Markov Chain Models and Applications: Latest Advances and Prospects

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D1: Probability and Statistics".

Deadline for manuscript submissions: closed (20 March 2025) | Viewed by 1370

Special Issue Editor


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Guest Editor
School of Mathematics and Statistics, University of St Andrews, St. Andrews KY16 9AJ, UK
Interests: statistics

Special Issue Information

Dear Colleagues,

Markov chains are ubiquitous stochastic processes that are of theoretical interest in their own right, but also used within statistical inference procedures and applied to many complex systems across applied sciences.

This Special Issue will host manuscripts pushing the frontiers of discrete and continuous-time Markov chains, covering problems of both theoretical and computational natures. Examples could include manuscripts related to the following themes:

  • Markov chain Monte Carlo methods and diagnostics.
  • Statistical inference and data science for and in Markov chains and processes.
  • Sensitivity and uncertainty analysis in Markov chain networks.
  • Applications of Markov chains to real-life problems, including, but not limited to, systems biology, ecology, epidemiology, and engineering.

Dr. Ben Swallow
Guest Editor

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Keywords

  • Markov chain Monte Carlo methods and diagnostics
  • statistical inference and data science for and in Markov chains and processes
  • sensitivity and uncertainty analysis in Markov chain networks
  • applications of Markov chains to real-life problems, including, but not limited to, systems biology, ecology, epidemiology, and engineering

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Published Papers (1 paper)

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Research

11 pages, 377 KiB  
Article
Confidence Regions for Steady-State Probabilities and Additive Functionals Based on a Single Sample Path of an Ergodic Markov Chain
by Yann Vestring and Javad Tavakoli
Mathematics 2024, 12(23), 3641; https://doi.org/10.3390/math12233641 - 21 Nov 2024
Viewed by 592
Abstract
Discrete, finite-state Markov chains are applied in many different fields. When a system is modeled as a discrete, finite-state Markov chain, the asymptotic properties of the system, such as the steady-state distribution, are often estimated based on a single, empirically observable sample path [...] Read more.
Discrete, finite-state Markov chains are applied in many different fields. When a system is modeled as a discrete, finite-state Markov chain, the asymptotic properties of the system, such as the steady-state distribution, are often estimated based on a single, empirically observable sample path of the system, whereas the actual steady-state distribution is unknown. A question that arises is: how close is the empirically estimated steady-state distribution to the actual steady-state distribution? In this paper, we propose a method to numerically determine asymptotically exact confidence regions for the steady-state probabilities and confidence intervals for additive functionals of an ergodic Markov chain based on a single sample path. Full article
(This article belongs to the Special Issue Markov Chain Models and Applications: Latest Advances and Prospects)
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