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We demonstrate a scaling method for non-Markovian Monte Carlo wave-function simulations used to study open quantum systems weakly coupled to their environments. We derive a scaling equation, from which the result for the expectation values…

Quantum Physics · Physics 2009-11-10 J. Piilo , S. Maniscalco , A. Messina , F. Petruccione

A general approach to provide approximate parameterizations of the "small" scales by the "large" ones, is developed for stochastic partial differential equations driven by linear multiplicative noise. This is accomplished via the concept of…

Analysis of PDEs · Mathematics 2013-10-16 Mickael D. Chekroun , Honghu Liu , Shouhong Wang

Markov Chain Monte Carlo (MCMC) methods, such as the Metropolis-Hastings (MH) algorithm, are widely used for Bayesian inference. One of the most important issues for any MCMC method is the convergence of the Markov chain, which depends…

Computation · Statistics 2015-11-20 Luca Martino , Jesse Read , David Luengo

Multiple importance sampling (MIS) is an increasingly used methodology where several proposal densities are used to approximate integrals, generally involving target probability density functions. The use of several proposals allows for a…

Statistics Theory · Mathematics 2022-07-12 Rahul Mukerjee , Víctor Elvira

Sequential optimization methods are often confronted with the curse of dimensionality in high-dimensional spaces. Current approaches under the Gaussian process framework are still burdened by the computational complexity of tracking…

Machine Learning · Computer Science 2024-01-08 Zeji Yi , Yunyue Wei , Chu Xin Cheng , Kaibo He , Yanan Sui

Non-convex sampling is a key challenge in machine learning, central to non-convex optimization in deep learning as well as to approximate probabilistic inference. Despite its significance, theoretically there remain many important…

Machine Learning · Computer Science 2024-09-18 Mohammad Reza Karimi , Ya-Ping Hsieh , Andreas Krause

Malliavin calculus provides a characterization of the centered model in regularity structures that is stable under removing the small-scale cut-off. In conjunction with a spectral gap inequality, it yields the stochastic estimates of the…

Probability · Mathematics 2025-10-08 Lucas Broux , Felix Otto , Markus Tempelmayr

Markov chain Monte Carlo (MCMC) methods are simulated by local exploration of complex statistical distributions, and while bypassing the cumbersome requirement of a specific analytical expression for the target, this stochastic exploration…

Computation · Statistics 2023-12-04 Xiongming Dai , Gerald Baumgartner

Weight averaging has become a standard technique for enhancing model performance. However, methods such as Stochastic Weight Averaging (SWA) and Latest Weight Averaging (LAWA) often require manually designed procedures to sample from the…

Machine Learning · Computer Science 2025-02-17 Peng Wang , Shengchao Hu , Zerui Tao , Guoxia Wang , Dianhai Yu , Li Shen , Quan Zheng , Dacheng Tao

In this study, we introduce a sensitivity analysis methodology for stochastic systems in chemistry, where dynamics are often governed by random processes. Our approach is based on gradient estimation via finite differences, averaging…

Quantitative Methods · Quantitative Biology 2026-01-12 Erika M. Herrera Machado , Jakob L. Andersen , Rolf Fagerberg , Daniel Merkle

In this paper, we provide a multiscale perspective on the problem of maximum marginal likelihood estimation. We consider and analyse a diffusion-based maximum marginal likelihood estimation scheme using ideas from multiscale dynamics. Our…

Computation · Statistics 2024-06-11 O. Deniz Akyildiz , Michela Ottobre , Iain Souttar

This paper is concerned with optimizing the global minimum-variance portfolio's (GMVP) weights in high-dimensional settings where both observation and population dimensions grow at a bounded ratio. Optimizing the GMVP weights is highly…

Signal Processing · Electrical Eng. & Systems 2022-04-13 Maaz Mahadi , Tarig Ballal , Muhammad Moinuddin , Tareq Y. Al-Naffouri , Ubaid Al-Saggaf

The weighted ensemble (WE) simulation strategy provides unbiased sampling of non-equilibrium processes, such as molecular folding or binding, but the extraction of rate constants relies on characterizing steady state behavior.…

Statistical Mechanics · Physics 2020-10-02 Jeremy Copperman , Daniel Zuckerman

We describe an adaptive Markov chain Monte Carlo method suitable for the estimation of rare failure probabilities in complex probabilistic models. This method, the Accelerated Weight Histogram (AWH) method, has its origin in statistical…

Computation · Statistics 2022-10-27 Jack Lidmar , Johan Spross , John Leander

Gaussian graphical models can capture complex dependency structures among variables. For such models, Bayesian inference is attractive as it provides principled ways to incorporate prior information and to quantify uncertainty through the…

Computation · Statistics 2023-04-05 Willem van den Boom , Alexandros Beskos , Maria De Iorio

Markov Chain Monte Carlo (MCMC) is one of the most powerful methods to sample from a given probability distribution, of which the Metropolis Adjusted Langevin Algorithm (MALA) is a variant wherein the gradient of the distribution is used…

Applications · Statistics 2022-01-21 Mariya Mamajiwala , Debasish Roy , Serge Guillas

The stochastic volatility model is a popular tool for modeling the volatility of assets. The model is a nonlinear and non-Gaussian state space model, and consequently is difficult to fit. Many approaches, both classical and Bayesian, have…

Methodology · Statistics 2019-07-22 Chen Gong , David S. Stoffer

In this paper we perform Bayesian estimation of stochastic volatility models with heavy tail distributions using Metropolis adjusted Langevin (MALA) and Riemman manifold Langevin (MMALA) methods. We provide analytical expressions for the…

Computation · Statistics 2015-07-20 Mauricio Zevallos , Loretta Gasco , Ricardo Ehlers

Macroscopic dynamical descriptions of complex physical systems are crucial for understanding and controlling material behavior. With the growing availability of data and compute, machine learning has become a promising alternative to…

Computational Physics · Physics 2026-03-24 Mengyi Chen , Pengru Huang , Kostya S. Novoselov , Qianxiao Li

Markov jump processes (MJPs) are continuous-time stochastic processes widely used in a variety of applied disciplines. Inference for MJPs typically proceeds via Markov chain Monte Carlo, the state-of-the-art being a uniformization-based…

Computation · Statistics 2020-04-14 Boqian Zhang , Vinayak Rao
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