English
Related papers

Related papers: Parameter Estimation for Weakly Interacting Hypoel…

200 papers

We consider the problem of inference for nonlinear, multivariate diffusion processes, satisfying It\^o stochastic differential equations (SDEs), using data at discrete times that may be incomplete and subject to measurement error. Our…

Computation · Statistics 2021-09-27 Andrew Golightly , Chris Sherlock

Parameter identification problems in partial differential equations (PDEs) consist in determining one or more functional coefficient in a PDE. In this article, the Bayesian nonparametric approach to such problems is considered. Focusing on…

Statistics Theory · Mathematics 2025-04-24 Matteo Giordano

We present two approximate Bayesian inference methods for parameter estimation in partial differential equation (PDE) models with space-dependent and state-dependent parameters. We demonstrate that these methods provide accurate and…

Methodology · Statistics 2019-09-04 David A. Barajas-Solano , Alexandre M. Tartakovsky

This paper considers the distributed sparse identification problem over wireless sensor networks such that all sensors cooperatively estimate the unknown sparse parameter vector of stochastic dynamic systems by using the local information…

Systems and Control · Electrical Eng. & Systems 2022-03-08 Die Gan , Zhixin Liu

We introduce a model of interacting Random Walk, whose hopping amplitude depends on the number of walkers/particles on the link. The mesoscopic counterpart of such a microscopic dynamics is a diffusing system whose diffusivity depends on…

Statistical Mechanics · Physics 2008-10-01 E. Agliari , M. Casartelli , A. Vezzani

We address the inverse problem of identifying nonlocal interaction potentials in nonlinear aggregation-diffusion equations from noisy discrete trajectory data. Our approach involves formulating and solving a regularized variational problem,…

Analysis of PDEs · Mathematics 2025-01-31 Jose A. Carrillo , Gissell Estrada-Rodriguez , Laszlo Mikolas , Sui Tang

Moderate deviation principles for empirical measure processes associated with weakly interacting Markov processes are established. Two families of models are considered: the first corresponds to a system of interacting diffusions whereas…

Probability · Mathematics 2015-10-09 Amarjit Budhiraja , Ruoyu Wu

Stochastic interacting particle systems are widely used to model collective phenomena across diverse fields, including statistical physics, biology, and social dynamics. The McKean-Vlasov equation arises as the mean-field limit of such…

Computational Physics · Physics 2025-09-17 Zhiqiang Cai , Chengyu Liu , Xiang Zhou

The application of Stochastic Differential Equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we…

Machine Learning · Statistics 2017-08-09 Constantino A. García , Abraham Otero , Paulo Félix , Jesús Presedo , David G. Márquez

For a large class of inhomogeneous interacting particle systems (IPS) on a lattice we develop a rigorous method for mapping them onto homogeneous IPS. Our novel approach provides a direct way of obtaining the statistical properties of such…

Cellular Automata and Lattice Gases · Physics 2007-05-23 Michael Blank

We study large deviation properties of systems of weakly interacting particles modeled by It\^{o} stochastic differential equations (SDEs). It is known under certain conditions that the corresponding sequence of empirical measures…

Probability · Mathematics 2012-09-26 Amarjit Budhiraja , Paul Dupuis , Markus Fischer

We consider numerical approximations of stochastic differential equations by the Euler method. In the case where the SDE is elliptic or hypoelliptic, we show a weak backward error analysis result in the sense that the generator associated…

Numerical Analysis · Mathematics 2011-05-04 Arnaud Debussche , Erwan Faou

We propose communication-efficient distributed estimation and inference methods for the transelliptical graphical model, a semiparametric extension of the elliptical distribution in the high dimensional regime. In detail, the proposed…

Machine Learning · Statistics 2016-12-30 Pan Xu , Lu Tian , Quanquan Gu

Interacting particle systems provide a fundamental framework for modeling collective behavior in biological, social, and physical systems. In many applications, stochastic perturbations are essential for capturing environmental variability…

Adaptation and Self-Organizing Systems · Physics 2026-02-04 Su Yang , Weiqi Chu , Panayotis G. Kevrekidis

Likelihood-based inference in stochastic non-linear dynamical systems, such as those found in chemical reaction networks and biological clock systems, is inherently complex and has largely been limited to small and unrealistically simple…

Computation · Statistics 2024-07-08 Ben Swallow , David A. Rand , Giorgos Minas

In this paper, an alternative approximation to the innovation method is introduced for the parameter estimation of diffusion processes from partial and noisy observations. This is based on a convergent approximation to the first two…

Optimization and Control · Mathematics 2013-12-19 J. C. Jimenez

We propose a data-adaptive probabilistic intensity remapping framework for structure-preserving transformation of grayscale images. The suggested method formulates intensity transformation as a continuous, data-driven remapping process, in…

Quantum Physics · Physics 2026-04-24 Debashis Saikia , Bikash K. Behera , Mayukha Pal , Prasanta K. Panigrahi

We consider the problem of Bayesian estimation of static parameters associated to a partially and discretely observed diffusion process. We assume that the exact transition dynamics of the diffusion process are unavailable, even up-to an…

Computation · Statistics 2023-09-26 Pierre Del Moral , Shulan Hu , Ajay Jasra , Hamza Ruzayqat , Xinyu Wang

Traditional partial differential equations with constant coefficients often struggle to capture abrupt changes in real-world phenomena, leading to the development of variable coefficient PDEs and Markovian switching models. Recently,…

Machine Learning · Statistics 2024-09-02 Yi Zhang , Zhikun Zhang , Xiangjun Wang

This work establishes the weak convergence of Euler-Maruyama's approximation for stochastic differential equations (SDEs) with singular drifts under the integrability condition in lieu of the widely used growth condition. This method is…

Probability · Mathematics 2018-08-23 Jinghai Shao