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Non-Parametric Bayesian Methods: Empirical Bayes Method, Chinese Restaurant Process, Dirichlet Process, Isotonic Regression(English)

Non-Parametric Bayesian Methods: Empirical Bayes Method, Chinese Restaurant Process, Dirichlet Process, Isotonic Regression(English)

          
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About the Book

Chapters: Empirical Bayes Method, Chinese Restaurant Process, Dirichlet Process, Isotonic Regression, Relevance Vector Machine, Bayesian Additive Regression Kernels, Pitman-yor Process. Source: Wikipedia. Pages: 30. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Empirical Bayes methods are procedures for statistical inference in which the prior distribution is estimated from the data. This approach stands in contrast to standard Bayesian methods, for which the prior distribution is fixed before any data are observed. Despite this difference in perspective, empirical Bayes may be viewed as an approximation to a fully Bayesian treatment of a hierarchical model wherein the parameters at the highest level of the hierarchy are set to their most likely values, instead of being integrated out. Empirical Bayes, also known as maximum marginal likelihood, represents one approach for setting hyperparameters. Empirical Bayes methods can be seen as an approximation to a fully Bayesian treatment of a hierarchical Bayes model. In for example a two-stage hierarchical Bayes model, observed data are assumed to be generated from an unobserved set of parameters, according to a probability distribution . The parameters in turn can be considered samples drawn from a population characterised by further hyperparameters, according to a probability distribution . Information about a particular quantity of interest therefore comes not only from the properties of those data which directly depend on it, but also from the properties of the population of parameters as a whole inferred from the data as a whole, summarised by the hyperparameters . Using Bayes' theorem, (where I is used as a placeholder to indicate "no other information apart from the design of the model"). In general, this integral will not be tractabl...More: http: //booksllc.net/?id=744988


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Product Details
  • ISBN-13: 9781157397786
  • Publisher: Books LLC
  • Publisher Imprint: Books LLC
  • Depth: 6
  • Language: English
  • Series Title: English
  • Sub Title: Empirical Bayes Method, Chinese Restaurant Process, Dirichlet Process, Isotonic Regression
  • Width: 229 mm
  • ISBN-10: 1157397786
  • Publisher Date: 15 Sep 2010
  • Binding: Paperback
  • Height: 152 mm
  • No of Pages: 30
  • Spine Width: 2 mm
  • Weight: 59 gr


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