Archive for TU Wien

ulΓimaΓe Pólγa

Posted in Books, pictures, Statistics, Travel with tags , , , , , , , , on July 18, 2023 by xi'an

Last week, Gegor  Zens, Sylvia Frühwirth-Schnatter, and Helga Wagner arXived a revision of their paper on latent Pólya-Gamma random variables for logistic regression models (which I had not read before). The central idea follows from Albert and Chib 1993 paper on a Gibbs sampler for binary and polychotomous data, namely a data augmentation (a.k.a. Gibbs sampling) that is natural as it allows for direct and uncalibrated sampling, but is not necessarily the best choice, since the completion by latent variables is prone to increase computing time and slow down exploration. In addition, since the posterior is close to Normal, a Metropolis scheme based on the MLE asymptotic distribution could perform well, w/o the completion step. As for other latent variable models such as mixtures, I keep wondering how efficiency could be improved by some latent variates not be changing at every iteration, given their almost Dirac (conditional) distribution. Especially in imbalanced cases. The paper proposes several novel mixture representations that lead to  know distributions on the mixing parameter, constructed as in Jun Liu’s and Xiao-Li Meng’s auxiliary scale (or location-scale) completions, but these require an artificial parameter that need be calibrated.