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Estimation of parameters of a diffusion based on discrete time observations poses a difficult problem due to the lack of a closed form expression for the likelihood. From a Bayesian computational perspective it can be casted as a missing…

Computation · Statistics 2017-05-30 Frank van der Meulen , Moritz Schauer

We propose a novel sequential Monte Carlo (SMC) method for sampling from unnormalized target distributions based on a reverse denoising diffusion process. While recent diffusion-based samplers simulate the reverse diffusion using…

Computation · Statistics 2025-11-06 Luhuan Wu , Yi Han , Christian A. Naesseth , John P. Cunningham

This paper introduces a class of Monte Carlo algorithms which are based upon the simulation of a Markov process whose quasi-stationary distribution coincides with a distribution of interest. This differs fundamentally from, say, current…

Methodology · Statistics 2020-04-14 Murray Pollock , Paul Fearnhead , Adam M. Johansen , Gareth O. Roberts

We study a class of stochastic semilinear damped wave equations driven by additive Wiener noise. Owing to the damping term, under appropriate conditions on the nonlinearity, the solution admits a unique invariant distribution. We apply…

Numerical Analysis · Mathematics 2023-06-27 Ziyi Lei , Charles-Edouard Bréhier , Siqing Gan

Conventional approaches for simulating steady-state distributions of particles under diffusive and advective transport at high P\'eclet numbers involve solving the diffusion and advection equations in at least two dimensions. Here, we…

Stochastic differential equations (SDEs) or diffusions are continuous-valued continuous-time stochastic processes widely used in the applied and mathematical sciences. Simulating paths from these processes is usually an intractable problem,…

Computation · Statistics 2020-05-27 Qi Wang , Vinayak Rao , Yee Whye Teh

We propose an unbiased Monte-Carlo estimator for $\mathbb{E}[g(X_{t_1}, \cdots, X_{t_n})]$, where $X$ is a diffusion process defined by a multi-dimensional stochastic differential equation (SDE). The main idea is to start instead from a…

Probability · Mathematics 2016-03-08 Pierre Henry-Labordere , Xiaolu Tan , Nizar Touzi

An indirect, hybrid Monte Carlo discretization of general relativistic kinetic theory suitable for the development of numerical schemes for radiation transport is presented. The discretization is based on surface flux estimators obtained…

Astrophysics · Physics 2012-12-12 Burkhard Zink

We propose a new simple and explicit numerical scheme for time-homogeneous stochastic differential equations. The scheme is based on sampling increments at each time step from a skew-symmetric probability distribution, with the level of…

Probability · Mathematics 2025-07-08 Yuga Iguchi , Samuel Livingstone , Nikolas Nüsken , Giorgos Vasdekis , Rui-Yang Zhang

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

Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…

Computation · Statistics 2021-06-23 Jeremy Heng , Adrian N. Bishop , George Deligiannidis , Arnaud Doucet

A common way to simulate the transport and spread of pollutants in the atmosphere is via stochastic Lagrangian dispersion models. Mathematically, these models describe turbulent transport processes with stochastic differential equations…

We present explicit methods for simulating diffusions whose generator is self-adjoint with respect to a known (but possibly not normalizable) density. These methods exploit this property and combine an optimized Runge-Kutta algorithm with a…

Numerical Analysis · Mathematics 2014-06-27 Nawaf Bou-Rabee , Aleksandar Donev , Eric Vanden-Eijnden

Diffusion models have shown remarkable empirical success in sampling from rich multi-modal distributions. Their inference relies on numerically solving a certain differential equation. This differential equation cannot be solved in closed…

Machine Learning · Computer Science 2026-01-16 Khashayar Gatmiry , Sitan Chen , Adil Salim

Reflected diffusions in convex polyhedral domains arise in a variety of applications, including interacting particle systems, queueing networks, biochemical reaction networks and mathematical finance. Under suitable conditions on the data,…

Probability · Mathematics 2017-05-08 David Lipshutz , Kavita Ramanan

We present a highly efficient proximal Markov chain Monte Carlo methodology to perform Bayesian computation in imaging problems. Similarly to previous proximal Monte Carlo approaches, the proposed method is derived from an approximation of…

Computation · Statistics 2020-03-20 Luis Vargas , Marcelo Pereyra , Konstantinos C. Zygalakis

Recent work incorporating geometric ideas in Markov chain Monte Carlo is reviewed in order to highlight these advances and their possible application in a range of domains beyond Statistics. A full exposition of Markov chains and their use…

Computation · Statistics 2015-06-19 Samuel Livingstone , Mark Girolami

This work is motivated by the need to study the impact of data uncertainties and material imperfections on the solution to optimal control problems constrained by partial differential equations. We consider a pathwise optimal control…

Optimization and Control · Mathematics 2016-03-01 Ahmad Ahmad Ali , Elisabeth Ullmann , Michael Hinze

We present an explicit method for simulating stochastic differential equations (SDEs) that have variable diffusion coefficients and satisfy the detailed balance condition with respect to a known equilibrium density. In Tupper and Yang…

Numerical Analysis · Mathematics 2014-06-27 Paul Tupper , Xin Yang

A diffusion Monte Carlo algorithm is introduced that can determine the correct nodal structure of the wave function of a few-fermion system and its ground-state energy without an uncontrolled bias. This is achieved by confining signed…

Computational Physics · Physics 2020-02-05 Alexander A. Kunitsa , So Hirata