UCSC-SOE-21-08: Bayesian Quantile Mixture Regression

Yifei Yan and Athanasios Kottas
06/12/2021 03:21 PM
Quantile regression is widely used to study the relationship between predictors and conditional quantiles of the response variable. We propose semiparametric Bayesian methodology for modeling the conditional response distribution with a weighted mixture of quantile regression components. We specify a common regression coefficient vector for all quantile mixture components in order to synthesize information from multiple parts of the response distribution. Different from simultaneous quantile regression, the goal is to obtain a combined estimate of the predictive effect of each covariate. At the same time, the percentile-structured mixture model allows identification of the most relevant parts of the response distribution through mixture weights associated with different quantiles. We consider two choices of kernel densities for the mixture model, the asymmetric Laplace distribution and the generalized asymmetric Laplace distribution, the latter offering more flexible tail behavior. The mixture weights are developed through increments of a random distribution function, which is modeled with a Dirichlet process prior. Under each kernel density, we formulate the hierarchical structure of the model and develop the posterior simulation method, using Markov chain Monte Carlo. Model performance in prediction and variable selection is studied with both synthetic and real data examples.

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