixed causal and noncausal models. Unlike previous Bayesian estimation methods developed for these models, Sequential Monte Carlo offers extensive…

Econometrics · Economics 2025-01-08 Gianluca Cubadda , Francesco Giancaterini , Stefano Grassi

An investigation is in progress to evaluate extensively and quantitatively the possible benefits and drawbacks of new programming paradigms in a Monte Carlo simulation environment, namely in the domain of physics modeling. The prototype…

This paper extends the Multilevel Monte Carlo variance reduction technique to nonlinear filtering. In particular, Multilevel Monte Carlo is applied to a certain variant of the particle filter, the Ensemble Transform Particle Filter. A key…

Numerical Analysis · Mathematics 2016-02-24 Alastair Gregory , Colin Cotter , Sebastian Reich

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

Discrete-state, continuous-time Markov models are becoming commonplace in the modelling of biochemical processes. The mathematical formulations that such models lead to are opaque, and, due to their complexity, are often considered…

Quantitative Methods · Quantitative Biology 2017-10-31 Christopher Lester

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

We propose a control variate multilevel Monte Carlo method for the kinetic BGK model of the Boltzmann equation subject to random inputs. The method combines a multilevel Monte Carlo technique with the computation of the optimal control…

Numerical Analysis · Mathematics 2020-04-17 Jingwei Hu , Lorenzo Pareschi , Yubo Wang

We consider the theoretical analysis of Multiscale Sampling Methods, which are a new class of gradient-free Markov chain Monte Carlo (MCMC) methods for high dimensional inverse differential equation problems. A detailed presentation of…

Methodology · Statistics 2025-03-06 Lucas Seiffert , Felipe Pereira