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Spectral gaps of random walk Metropolis chains. (English) Zbl 1167.60345

Summary: We present explicit bounds on the convergence rates of some symmetric random walk Metropolis Markov chains on \(\mathbb R\) with various target distributions. The bounds are obtained from existing and improved decomposition bounds for spectral gaps of Markov chains. The results are significant improvements on existing conductance bounds by S. F. Jarner and W. K. Yuen [Adv. Appl. Probab. 36, No. 1, 243–266 (2004; Zbl 1042.60040)].

MSC:

60J22 Computational methods in Markov chains
60J05 Discrete-time Markov processes on general state spaces
65C05 Monte Carlo methods

Citations:

Zbl 1042.60040
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