Bayesian Density Regression. Author: David B. Dunson and Natesh Pillai Presenter: Ya Xue April 28, 2006. Outline. Key idea Proof Application to HME. Bayesian Density Regression with Standard DP. The regression model: (i=1,...,n) Two cases:. Parametric model.
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Author: David B. Dunson and Natesh Pillai
Presenter: Ya Xue
April 28, 2006
Standard Dirichlet process mixture model
where is a kernel function.
monotonically as increases.
Equation (1) implies
A mixture of an innovation random measure
and neighboring random measures
j~i indexes samples
if sample i and j belong to the same mixture component.
For example, n=4,
Hence, Eqn. (3) is equivalent to