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We study the problem of sampling from strongly log-concave distributions over $\mathbb{R}^d$ using the Poisson midpoint discretization (a variant of the randomized midpoint method) for overdamped/underdamped Langevin dynamics. We prove its…

Probability · Mathematics 2025-10-02 Rishikesh Srinivasan , Dheeraj Nagaraj

We introduce a novel approach for estimating Latent Dirichlet Allocation (LDA) parameters from collapsed Gibbs samples (CGS), by leveraging the full conditional distributions over the latent variable assignments to efficiently average over…

Machine Learning · Statistics 2017-04-12 Yannis Papanikolaou , James R. Foulds , Timothy N. Rubin , Grigorios Tsoumakas

We provide a refined explicit estimate of exponential decay rate of underdamped Langevin dynamics in $L^2$ distance, based on a framework developed in [1]. To achieve this, we first prove a Poincar\'{e}-type inequality with Gibbs measure in…

Analysis of PDEs · Mathematics 2023-08-25 Yu Cao , Jianfeng Lu , Lihan Wang

Discretizations of Langevin diffusions provide a powerful method for sampling and Bayesian inference. However, such discretizations require evaluation of the gradient of the potential function. In several real-world scenarios, obtaining…

Statistics Theory · Mathematics 2021-01-19 Abhishek Roy , Lingqing Shen , Krishnakumar Balasubramanian , Saeed Ghadimi

In this paper we introduce and analyse Langevin samplers that consist of perturbations of the standard underdamped Langevin dynamics. The perturbed dynamics is such that its invariant measure is the same as that of the unperturbed dynamics.…

Probability · Mathematics 2017-12-06 A. B. Duncan , N. Nuesken , G. A. Pavliotis

In this paper the filtering of partially observed diffusions, with discrete-time observations, is considered. It is assumed that only biased approximations of the diffusion can be obtained, for choice of an accuracy parameter indexed by…

Computation · Statistics 2015-10-19 Ajay Jasra , Kengo Kamatani , Kody J. H. Law , Yan Zhou

The inadequate mixing of conventional Markov Chain Monte Carlo (MCMC) methods for multi-modal distributions presents a significant challenge in practical applications such as Bayesian inference and molecular dynamics. Addressing this, we…

Machine Learning · Statistics 2024-05-30 Wenlin Chen , Mingtian Zhang , Brooks Paige , José Miguel Hernández-Lobato , David Barber

Subordinate diffusions are constructed by time changing diffusion processes with an independent L\'{e}vy subordinator. This is a rich family of Markovian jump processes which exhibit a variety of jump behavior and have found many…

Statistics Theory · Mathematics 2017-06-29 Weiwei Guo , Lingfei Li

In this paper approximation methods for infinite-dimensional Levy processes, also called (time-dependent) Levy fields, are introduced. For square integrable fields beyond the Gaussian case, it is no longer given that the one-dimensional…

Probability · Mathematics 2017-12-14 Andrea Barth , Andreas Stein

We develop an efficient sampling method by simulating Langevin dynamics with an artificial force rather than a natural force by using the gradient of the potential energy. The standard technique for sampling following the predetermined…

Statistical Mechanics · Physics 2015-09-30 M. Ohzeki , A. Ichiki

In this article we consider likelihood-based estimation of static parameters for a class of partially observed McKean-Vlasov (POMV) diffusion process with discrete-time observations over a fixed time interval. In particular, using the…

Methodology · Statistics 2024-11-12 Ajay Jasra , Mohamed Maama , Raul Tempone

We consider the problem of approximating the Langevin dynamics of inertial particles being transported by a background flow. In particular, we study an acceleration corrected advection-diffusion approximation to the Langevin dynamics, a…

Probability · Mathematics 2026-02-24 Yoichiro Mori , Chanoknun Sintavanuruk , Truong-Son P. Van

Stochastic differential equations provide a powerful tool for modelling dynamic phenomena affected by random noise. In case of repeated observations of time series for several experimental units, it is often the case that some of the…

Methodology · Statistics 2024-09-06 Fernando Baltazar-Larios , Mogens Bladt , Michael Sørensen

Occupied diffusions offer a Markovian framework for path-dependent dynamics by lifting the state space with a flow of occupation measures. Because this additional feature is infinite-dimensional, the simulation of these processes remains…

Numerical Analysis · Mathematics 2026-04-29 Valentin Tissot-Daguette , Xin Zhang

The random splitting Langevin Monte Carlo could mitigate the first order bias in Langevin Monte Carlo with little extra work compared other high order schemes. We develop in this work an analysis framework for the sampling error under…

Numerical Analysis · Mathematics 2025-10-10 Lei Li , Chen Wang , Mengchao Wang

We introduce a numerical method for Brownian dynamics with position dependent diffusion tensor which is second order accurate for sampling the invariant measure while requiring only one force evaluation per timestep. Analysis of the…

Numerical Analysis · Mathematics 2025-01-09 Eugen Bronasco , Benedict Leimkuhler , Dominic Phillips , Gilles Vilmart

We consider a generic class of log-concave, possibly random, (Gibbs) measures. We prove the concentration of an infinite family of order parameters called multioverlaps. Because they completely parametrise the quenched Gibbs measure of the…

Probability · Mathematics 2022-12-22 Jean Barbier , Dmitry Panchenko , Manuel Sáenz

A canonical algorithm for log-concave sampling is the Langevin Algorithm, aka the Langevin Diffusion run with some discretization stepsize $\eta > 0$. This discretization leads the Langevin Algorithm to have a stationary distribution…

Machine Learning · Statistics 2024-10-22 Jason M. Altschuler , Kunal Talwar

Envelope models provide a sufficient dimension reduction framework for multivariate regression analysis. Bayesian inference for these models has been developed primarily using Markov chain Monte Carlo (MCMC) methods. Specifically, Gibbs…

Methodology · Statistics 2026-03-03 Seunghyeon Kim , Kwangmin Lee , Yeonhee Park

We introduce stochastic models for continuous-time evolution of angles and develop their estimation. We focus on studying Langevin diffusions with stationary distributions equal to well-known distributions from directional statistics, since…