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A computable bound of the essential spectral radius of finite range Metropolis–Hastings kernels

Loïc Hervé and James Ledoux

Statistics & Probability Letters, 2016, vol. 117, issue C, 72-79

Abstract: Let π be a positive continuous target density on R. Let P be the Metropolis–Hastings operator on the Lebesgue space L2(π) corresponding to a proposal Markov kernel Q on R. When using the quasi-compactness method to estimate the spectral gap of P, a mandatory first step is to obtain an accurate bound of the essential spectral radius ress(P) of P. In this paper a computable bound of ress(P) is obtained under the following assumption on the proposal kernel: Q has a bounded continuous density q(x,y) on R2 satisfying the following finite range assumption : |u|>s⇒q(x,x+u)=0 (for some s>0). This result is illustrated with Random Walk Metropolis–Hastings kernels.

Keywords: Markov chain operator; Metropolis–Hastings algorithms; Spectral gap (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1016/j.spl.2016.05.007

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