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.
"Bayesian statistics with a smile: A resampling–sampling perspective." Braz. J. Probab. Stat. 26 (4) 358 - 371, November 2012. https://doi.org/10.1214/11-BJPS144