Data augmentation for non-Gaussian regression models using variance-mean mixtures
نویسندگان
چکیده
We use the theory of normal variance-mean mixtures to derive a data-augmentation scheme that unifies a wide class of statistical models under a single framework. This generalizes existing theory on normal variance mixtures for priors in regression and classification. It also allows variants of the expectation-maximization algorithm to be brought to bear on a much wider range of models than previously appreciated. We demonstate the resulting gains in accuracy and stability on several examples, including sparse quantile regression and binary logistic regression.
منابع مشابه
Sparse Bayes estimation in non-Gaussian models via data augmentation
In this paper we provide a data-augmentation scheme that unifies many common sparse Bayes estimators into a single class. This leads to simple iterative algorithms for estimating the posterior mode under arbitrary combinations of likelihoods and priors within the class. The class itself is quite large: for example, it includes quantile regression, support vector machines, and logistic and multi...
متن کاملDependency Models based on Generalized Gaussian Scale Mixtures and Normal Variance Mean Mixtures
We extend the Gaussian scale mixture model of dependent subspace source densities to include non-radially symmetric densities using Generalized Gaussian random variables linked by a common variance. We also introduce the modeling of skew using the Normal Variance-Mean mixture model. We give closed form expressions for likelihoods and parameter updates in the EM algorithm.
متن کاملBayesian nonparametric regression with varying residual density.
We consider the problem of robust Bayesian inference on the mean regression function allowing the residual density to change flexibly with predictors. The proposed class of models is based on a Gaussian process prior for the mean regression function and mixtures of Gaussians for the collection of residual densities indexed by predictors. Initially considering the homoscedastic case, we propose ...
متن کاملPortfolio performance evaluation in modified mean-variance models
The present study is an attempt toward evaluating the performance of portfolios and assets selecting using modified mean-variance models by utilizing a non-parametric efficiency analysis tool, namely Data Envelopment Analysis (DEA). Huge amounts of money are being invested in financial market. As a result, portfolio performance evaluation has created a great deal of interest among people. We kn...
متن کاملBayesian Analysis of Censored Spatial Data Based on a Non-Gaussian Model
Abstract: In this paper, we suggest using a skew Gaussian-log Gaussian model for the analysis of spatial censored data from a Bayesian point of view. This approach furnishes an extension of the skew log Gaussian model to accommodate to both skewness and heavy tails and also censored data. All of the characteristics mentioned are three pervasive features of spatial data. We utilize data augme...
متن کامل