{
  "id": "1611.07809",
  "version": "v1",
  "published": "2016-11-23T14:22:34.000Z",
  "updated": "2016-11-23T14:22:34.000Z",
  "title": "A computable bound of the essential spectral radius of finite range Metropolis--Hastings kernels",
  "authors": [
    "Loïc Hervé",
    "James Ledoux"
  ],
  "journal": "Statistics and Probability Letters, Elsevier, 2016, 117, pp.72-79",
  "doi": "10.1016/j.spl.2016.05.007",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $\\pi$ be a positive continuous target density on $\\mathbb{R}$. Let $P$ be the Metropolis-Hastings operator on the Lebesgue space $\\mathbb{L}^2(\\pi)$ corresponding to a proposal Markov kernel $Q$ on $\\mathbb{R}$. 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 $r\\_{ess}(P)$ of $P$. In this paper a computable bound of $r\\_{ess}(P)$ is obtained under the following assumption on the proposal kernel: $Q$ has a bounded continuous density $q(x,y)$ on $\\mathbb{R}^2$ satisfying the following finite range assumption : $|u| \\textgreater{} s \\, \\Rightarrow\\, q(x,x+u) = 0$ (for some $s\\textgreater{}0$). This result is illustrated with Random Walk Metropolis-Hastings kernels.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-23T14:22:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite range metropolis-hastings kernels",
      "essential spectral radius",
      "computable bound",
      "random walk metropolis-hastings kernels",
      "proposal markov kernel"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}