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FUNCTIONAL REGRESSION APPROXIMATE BAYESIAN COMPUTATION FOR GAUSSIAN PROCESS DENSITY ESTIMATION
A novel Bayesian nonparametric method is proposed 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, a hierarchically structured prior, defined over a set of univariate density functions using convenient transformations of Gaussian processes, is introduced. Inference is performed through approximate Bayesian computation (ABC) via a novel functional regression adjustment. The performance of the proposed method is illustrated via simulation studies and an analysis of rural high school exam performance in Brazil.
approximate Bayesian computation; nonparametric density estimation; Gaussian process prior; hierarchical models
Guilherme Souza Rodrigues, Scott Anthony Sisson, David John Nott