Abstract
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 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.
Original language | English |
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Pages (from-to) | 4022-4071 |
Number of pages | 50 |
Journal | Annals of Applied Probability |
Volume | 34 |
Issue number | 4 |
DOIs | |
Publication status | Published - 1 Aug 2024 |
Bibliographical note
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