English
Related papers

Related papers: Quantifying uncertain system outputs via the multi…

200 papers

A system to update estimates from a sequence of probability distributions is presented. The aim of the system is to quickly produce estimates with a user-specified bound on the Monte Carlo error. The estimates are based upon weighted…

Methodology · Statistics 2014-06-04 F. Din-Houn Lau , Axel Gandy

We introduce an extension of the time-dependent variational Monte Carlo (tVMC) method that adaptively controls the expressivity of the variational quantum state during the simulation of the dynamics. This adaptive tVMC (atVMC) approach is…

Quantum Physics · Physics 2026-01-09 Raffaele Salioni , Rocco Martinazzo , Davide Emilio Galli , Christian Apostoli

Multilevel Monte Carlo can efficiently compute statistical estimates of discretized random variables, for a given error tolerance. Traditionally, only a certain statistic is computed from a particular implementation of multilevel Monte…

Methodology · Statistics 2017-08-02 Alastair Gregory , Colin Cotter

We propose and analyze algorithms for distributionally robust optimization of convex losses with conditional value at risk (CVaR) and $\chi^2$ divergence uncertainty sets. We prove that our algorithms require a number of gradient…

Optimization and Control · Mathematics 2020-12-14 Daniel Levy , Yair Carmon , John C. Duchi , Aaron Sidford

A multilevel Monte Carlo (MLMC) method for quantifying model-form uncertainties associated with the Reynolds-Averaged Navier-Stokes (RANS) simulations is presented. Two, high-dimensional, stochastic extensions of the RANS equations are…

Computational Physics · Physics 2018-11-05 Prashant Kumar , Martin Schmelzer , Richard P. Dwight

In a multi-fidelity setting, data are available from two sources, high- and low-fidelity. Low-fidelity data has larger size and can be leveraged to make more efficient inference about quantities of interest, e.g. the mean, for high-fidelity…

Methodology · Statistics 2026-03-12 Minji Kim , Brendan Brown , Vladas Pipiras

We study the empirical likelihood approach to construct confidence intervals for the optimal value and the optimality gap of a given solution, henceforth quantify the statistical uncertainty of sample average approximation, for optimization…

Methodology · Statistics 2016-10-25 Henry Lam , Enlu Zhou

We introduce a variational algorithm to estimate the likelihood of a rare event within a nonequilibrium molecular dynamics simulation through the evaluation of an optimal control force. Optimization of a control force within a chosen basis…

Statistical Mechanics · Physics 2021-01-14 Avishek Das , David T. Limmer

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…

Computation · Statistics 2022-01-21 L. Martino , V. Elvira , D. Luengo , J. Corander

In this paper we discuss the possibility of using multilevel Monte Carlo (MLMC) methods for weak approximation schemes. It turns out that by means of a simple coupling between consecutive time discretisation levels, one can achieve the same…

Computational Finance · Quantitative Finance 2014-10-07 Denis Belomestny , Tigran Nagapetyan

Optimization is a key tool for scientific and engineering applications, however, in the presence of models affected by uncertainty, the optimization formulation needs to be extended to consider statistics of the quantity of interest.…

This paper addresses the problem of Monte Carlo approximation of posterior probability distributions. In particular, we have considered a recently proposed technique known as population Monte Carlo (PMC), which is based on an iterative…

Computation · Statistics 2016-06-03 Eugenia Koblents , Joaquín Míguez

This paper presents a distributionally robust stochastic model predictive control (SMPC) approach for linear discrete-time systems subject to unbounded and correlated additive disturbances. We consider hard input constraints and state…

Optimization and Control · Mathematics 2021-09-21 Christoph Mark , Steven Liu

We provide a general methodology for unbiased estimation for intractable stochastic models. We consider situations where the target distribution can be written as an appropriate limit of distributions, and where conventional approaches…

Methodology · Statistics 2014-12-01 Sergios Agapiou , Gareth O. Roberts , Sebastian J. Vollmer

We propose sequential Monte Carlo based algorithms for maximum likelihood estimation of the static parameters in hidden Markov models with an intractable likelihood using ideas from approximate Bayesian computation. The static parameter…

Computation · Statistics 2013-11-19 Sinan Yildirim , Sumeetpal Singh , Thomas Dean , Ajay Jasra

We establish a notion of random entropy solution for degenerate fractional conservation laws incorporating randomness in the initial data, convective flux and diffusive flux. In order to quantify the solution uncertainty, we design a…

Numerical Analysis · Mathematics 2020-10-02 Ujjwal Koley , Deep Ray , Tanmay Sarkar

We develop a framework that allows the use of the multi-level Monte Carlo (MLMC) methodology (Giles2015) to calculate expectations with respect to the invariant measure of an ergodic SDE. In that context, we study the (over-damped) Langevin…

Numerical Analysis · Mathematics 2019-08-13 Michael B. Giles , Mateusz B. Majka , Lukasz Szpruch , Sebastian Vollmer , Konstantinos Zygalakis

A weighted likelihood technique for robust estimation of a multivariate Wrapped Normal distribution for data points scattered on a p-dimensional torus is proposed. The occurrence of outliers in the sample at hand can badly compromise…

Methodology · Statistics 2021-07-01 Giovanni Saraceno , Claudio Agostinelli , Luca Greco

For basic machine learning problems, expected error is used to evaluate model performance. Since the distribution of data is usually unknown, we can make simple hypothesis that the data are sampled independently and identically distributed…

Machine Learning · Computer Science 2022-12-01 Xuli Shen , Qing Xu , Xiangyang Xue

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