A Note on Dirichlet Process based Semiparametric Bayesian Models
Authors: Arpita Chatterjee
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Parametric models have been the dominant paradigm for Bayesian inferential works. This is mainly due to its simplicity and straightforward computations. However, given recent computational advances, Semiparametric Bayesian models have become increasingly popular to fit models under flexible distributional assumption. Dirichlet process mixture models form a particular class of Bayesian semiparametric models by assuming a random mixing distribution, taken to be a realization from a Dirichlet process. In this research, we show that even though hierarchical DP models provide flexibility in model fit, they may not perform uniformly better in other aspects as compared to the parametric models. If the DP model gives a better fit, then it should be used regardless of any effect it might have on the power. However, if it results in a reduction in power, then that is just the price of doing a good statistical analysis.