Bayesian statistics with a smile: A resampling-sampling perspective

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.