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Computing the nearest reversible Markov chain

  • Reversible Markov chains are the basis of many applications. However, computing transition probabilities by a finite sampling of a Markov chain can lead to truncation errors. Even if the original Markov chain is reversible, the approximated Markov chain might be non-reversible and will lose important properties, like the real valued spectrum. In this paper, we show how to find the closest reversible Markov chain to a given transition matrix. It turns out that this matrix can be computed by solving a convex minimization problem.

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Metadaten
Author:Adam Nielsen, Marcus Weber
Document Type:Article
Parent Title (English):Numerical Linear Algebra with Applications
Volume:22
Issue:3
First Page:483
Last Page:499
Tag:Convex Optimization; MSM
Reversible Markov Chain
MSC-Classification:15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY
68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area)
Year of first publication:2015
Preprint:urn:nbn:de:0297-zib-53292
DOI:https://doi.org/10.1002/nla.1967