{
  "id": "1909.11626",
  "version": "v1",
  "published": "2019-09-25T17:12:44.000Z",
  "updated": "2019-09-25T17:12:44.000Z",
  "title": "Exact simulation of coupled Wright-Fisher diffusions",
  "authors": [
    "Celia García-Pareja",
    "Henrik Hult",
    "Timo Koski"
  ],
  "comment": "27 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper an exact rejection algorithm for simulating paths of the coupled Wright-Fisher diffusion is introduced. The coupled Wright-Fisher diffusion is a family of multidimensional Wright-Fisher diffusions that have drifts depending on each other through a coupling term and that find applications in the study of interacting genes' networks as those encountered in studies of antibiotic resistance. Our algorithm uses independent neutral Wright-Fisher diffusions as candidate proposals, which can be sampled exactly by means of existing algorithms and are only needed at a finite number of points. Once a candidate is accepted, the remaining of the path can be recovered by sampling from a neutral multivariate Wright-Fisher bridge, for which we also provide an exact sampling strategy. The technique relies on a modification of the alternating series method and extends existing algorithms that are currently available for the one-dimensional case. Finally, the algorithm's complexity is derived and its performance demonstrated in a simulation study.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-25T17:12:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J60",
      "65C30",
      "60H35",
      "65C05"
    ],
    "keywords": [
      "coupled wright-fisher diffusion",
      "exact simulation",
      "neutral multivariate wright-fisher bridge",
      "independent neutral wright-fisher diffusions",
      "exact rejection algorithm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}