{
  "id": "1512.04831",
  "version": "v1",
  "published": "2015-12-15T15:59:56.000Z",
  "updated": "2015-12-15T15:59:56.000Z",
  "title": "Coupling stochastic EM and Approximate Bayesian Computation for parameter inference in state-space models",
  "authors": [
    "Umberto Picchini",
    "Adeline Samson"
  ],
  "comment": "24 pages, 7 figures",
  "categories": [
    "stat.CO",
    "stat.ME"
  ],
  "abstract": "We study the class of state-space models (or hidden Markov models) and perform maximum likelihood inference on the model parameters. We consider a stochastic approximation expectation-maximization (SAEM) algorithm to maximize the likelihood function with the novelty of using approximate Bayesian computation (ABC) within SAEM. The task is to provide each iteration of SAEM with a filtered state of the system and this is achieved using ABC-SMC, that is we used an approximate sequential Monte Carlo (SMC) sampler for the hidden state. Three simulation studies are presented, first a nonlinear Gaussian state-space model then a state-space model having dynamics expressed by a stochastic differential equation, finally a stochastic volatility model. In our examples, ten iterations of our SAEM-ABC-SMC strategy were enough to return sensible parameter estimates. Comparisons with results using SAEM coupled with a standard, non-ABC, SMC sampler show that the ABC algorithm can be calibrated to return accurate solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-15T15:59:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "approximate bayesian computation",
      "coupling stochastic em",
      "parameter inference",
      "approximate sequential monte carlo",
      "perform maximum likelihood inference"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151204831P"
    }
  }
}