Optimistic Estimation of Convergence in Markov Chains with the Average-Mixing Time
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910012335456256 |
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| author | Wolfer, Geoffrey Alquier, Pierre |
| author_facet | Wolfer, Geoffrey Alquier, Pierre |
| contents | The convergence rate of a Markov chain to its stationary distribution is typically assessed using the concept of total variation mixing time. However, this worst-case measure often yields pessimistic estimates and is challenging to infer from observations. In this paper, we advocate for the use of the average-mixing time as a more optimistic and demonstrably easier-to-estimate alternative. We further illustrate its applicability across a range of settings, from two-point to countable spaces, and discuss some practical implications. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_10506 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimistic Estimation of Convergence in Markov Chains with the Average-Mixing Time Wolfer, Geoffrey Alquier, Pierre Statistics Theory Probability The convergence rate of a Markov chain to its stationary distribution is typically assessed using the concept of total variation mixing time. However, this worst-case measure often yields pessimistic estimates and is challenging to infer from observations. In this paper, we advocate for the use of the average-mixing time as a more optimistic and demonstrably easier-to-estimate alternative. We further illustrate its applicability across a range of settings, from two-point to countable spaces, and discuss some practical implications. |
| title | Optimistic Estimation of Convergence in Markov Chains with the Average-Mixing Time |
| topic | Statistics Theory Probability |
| url | https://arxiv.org/abs/2402.10506 |