Marathon: An Open Source Software Library for the Analysis of Markov-Chain Monte Carlo Algorithms
We present the software library marathon, which is designed to support the analysis of sampling algorithms that are based on the Markov-Chain Monte Carlo principle. The main application of this library is the computation of properties of so-called state graphs, which represent the structure of Marko...
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| Veröffentlicht in: | PloS one 2016-01, Vol.11 (1), p.e0147935-e0147935 |
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| description | We present the software library marathon, which is designed to support the analysis of sampling algorithms that are based on the Markov-Chain Monte Carlo principle. The main application of this library is the computation of properties of so-called state graphs, which represent the structure of Markov chains. We demonstrate applications and the usefulness of marathon by investigating the quality of several bounding methods on four well-known Markov chains for sampling perfect matchings and bipartite graphs. In a set of experiments, we compute the total mixing time and several of its bounds for a large number of input instances. We find that the upper bound gained by the famous canonical path method is often several magnitudes larger than the total mixing time and deteriorates with growing input size. In contrast, the spectral bound is found to be a precise approximation of the total mixing time. |
| doi_str_mv | 10.1371/journal.pone.0147935 |
| format | Article |
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The main application of this library is the computation of properties of so-called state graphs, which represent the structure of Markov chains. We demonstrate applications and the usefulness of marathon by investigating the quality of several bounding methods on four well-known Markov chains for sampling perfect matchings and bipartite graphs. In a set of experiments, we compute the total mixing time and several of its bounds for a large number of input instances. We find that the upper bound gained by the famous canonical path method is often several magnitudes larger than the total mixing time and deteriorates with growing input size. In contrast, the spectral bound is found to be a precise approximation of the total mixing time.</description><identifier>ISSN: 1932-6203</identifier><identifier>EISSN: 1932-6203</identifier><identifier>DOI: 10.1371/journal.pone.0147935</identifier><identifier>PMID: 26824442</identifier><language>eng</language><publisher>United States: Public Library of Science</publisher><subject>Algorithms ; Applied mathematics ; Computer and Information Sciences ; Computer programs ; Computer science ; Computer simulation ; Freeware ; Graphs ; Libraries ; Libraries, Digital ; Marathons ; Markov analysis ; Markov Chains ; Markov processes ; Methods ; Monte Carlo Method ; Monte Carlo methods ; Monte Carlo simulation ; Open source software ; Physical Sciences ; Probability distribution ; Problems ; Research and Analysis Methods ; Sampling ; Software ; Technology application ; Upper bounds</subject><ispartof>PloS one, 2016-01, Vol.11 (1), p.e0147935-e0147935</ispartof><rights>COPYRIGHT 2016 Public Library of Science</rights><rights>2016 Rechner, Berger. 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The main application of this library is the computation of properties of so-called state graphs, which represent the structure of Markov chains. We demonstrate applications and the usefulness of marathon by investigating the quality of several bounding methods on four well-known Markov chains for sampling perfect matchings and bipartite graphs. In a set of experiments, we compute the total mixing time and several of its bounds for a large number of input instances. We find that the upper bound gained by the famous canonical path method is often several magnitudes larger than the total mixing time and deteriorates with growing input size. 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| subjects | Algorithms Applied mathematics Computer and Information Sciences Computer programs Computer science Computer simulation Freeware Graphs Libraries Libraries, Digital Marathons Markov analysis Markov Chains Markov processes Methods Monte Carlo Method Monte Carlo methods Monte Carlo simulation Open source software Physical Sciences Probability distribution Problems Research and Analysis Methods Sampling Software Technology application Upper bounds |
| title | Marathon: An Open Source Software Library for the Analysis of Markov-Chain Monte Carlo Algorithms |
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