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Adaptive-modal Bayesian nonparametric regression. (English) Zbl 1335.62051

Summary: We introduce a novel, Bayesian nonparametric, infinite-mixture regression model. The model has unimodal kernel (component) densities, and has covariate-dependent mixture weights that are defined by an infinite ordered-category probits regression. Based on these mixture weights, the regression model predicts a probability density that becomes increasingly unimodal as the explanatory power of the covariate (vector) increases, and increasingly multimodal as this explanatory power decreases, while allowing the explanatory power to vary from one covariate (vector) value to another. The model is illustrated and compared against many other regression models in terms of predictive performance, through the analysis of many real and simulated data sets.

MSC:

62F15 Bayesian inference
62C10 Bayesian problems; characterization of Bayes procedures
62G08 Nonparametric regression and quantile regression
62J12 Generalized linear models (logistic models)
65C60 Computational problems in statistics (MSC2010)
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