| Autor: |
Andrieu, Christophe, Lee, Anthony, Power, Sam, Wang, Andi Q. |
| Rok vydání: |
2022 |
| Předmět: |
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| Zdroj: |
Ann. Appl. Probab. 34(4): 4022-4071 (August 2024) |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1214/24-AAP2058 |
| Popis: |
We derive the first explicit bounds for the spectral gap of a random walk Metropolis algorithm on $R^d$ for any value of the proposal variance, which when scaled appropriately recovers the correct $d^{-1}$ dependence on dimension for suitably regular invariant distributions. We also obtain explicit bounds on the ${\rm L}^2$-mixing time for a broad class of models. In obtaining these results, we refine the use of isoperimetric profile inequalities to obtain conductance profile bounds, which also enable the derivation of explicit bounds in a much broader class of models. We also obtain similar results for the preconditioned Crank--Nicolson Markov chain, obtaining dimension-independent bounds under suitable assumptions. |
| Databáze: |
arXiv |
| Externí odkaz: |
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