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.
In recent work, REF developed a hierarchical Gaussian process prior to model a set of related density functions, where grouped data in the form of samples assumed to be drawn under each density function are available.
Functional regression approximate Bayesian computation for Gaussian process density estimation
arXiv: Computation
Mathematics Computer Science