Functional regression approximate Bayesian computation for Gaussian process density estimation

2014/10/30 by G. S. Rodrigues, Rodrigues, G. S., David J. Nott +3
Computer Science · #62G07 #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning and Algorithms

paper · pdf · doi:10.48550/arxiv.1410.8276

openalex publication_date 2014/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Bayesian Density Estimation and Inference Using Mixtures

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