{
  "id": "1511.07464",
  "version": "v1",
  "published": "2015-11-23T21:16:15.000Z",
  "updated": "2015-11-23T21:16:15.000Z",
  "title": "On the Poisson equation for Metropolis-Hastings chains",
  "authors": [
    "Aleksandar Mijatovic",
    "Jure Vogrinc"
  ],
  "comment": "34 pages, 2 figures",
  "categories": [
    "math.PR",
    "stat.ME"
  ],
  "abstract": "This paper defines an approximation scheme for a solution of the Poisson equation of a geometrically ergodic Metropolis-Hastings chain $\\Phi$. The approximations give rise to a natural sequence of control variates for the ergodic average $S_k(F)=(1/k)\\sum_{i=1}^{k} F(\\Phi_i)$, where $F$ is the force function in the Poisson equation. The main result of the paper shows that the sequence of the asymptotic variances (in the CLTs for the control-variate estimators) converges to zero. We apply the algorithm to geometrically and non-geometrically ergodic chains and present numerical evidence for a significant variance reduction in both cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-23T21:16:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J10",
      "60J22"
    ],
    "keywords": [
      "poisson equation",
      "geometrically ergodic metropolis-hastings chain",
      "significant variance reduction",
      "paper defines",
      "approximation scheme"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151107464M"
    }
  }
}