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Activity Number:
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506
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Type:
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Contributed
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Date/Time:
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Thursday, August 10, 2006 : 8:30 AM to 10:20 AM
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Sponsor:
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IMS
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| Abstract - #306624 |
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Title:
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Markov Chain Monte Carlo Approximation of the Posterior in Hierarchical Linear Models
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Author(s):
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Galin Jones*+
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Companies:
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University of Minnesota
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Address:
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224 Church Street, SE, Minneapolis, MN, 55455,
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Keywords:
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Markov chain ; Monte Carlo ; hierarchical model
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Abstract:
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We consider constructing a Monte Carlo-based approximation to the posterior for a general Bayesian hierarchical linear model. In particular, we provide a method of using simulations from the Markov chain to construct a statistical estimate of the posterior from which it is straightforward to sample. We show that this estimate is strongly consistent in the sense that the total variation distance between the estimate and the posterior converges to 0 almost surely as the number of simulations grows. Moreover, we use some recently developed asymptotic results to provide guidance as to how much simulation is necessary. Draws from the estimate can be used to approximate features of the posterior or as intelligent starting values for the original Markov chain.
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- The address information is for the authors that have a + after their name.
- Authors who are presenting talks have a * after their name.
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