On Choosing Mixture Components via Non-Local Priors
Staff - Faculty of Informatics
Date: / -
USI Lugano Campus, room SI-003, Informatics building (Via G. Buffi 13)
Mark Steel, Warwick University, UK
Choosing the number of mixture components remains an elusive challenge. Model selection criteria can be either overly liberal or conservative and return poorly-separated components of limited practical use. We formalize non-local priors (NLPs) for mixtures and show how they lead to well-separated components with non-negligible weight, interpretable as distinct subpopulations. We also propose an estimator for posterior model probabilities under local and non-local priors, showing that Bayes factors are ratios of posterior to prior empty-cluster probabilities. The estimator is widely applicable and helps set thresholds to drop unoccupied components in over fitted mixtures. We suggest default prior parameters based on multi-modality for Normal/T mixtures and minimal informativeness for categorical outcomes. We characterise theoretically the NLP-induced sparsity, derive tractable expressions and algorithms. We fully develop Normal, Binomial and product Binomial mixtures but the theory, computation and principles hold more generally. We observed a serious lack of sensitivity of the Bayesian information criterion (BIC), insufficient parsimony of the AIC and a local prior, and a mixed behavior of the singular BIC. We also considered overfitted mixtures: their performance was competitive but depended on tuning parameters. Under our default prior elicitation NLPs offered a good compromise between sparsity and power to detect meaningfully-separated components. This is joint work with Jairo Fuquene and David Rossell.
Professor Mark Steel is interested in theoretical and applied Bayesian statistics, particularly distribution theory, Bayesian model averaging, spatial statistics, non- and semiparametric inference, survival models, stochastic frontier models, contingent valuation and stochastic volatility models. Part of his interests stem from his background in economics: he held a Chair in Economics at the University of Edinburgh from 1998-2000. He then moved to a Chair of Statistics at the University of Kent at Canterbury and has joined the University of Warwick in 2003.
He is an Associate Editor of the Journal of Productivity Analysis, Econometrics & Statistics and of the Central European Journal of Economic Modelling and Econometrics. Previously, he was Editor of Bayesian Analysis (2010-2019) and Associate Editor of the Journal of Econometrics (2010-2013), the Journal of the Royal Statistical Society, Series B (2003-2007), the Journal of Business and Economic Statistics (2000-2006) and of Econometric Theory (1994-2005). He has had a variety of roles in the International Society for Bayesian Analysis and in the Royal Statistical Society. He was Head of the Statistics Department at Warwick from September 2014 until September 2018.
Host: Prof. Ernst Wit