{
  "id": "math/0610317",
  "version": "v1",
  "published": "2006-10-10T10:57:12.000Z",
  "updated": "2006-10-10T10:57:12.000Z",
  "title": "On the ergodicity properties of some adaptive MCMC algorithms",
  "authors": [
    "Christophe Andrieu",
    "Éric Moulines"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/105051606000000286 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Applied Probability 2006, Vol. 16, No. 3, 1462-1505",
  "doi": "10.1214/105051606000000286",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we study the ergodicity properties of some adaptive Markov chain Monte Carlo algorithms (MCMC) that have been recently proposed in the literature. We prove that under a set of verifiable conditions, ergodic averages calculated from the output of a so-called adaptive MCMC sampler converge to the required value and can even, under more stringent assumptions, satisfy a central limit theorem. We prove that the conditions required are satisfied for the independent Metropolis--Hastings algorithm and the random walk Metropolis algorithm with symmetric increments. Finally, we propose an application of these results to the case where the proposal distribution of the Metropolis--Hastings update is a mixture of distributions from a curved exponential family.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-10T10:57:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65C05",
      "65C40",
      "60J27",
      "60J35",
      "93E35"
    ],
    "keywords": [
      "adaptive mcmc algorithms",
      "ergodicity properties",
      "markov chain monte carlo algorithms",
      "random walk metropolis algorithm",
      "adaptive markov chain monte carlo"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10317A"
    }
  }
}