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Improving the Gibbs sampler

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Abstract The Gibbs sampler is a simple but very powerful algorithm used to simulate from a complex high‐dimensional distribution. It is particularly useful in Bayesian analysis when a complex Bayesian model involves a number of model parameters and the conditional posterior distribution of each component given the others can be derived as a standard distribution. In the presence of a strong correlation structure among components, however, the Gibbs sampler can be criticized for its slow convergence. Here we discuss several algorithmic strategies such as blocking, collapsing, and partial collapsing that are available for improving the convergence characteristics of the Gibbs sampler. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory Statistical and Graphical Methods of Data Analysis > Sampling
Comparison between Gibbs (top panels), BG (second to top panels), CG/PCG (second to bottom panels), and MH‐within‐PCG (bottom panels) in terms of trace plots (left panels), autocorrelation plots (middle panels), and scatterplots of x1 versus x3 (right panels) after simulating a multimodal joint distribution with Gaussian full conditional distributions
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Contour plots for a multimodal joint distribution with Gaussian full conditional distributions: x1 versus x2 (left), x1 versus x3 (middle), and x2 versus x3 (right)
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Side‐by‐side boxplot of integrated autocorrelation time (IAT) for the comparison of four sampling algorithms constructed for simulating a multimodal joint distribution with Gaussian full conditional distributions. Each algorithm runs multiple chains of 10,000 iterations each with 100 different starting values
[ Normal View | Magnified View ]

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Statistical and Graphical Methods of Data Analysis > Sampling
Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory

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