Related papers: Markov-type state models to describe non-Markovian…
The conformational kinetics of enzymes can be reliably revealed when they are governed by Markovian dynamics. Hidden Markov Models (HMMs) are appropriate especially in the case of conformational states that are hardly distinguishable.…
Leveraging recent work on data-driven methods for constructing a finite state space Markov process from dynamical systems, we address two problems for obtaining further reduced statistical representations. The first problem is to extract…
Transition probability estimation plays a critical role in multi-state modeling, especially in clinical research. This paper investigates the application of semi-Markov and Markov renewal frameworks to the EBMT dataset, focusing on six…
In this paper, we consider statistical estimation of time-inhomogeneous aggregate Markov models. Unaggregated models, which corresponds to Markov chains, are commonly used in multi-state life insurance to model the biometric states of an…
Markov state models (MSMs) are widely employed to analyze the kinetics of complex systems. But despite their effectiveness in many applications, MSMs are prone to systematic or statistical errors, often exacerbated by suboptimal…
Many problems of practical interest rely on Continuous-time Markov chains~(CTMCs) defined over combinatorial state spaces, rendering the computation of transition probabilities, and hence probabilistic inference, difficult or impossible…
Stochastic kinetic models (SKMs) are increasingly used to account for the inherent stochasticity exhibited by interacting populations of species in areas such as epidemiology, population ecology and systems biology. Species numbers are…
Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…
Non-linear state space models are a widely-used class of models for biological, economic, and physical processes. Fitting these models to observed data is a difficult inference problem that has no straightforward solution. We take a…
State-space models (SSM) with Markov switching offer a powerful framework for detecting multiple regimes in time series, analyzing mutual dependence and dynamics within regimes, and asserting transitions between regimes. These models…
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.…
Multistate Markov models are a canonical parametric approach for data modeling of observed or latent stochastic processes supported on a finite state space. Continuous-time Markov processes describe data that are observed irregularly over…
Modeling unknown systems from data is a precursor of system optimization and sequential decision making. In this paper, we focus on learning a Markov model from a single trajectory of states. Suppose that the transition model has a small…
Stochastic models for performance analysis, optimization and control of queues hinge on a multitude of alternatives for input point processes. In case of bursty traffic, one very popular model is the \textit{Markov Modulated Poisson…
Markov state models (MSMs) have been demonstrated to be a powerful method for computationally studying intramolecular processes such as protein folding and macromolecular conformational changes. In this article, we present a new approach to…
This paper studies how to find compact state embeddings from high-dimensional Markov state trajectories, where the transition kernel has a small intrinsic rank. In the spirit of diffusion map, we propose an efficient method for learning a…
Rate processes are often modeled using Markov-State Models (MSM). Suppose you know a prior MSM, and then learn that your prediction of some particular observable rate is wrong. What is the best way to correct the whole MSM? For example,…
In this paper we propose a new method for approximating the nonstationary moment dynamics of one dimensional Markovian birth-death processes. By expanding the transition probabilities of the Markov process in terms of Poisson-Charlier…
Markov state models (MSMs)---or discrete-time master equation models---are a powerful way of modeling the structure and function of molecular systems like proteins. Unfortunately, MSMs with sufficiently many states to make a quantitative…
Spatial multiscale methods have established themselves as useful tools for extending the length scales accessible by conventional statics (i.e., zero temperature molecular dynamics). Recently, extensions of these methods, such as the…