An Iterative Monte Carlo Method for Nonconjugate Bayesian Analysis B. P. Carlin and A. E. Gelfand

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An Iterative Monte Carlo Method for Nonconjugate
Bayesian AnalysisB. P. Carlin and A. E. Gelfand 
Statistics and Computing 1991A Generic
Approach to Posterior Integration and Gibbs
Sampling P. Muller Alternatives to the Gibbs
Sampling SchemesP. MullerMetropolized Gibbs
Sampler An Improvement Jun S. Liu

• Presented by Mingyuan Zhou
• Duke University, ECE
• July 25, 2011

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Outline
An Iterative Monte Carlo Method for Nonconjugate
Bayesian AnalysisB. P. Carlin and A. E. Gelfand 
Statistics and Computing 1991

• Introduction
• Gibbs sampler
• Tailored rejection method

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Introduction

• Gibbs sampler (Geman and Geman, 1984 Gelfand and
  Smith, 1990) requires conjugacy
• Sampling under nonconjugacy
• Rejection algorithm
• Tailored general rejection method

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Gibbs sampler

• Random variables
• Conditional densities
• Gibbs sampler provides an iterative Markovian
  updating scheme which enables us to make
  sample-based estimates of the marginal densities
  .
• Gelfand and Smith (1990) show that
• is better than a kernel density estimate for

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Rejection algorithm
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Tailored rejection method

• Split-normal and split-t envelope function

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Split-normal
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Split-t
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Split-normal and Split-t
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Split-normal
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Split-t
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Summary of tailored rejection method
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Summary of tailored rejection method
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Outline
A Generic Approach to Posterior Integration and
Gibbs SamplingP. Muller

• Introduction
• Algorithm
• Applications to Gibbs Sampler
• Examples

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Algorithm
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Implementation
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Implementation

• Initialization
• Candidate generating ,
• Updating mean and covariance
• Accessing convergence
• Posterior inference

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Convergence
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Application to Gibbs Sampler
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Alternatives to the Gibbs Sampling SchemesP.
Muller
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Metropolized Gibbs Sampler An Improvement Jun
S. Liu
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