Beraha, Mario; Griffin, James; (2023) Normalized Latent Measure Factor Models. Journal of the Royal Statistical Society Series B: Statistical Methodology , 85 (4) pp. 1247-1270. 10.1093/jrsssb/qkad062.

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Abstract

We propose a methodology for modelling and comparing probability distributions within a Bayesian nonparametric framework. Building on dependent normalised random measures, we consider a prior distribution for a collection of discrete random measures where each measure is a linear combination of a set of latent measures, interpretable as characteristic traits shared by different distributions, with positive random weights. The model is nonidentified and a method for postprocessing posterior samples to achieve identified inference is developed. This uses Riemannian optimisation to solve a nontrivial optimisation problem over a Lie group of matrices. The effectiveness of our approach is validated on simulated data and in two applications to two real-world data sets: school student test scores and personal incomes in California. Our approach leads to interesting insights for populations and easily interpretable posterior inference.

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