Statistical identification of Markov chain on trees
type: Item
instance of: scholarly article
title: Statistical identification of Markov chain on trees
zbMATH Open document ID: 1426.60104
DOI: 10.1155/2018/2036248
author: Xiao Zhang
author: Xu-yan Xiang
author: Xiaoyun Mo
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: The theoretical study of continuous-time homogeneous Markov chains is usually based on a natural assumption of a known transition rate matrix (TRM). However, the TRM of a Markov chain in realistic systems might be unknown and might even need to be identified by partially observable data. Thus, an issue on how to identify the TRM of the underlying Markov chain by partially observable information is derived from the great significance in applications. That is what we call the statistical identification of Markov chain. The Markov chain inversion approach has been derived for basic Markov chains by partial observation at few states. In the current letter, a more extensive class of Markov chain on trees is investigated. Firstly, a type of a more operable derivative constraint is developed. Then, it is shown that all Markov chains on trees can be identified only by such derivative constraints of univariate distributions of sojourn time and/or hitting time at a few states. A numerical example is included to demonstrate the correctness of the proposed algorithms.
Mathematics Subject Classification ID: 60J27
Mathematics Subject Classification ID: 60J10
Mathematics Subject Classification ID: 62M05
Mathematics Subject Classification ID: 60J20
zbMATH DE Number: 7018590
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/2036248
OpenAlex ID: W2794873331
cites work: Marked continuous-time Markov chain modelling of burst behaviour for single ion channels
cites work: Q4323296
cites work: Mixtures of exponential distributions
cites work: A canonical representation for aggregated Markov processes
cites work: Utilizing the information content in two-state trajectories
cites work: On aggregated Markov processes
cites work: A second perspective on the Amann–Schmiedl–Seifert criterion for non-equilibrium in a three-state system
cites work: Identifying transition rates of ionic channels via observations at asinglestate
cites work: Identifying transition rates of ionic channels of star-graph branch type
cites work: A Markov chain inversion approach to identify the transition rates of ion channels
cites work: Q3855869
cites work: Q4693718
cites work: Operations of interlaced trees and graceful trees
Wikidata QID: Q130110531
Recommended article: On the link between Markovian trees and tree-structured Markov chains
Recommended article: Markov chains indexed by trees
Recommended article: Q4541869
Recommended article: Q5690363
Recommended article: Q3999923
Recommended article: A Fixed Point Approach to the Classification of Markov Chains with a Tree Structure
Recommended article: Q4496332
Recommended article: Q4998092
description: scientific article; zbMATH DE number 7018590