Abstract
In this paper, Spike-and-Slab Dirichlet Process (SS-DP) priors are introduced and discussed for non-parametric Bayesian modeling and inference, especially in the mixture models context. Specifying a spike-and-slab base measure for DP priors combines the merits of Dirichlet process and spike-and-slab priors and serves as a flexible approach in Bayesian model selection and averaging. Computationally, Bayesian Expectation-Maximization (BEM) is utilized to obtain MAP estimates. Two simulated examples in mixture modeling and time series analysis contexts demonstrate the models and computational methodology.
Highlights
Dirichlet Process (DP) priors are used across a wide variety of applications of Bayesian analysis, including Bayesian model validation, density estimation and mixture modeling
We propose the use of Spike-and-Slab Dirichlet process (SS-DP) priors, especially in mixture models
We show that Spike-and-Slab Dirichlet Process (SS-DP) mixture models are flexible models allowing both unknown number of components and different component-specific parameter spaces
Summary
Dirichlet Process (DP) priors are used across a wide variety of applications of Bayesian analysis, including Bayesian model validation, density estimation and mixture modeling. If the typical Dirichlet process prior with a continuous base measure G0 is used as the prior for the distribution of parameter , this requires a known parametric model and fixed parameter space In mixture models, we often deal with cases with model uncertainty where the parameter space of one mixture component might be smaller than that of another In these cases, a DP priors with continuous base measure are both theoretically and philosophically not right to use. The use of spike-and-slab distribution combined with Dirichlet process prior has been proposed in multiple hypothesis testing [4,5] This approach is shown to readily accommodate sharp hypothesis, which cannot be tested using regular Dirichlet process with continuous base measure (due to the fact that sharp hypotheses will have zero posterior probability) [6]. We show that SS-DP mixture models are flexible models allowing both unknown number of components and different component-specific parameter spaces
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