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

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  • Hervé, Loïc
  • Ledoux, James

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.

Suggested Citation

  • Hervé, Loïc & Ledoux, James, 2016. "A computable bound of the essential spectral radius of finite range Metropolis–Hastings kernels," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 72-79.
    • Handle: RePEc:eee:stapro:v:117:y:2016:i:c:p:72-79
    DOI: 10.1016/j.spl.2016.05.007
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    References listed on IDEAS

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    1. Hervé, Loïc & Ledoux, James, 2014. "Approximating Markov chains and V-geometric ergodicity via weak perturbation theory," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 613-638.
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