Marathon: An Open Source Software Library for the Analysis of Markov-Chain Monte Carlo Algorithms

PLoS One. 2016 Jan 29;11(1):e0147935. doi: 10.1371/journal.pone.0147935. eCollection 2016.

Abstract

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.

MeSH terms

  • Algorithms
  • Libraries, Digital
  • Markov Chains*
  • Monte Carlo Method*
  • Software*

Grants and funding

The authors have no support or funding to report.