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Bayesian statistics with a smile: A resampling-sampling perspective

Hedibert F. Lopes, Nicholas G. Polson and Carlos M. Carvalho
Brazilian Journal of Probability and Statistics
Vol. 26, No. 4, Contributions to the 10th Bayesian Statistics Brazilian Meeting (November 2012), pp. 358-371
Stable URL: http://www.jstor.org/stable/43601224
Page Count: 14
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Bayesian statistics with a smile: A resampling-sampling perspective
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Abstract

In this paper we develop a simulation-based approach to sequential inference in Bayesian statistics. Our resampling-sampling perspective provides draws from posterior distributions of interest by exploiting the sequential nature of Bayes theorem. Predictive inferences are a direct byproduct of our analysis as are marginal likelihoods for model assessment. We illustrate our approach in a hierarchical normal-means model and in a sequential version of Bayesian lasso. This approach provides a simple yet powerful framework for the construction of alternative posterior sampling strategies for a variety of commonly used models.

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