{
  "id": "0809.4178",
  "version": "v2",
  "published": "2008-09-24T13:09:50.000Z",
  "updated": "2009-02-23T09:51:42.000Z",
  "title": "Non-linear regression models for Approximate Bayesian Computation",
  "authors": [
    "M. G. B. Blum",
    "O. Francois"
  ],
  "comment": "4 figures; version 3 minor changes; to appear in Statistics and Computing",
  "journal": "Statistics and Computing, 20: 63-73 (2010)",
  "doi": "10.1007/s11222-009-9116-0",
  "categories": [
    "stat.CO",
    "stat.ML"
  ],
  "abstract": "Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the curse of dimensionality when the number of summary statistics is increased. Here we propose a machine-learning approach to the estimation of the posterior density by introducing two innovations. The new method fits a nonlinear conditional heteroscedastic regression of the parameter on the summary statistics, and then adaptively improves estimation using importance sampling. The new algorithm is compared to the state-of-the-art approximate Bayesian methods, and achieves considerable reduction of the computational burden in two examples of inference in statistical genetics and in a queueing model.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-02-23T09:51:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "approximate bayesian computation",
      "non-linear regression models",
      "summary statistics",
      "nonlinear conditional heteroscedastic regression",
      "state-of-the-art approximate bayesian methods"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.4178B"
    }
  }
}