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Modeling Conditional Densities using Finite Smooth Mixtures
Stockholm University, Faculty of Social Sciences, Department of Statistics.
Stockholm University, Faculty of Social Sciences, Department of Statistics.
2011 (English)In: Mixtures: Estimation and Applications / [ed] Kerrie L. Mengersen, Christian P. Robert, D. Michael Titterington, Chichester: John Wiley & Sons, 2011, , 20 p.123-144 p.Chapter in book (Refereed)
Abstract [en]

Smooth mixtures, i.e. mixture models with covariate-dependent mixing weights,are very useful flexible models for conditional densities. Previous work shows that using toosimple mixture components for modeling heteroscedastic and/or heavy tailed data can givea poor fit, even with a large number of components. This paper explores how well a smoothmixture of symmetric components can capture skewed data. Simulations and applications onreal data show that including covariate-dependent skewness in the components can lead tosubstantially improved performance on skewed data, often using a much smaller number ofcomponents. Furthermore, variable selection is effective in removing unnecessary covariates inthe skewness, which means that there is little loss in allowing for skewness in the componentswhen the data are actually symmetric. We also introduce smooth mixtures of gamma andlog-normal components to model positively-valued response variables.

Place, publisher, year, edition, pages
Chichester: John Wiley & Sons, 2011. , 20 p.123-144 p.
Series
Wiley series in probability and statistics
Keyword [en]
Bayesian inference, Markov chain Monte Carlo, Mixture of Experts, Variable selection
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
URN: urn:nbn:se:su:diva-43078DOI: 10.1002/9781119995678.ch6ISBN: 978-1-119-99389-6 (print)OAI: oai:DiVA.org:su-43078DiVA: diva2:353504
Available from: 2010-11-10 Created: 2010-09-27 Last updated: 2013-05-02Bibliographically approved
In thesis
1. Bayesian Modeling of Conditional Densities
Open this publication in new window or tab >>Bayesian Modeling of Conditional Densities
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis develops models and associated Bayesian inference methods for flexible univariate and multivariate conditional density estimation. The models are flexible in the sense that they can capture widely differing shapes of the data. The estimation methods are specifically designed to achieve flexibility while still avoiding overfitting. The models are flexible both for a given covariate value, but also across covariate space. A key contribution of this thesis is that it provides general approaches of density estimation with highly efficient Markov chain Monte Carlo methods. The methods are illustrated on several challenging non-linear and non-normal datasets.

In the first paper, a general model is proposed for flexibly estimating the density of a continuous response variable conditional on a possibly high-dimensional set of covariates. The model is a finite mixture of asymmetric student-t densities with covariate-dependent mixture weights. The four parameters of the components, the mean, degrees of freedom, scale and skewness, are all modeled as functions of the covariates. The second paper explores how well a smooth mixture of symmetric components can capture skewed data. Simulations and applications on real data show that including covariate-dependent skewness in the components can lead to substantially improved performance on skewed data, often using a much smaller number of components. We also introduce smooth mixtures of gamma and log-normal components to model positively-valued response variables. In the third paper we propose a multivariate Gaussian surface regression model that combines both additive splines and interactive splines, and a highly efficient MCMC algorithm that updates all the multi-dimensional knot locations jointly. We use shrinkage priors to avoid overfitting with different estimated shrinkage factors for the additive and surface part of the model, and also different shrinkage parameters for the different response variables. In the last paper we present a general Bayesian approach for directly modeling dependencies between variables as function of explanatory variables in a flexible copula context. In particular, the Joe-Clayton copula is extended to have covariate-dependent tail dependence and correlations. Posterior inference is carried out using a novel and efficient simulation method. The appendix of the thesis documents the computational implementation details.

Place, publisher, year, edition, pages
Stockholm: Department of Statistics, Stockholm University, 2013. 13 p.
Keyword
Bayesian inference, Density estimation, smooth mixtures, surface regression, copulas, Markov chain Monte Carlo
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:su:diva-89426 (URN)978-91-7447-665-1 (ISBN)
Public defence
2013-06-10, William-Olssonsalen, Geovetenskapens hus, Svante Arrhenius väg 14, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 3: In press. Paper 4: Manuscript.

Available from: 2013-05-16 Created: 2013-04-24 Last updated: 2013-05-06Bibliographically approved

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