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Improving inference of Gaussian mixtures using auxiliary variables
Author(s) -
Mercatanti Andrea,
Li Fan,
Mealli Fabrizia
Publication year - 2015
Publication title -
statistical analysis and data mining: the asa data science journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.381
H-Index - 33
eISSN - 1932-1872
pISSN - 1932-1864
DOI - 10.1002/sam.11256
Subject(s) - inference , univariate , mixture model , bivariate analysis , context (archaeology) , computer science , outcome (game theory) , multivariate statistics , perspective (graphical) , multivariate normal distribution , range (aeronautics) , mathematics , statistics , machine learning , artificial intelligence , econometrics , paleontology , materials science , mathematical economics , composite material , biology
Abstract Expanding a lower‐dimensional problem to a higher‐dimensional space and then projecting back is often beneficial. This article rigorously investigates this perspective in the context of finite mixture models, specifically how to improve inference for mixture models by using auxiliary variables. Despite the large literature in mixture models and several empirical examples, there is no previous work that gives general theoretical justification for including auxiliary variables in mixture models, even for special cases. We provide a theoretical basis for comparing inference for mixture multivariate models with the corresponding inference for marginal univariate mixture models. Analytical results for several special cases are established. We show that the probability of correctly allocating mixture memberships and the information number for the means of the primary outcome in a bivariate model with two Gaussian mixtures are generally larger than those in each univariate model. Simulations under a range of scenarios, including mis‐specified models, are conducted to examine the improvement. The method is illustrated by two real applications in ecology and causal inference.