{
  "id": "1902.03321",
  "version": "v1",
  "published": "2019-02-08T23:00:00.000Z",
  "updated": "2019-02-08T23:00:00.000Z",
  "title": "Exchangeable and Sampling Consistent Distributions on Rooted Binary Trees",
  "authors": [
    "Ben Hollering",
    "Seth Sullivant"
  ],
  "comment": "19 pages, 9 figures",
  "categories": [
    "math.CO",
    "math.PR",
    "q-bio.PE"
  ],
  "abstract": "We introduce a notion of finite sampling consistency for phylogenetic trees and show that the set of finitely sampling consistent and exchangeable distributions on n leaf phylogenetic trees is a polytope. We use this polytope to show that the set of all exchangeable and infinite sampling consistent distributions on 4 leaf phylogenetic trees is exactly Aldous' beta-splitting model and give a description of some of the vertices for the polytope of distributions on 5 leaves. We also introduce a new semialgebraic set of exchangeable and sampling consistent models we call the multinomial model and use it to characterize the set of exchangeable and sampling consistent distributions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-08T23:00:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C05",
      "60C05",
      "92B10"
    ],
    "keywords": [
      "rooted binary trees",
      "leaf phylogenetic trees",
      "exchangeable",
      "infinite sampling consistent distributions",
      "multinomial model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}