{
  "id": "2102.12976",
  "version": "v1",
  "published": "2021-02-24T05:09:41.000Z",
  "updated": "2021-02-24T05:09:41.000Z",
  "title": "A Hybrid Approximation to the Marginal Likelihood",
  "authors": [
    "Eric Chuu",
    "Debdeep Pati",
    "Anirban Bhattacharya"
  ],
  "categories": [
    "stat.CO",
    "stat.ME"
  ],
  "abstract": "Computing the marginal likelihood or evidence is one of the core challenges in Bayesian analysis. While there are many established methods for estimating this quantity, they predominantly rely on using a large number of posterior samples obtained from a Markov Chain Monte Carlo (MCMC) algorithm. As the dimension of the parameter space increases, however, many of these methods become prohibitively slow and potentially inaccurate. In this paper, we propose a novel method in which we use the MCMC samples to learn a high probability partition of the parameter space and then form a deterministic approximation over each of these partition sets. This two-step procedure, which constitutes both a probabilistic and a deterministic component, is termed a Hybrid approximation to the marginal likelihood. We demonstrate its versatility in a plethora of examples with varying dimension and sample size, and we also highlight the Hybrid approximation's effectiveness in situations where there is either a limited number or only approximate MCMC samples available.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-24T05:09:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "marginal likelihood",
      "markov chain monte carlo",
      "approximate mcmc samples",
      "parameter space increases",
      "high probability partition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}