| Autor: |
Chang, Hyunwoong, Zhou, Quan |
| Rok vydání: |
2024 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
Convergence analysis of Markov chain Monte Carlo methods in high-dimensional statistical applications is increasingly recognized. In this paper, we develop general mixing time bounds for Metropolis-Hastings algorithms on discrete spaces by building upon and refining some recent theoretical advancements in Bayesian model selection problems. We establish sufficient conditions for a class of informed Metropolis-Hastings algorithms to attain relaxation times that are independent of the problem dimension. These conditions are grounded in high-dimensional statistical theory and allow for possibly multimodal posterior distributions. We obtain our results through two independent techniques: the multicommodity flow method and single-element drift condition analysis; we find that the latter yields a tighter mixing time bound. Our results and proof techniques are readily applicable to a broad spectrum of statistical problems with discrete parameter spaces. |
| Databáze: |
arXiv |
| Externí odkaz: |
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