Convergence Bounds for Monte Carlo Markov Chains
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912040467038208 |
|---|---|
| author | Qin, Qian |
| author_facet | Qin, Qian |
| contents | This review paper, written for the second edition of the Handbook of Markov Chain Monte Carlo, provides an introduction to the study of convergence analysis for Markov chain Monte Carlo (MCMC), aimed at researchers new to the field. We focus on methods for constructing bounds on the distance between the distribution of a Markov chain at a given time and its stationary distribution. Two widely-used approaches are explored: the coupling method and the L2 theory of Markov chains. For the latter, we emphasize techniques based on conductance and isoperimetric inequalities. Additionally, we briefly discuss strategies for identifying slow convergence in Markov chains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14656 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence Bounds for Monte Carlo Markov Chains Qin, Qian Statistics Theory Probability 60J05 This review paper, written for the second edition of the Handbook of Markov Chain Monte Carlo, provides an introduction to the study of convergence analysis for Markov chain Monte Carlo (MCMC), aimed at researchers new to the field. We focus on methods for constructing bounds on the distance between the distribution of a Markov chain at a given time and its stationary distribution. Two widely-used approaches are explored: the coupling method and the L2 theory of Markov chains. For the latter, we emphasize techniques based on conductance and isoperimetric inequalities. Additionally, we briefly discuss strategies for identifying slow convergence in Markov chains. |
| title | Convergence Bounds for Monte Carlo Markov Chains |
| topic | Statistics Theory Probability 60J05 |
| url | https://arxiv.org/abs/2409.14656 |