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Piecewise-deterministic Markov processes combine continuous in time dynamics with jump events, the rates of which generally depend on the continuous variables and thus are not constants. This leads to a problem in a Monte-Carlo simulation…

Computational Physics · Physics 2025-01-14 Arkady Pikovsky

Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past…

Methodology · Statistics 2023-02-03 Nicholas W. Barendregt , Emily G. Webb , Zachary P. Kilpatrick

We consider the problem of inferring a latent function in a probabilistic model of data. When dependencies of the latent function are specified by a Gaussian process and the data likelihood is complex, efficient computation often involve…

Machine Learning · Statistics 2018-07-23 Martin Tegner , Benjamin Bloem-Reddy , Stephen Roberts

The goal of this paper is to analyze distributional Markov Decision Processes as a class of control problems in which the objective is to learn policies that steer the distribution of a cumulative reward toward a prescribed target law,…

Optimization and Control · Mathematics 2026-02-09 Nicole Bäuerle , Athanasios Vasileiadis

Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…

Machine Learning · Computer Science 2021-09-30 Lukas Köhs , Bastian Alt , Heinz Koeppl

Markov models are widely used to describe processes of stochastic dynamics. Here, we show that Markov models are a natural consequence of the dynamical principle of Maximum Caliber. First, we show that when there are different possible…

Statistical Mechanics · Physics 2015-05-28 Hao Ge , Steve Presse , Kingshuk Ghosh , Ken Dill

In this paper, we consider a class of stochastic optimal control problems with risk constraints that are expressed as bounded probabilities of failure for particular initial states. We present here a martingale approach that diffuses a risk…

Systems and Control · Computer Science 2015-07-09 Vu Anh Huynh , Leonid Kogan , Emilio Frazzoli

Discrete-state, continuous-time Markov models are becoming commonplace in the modelling of biochemical processes. The mathematical formulations that such models lead to are opaque, and, due to their complexity, are often considered…

Quantitative Methods · Quantitative Biology 2017-10-31 Christopher Lester

The aim of this paper is to approximate a finite-state Markov process by another process with fewer states, called herein the approximating process. The approximation problem is formulated using two different methods. The first method,…

The efficient calculation of rare-event kinetics in complex dynamical systems, such as the rate and pathways of ligand dissociation from a protein, is a generally unsolved problem. Markov state models can systematically integrate ensembles…

Chemical Physics · Physics 2016-02-03 Benjamin Trendelkamp-Schroer , Frank Noe

Rate processes are simple and analytically tractable models for many dynamical systems which switch stochastically between a discrete set of quasi stationary states but they may also approximate continuous processes by coarse grained,…

Statistical Mechanics · Physics 2013-03-11 R. Toenjes , H. Kori

An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…

Statistical Mechanics · Physics 2021-08-04 Piero Olla

Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…

Probability · Mathematics 2021-04-13 Suryadeepto Nag

We present a simulation methodology for Bayesian estimation of rate parameters in Markov jump processes arising for example in stochastic kinetic models. To handle the problem of missing components and measurement errors in observed data,…

Computation · Statistics 2010-09-01 Michael Amrein , Hans R. Kuensch

We study classical stochastic systems with discrete states, coupled to switching external environments. For fast environmental processes we derive reduced dynamics for the system itself, focusing on corrections to the adiabatic limit of…

Statistical Mechanics · Physics 2019-03-27 Peter G. Hufton , Yen Ting Lin , Tobias Galla

Molecular simulations can provide microscopic insight into the physical and chemical driving forces of complex molecular processes. Despite continued advancement of simulation methodology, model errors may lead to inconsistencies between…

Chemical Physics · Physics 2016-02-12 Joseph F. Rudzinski , Kurt Kremer , Tristan Bereau

We develop a new algorithm for the estimation of rare event probabilities associated with the steady-state of a Markov stochastic process with continuous state space $\mathbb R^d$ and discrete time steps (i.e. a discrete-time $\mathbb…

Probability · Mathematics 2019-04-09 Krzysztof Bisewski , Daan Crommelin , Michel Mandjes

A general, variational approach to derive low-order reduced systems for nonlinear systems subject to an autonomous forcing, is introduced. The approach is based on the concept of optimal parameterizing manifold (PM) that substitutes the…

Dynamical Systems · Mathematics 2020-01-08 Mickaël D. Chekroun , Honghu Liu , James C. McWilliams

This paper considers a simulation-based estimator for a general class of Markovian processes and explores some strong consistency properties of the estimator. The estimation problem is defined over a continuum of invariant distributions…

Probability · Mathematics 2010-01-14 Manuel S. Santos

A parameter estimation method is devised for a slow-fast stochastic dynamical system, where often only the slow component is observable. By using the observations only on the slow component, the system parameters are estimated by working on…

Dynamical Systems · Mathematics 2013-03-20 Jian Ren , Jinqiao Duan