{
  "id": "2009.12424",
  "version": "v1",
  "published": "2020-09-25T20:29:26.000Z",
  "updated": "2020-09-25T20:29:26.000Z",
  "title": "Skew Brownian Motion and Complexity of the ALPS Algorithm",
  "authors": [
    "Gareth O. Roberts",
    "Jeffrey S. Rosenthal",
    "Nicholas G. Tawn"
  ],
  "categories": [
    "math.PR",
    "stat.CO"
  ],
  "abstract": "Simulated tempering is a popular method of allowing MCMC algorithms to move between modes of a multimodal target density {\\pi}. The paper [24] introduced the Annealed Leap-Point Sampler (ALPS) to allow for rapid movement between modes. In this paper, we prove that, under appropriate assumptions, a suitably scaled version of the ALPS algorithm converges weakly to skew Brownian motion. Our results show that under appropriate assumptions, the ALPS algorithm mixes in time O(d[log(d)]^2 ) or O(d), depending on which version is used.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-25T20:29:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "skew brownian motion",
      "complexity",
      "appropriate assumptions",
      "alps algorithm mixes",
      "alps algorithm converges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}