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Functional regression approximate Bayesian computation for Gaussian process density estimation
TL;DR: A hierarchically structured prior, defined over a set of univariate density functions using convenient transformations of Gaussian processes, is introduced andference is performed through approximate Bayesian computation (ABC) via a novel functional regression adjustment.
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Abstract: We propose a novel Bayesian nonparametric method for hierarchical modelling on a set of related density functions, where grouped data in the form of samples from each density function are available. Borrowing strength across the groups is a major challenge in this context. To address this problem, we introduce a hierarchically structured prior, defined over a set of univariate density functions, using convenient transformations of Gaussian processes. Inference is performed through approximate Bayesian computation (ABC), via a novel functional regression adjustment. The performance of the proposed method is illustrated via a simulation study and an analysis of rural high school exam performance in Brazil.
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Bayesian Density Estimation and Inference Using Mixtures
Michael Escobar,Mike West +1 more
TL;DR: In this article, the authors describe and illustrate Bayesian inference in models for density estimation using mixtures of Dirichlet processes and show convergence results for a general class of normal mixture models.
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On a Class of Bayesian Nonparametric Estimates: I. Density Estimates
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