Bayesian inference for finite mixtures of univariate and multivariate skew-normal and skew-t distributions

Biostatistics
Sylvia Frühwirth-Schnatter, Saumyadipta Pyne

Abstract

Skew-normal and skew-t distributions have proved to be useful for capturing skewness and kurtosis in data directly without transformation. Recently, finite mixtures of such distributions have been considered as a more general tool for handling heterogeneous data involving asymmetric behaviors across subpopulations. We consider such mixture models for both univariate as well as multivariate data. This allows robust modeling of high-dimensional multimodal and asymmetric data generated by popular biotechnological platforms such as flow cytometry. We develop Bayesian inference based on data augmentation and Markov chain Monte Carlo (MCMC) sampling. In addition to the latent allocations, data augmentation is based on a stochastic representation of the skew-normal distribution in terms of a random-effects model with truncated normal random effects. For finite mixtures of skew normals, this leads to a Gibbs sampling scheme that draws from standard densities only. This MCMC scheme is extended to mixtures of skew-t distributions based on representing the skew-t distribution as a scale mixture of skew normals. As an important application of our new method, we demonstrate how it provides a new computational framework for automated analysi...Continue Reading

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Citations

Aug 21, 2013·Journal of Biopharmaceutical Statistics·Getachew A Dagne
Mar 5, 2011·Bioinformatics·Jangsun Baek, Geoffrey J McLachlan
May 2, 2012·BMC Bioinformatics·Hsiu J HoSaumyadipta Pyne
Oct 23, 2015·Cytometry. Part a : the Journal of the International Society for Analytical Cytology·Sharon X LeeSaumyadipta Pyne
Jan 13, 2016·BMC Bioinformatics·Kerstin JohnssonMagnus Fontes
Feb 24, 2016·Statistics and Computing·Gertraud Malsiner-WalliBettina Grün
Apr 20, 2016·Neural Networks : the Official Journal of the International Neural Network Society·F Chamroukhi
Dec 22, 2017·Cytometry. Part a : the Journal of the International Society for Analytical Cytology·Stefano AmalfitanoAndrea Butturini
Feb 16, 2018·Journal of Biomedical Optics·Tyler BowmanMagda El-Shenawee
Dec 12, 2018·Statistical Methods in Medical Research·Zihang Lu, Wendy Lou
Nov 19, 2011·Statistics in Medicine·Esther Herberich, Torsten Hothorn
Nov 19, 2011·Biometrical Journal. Biometrische Zeitschrift·Donna P AnkerstIan M Thompson
Apr 23, 2019·Advances in Data Analysis and Classification·Sylvia Frühwirth-Schnatter, Gertraud Malsiner-Walli
Mar 30, 2019·Statistics in Medicine·Tao FengWendy J Mack
Jun 20, 2017·Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America·Gertraud Malsiner-WalliBettina Grün

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