Sparse Probit Linear Mixed Model

Linear Mixed Models (LMMs) are important tools in statistical genetics. When used for feature selection, they allow to find a sparse set of genetic traits that best predict a continuous phenotype of interest, while simultaneously correcting for various confounding factors such as age, ethnicity and population structure. Formulated as models for linear regression, LMMs have been restricted to continuous phenotypes. We introduce the Sparse Probit Linear Mixed Model (Probit-LMM), where we generalize the LMM modeling paradigm to binary phenotypes. As a technical challenge, the model no longer possesses a closed-form likelihood function. In this paper, we present a scalable approximate inference algorithm that lets us fit the model to high-dimensional data sets. We show on three real-world examples from different domains that in the setup of binary labels, our algorithm leads to better prediction accuracies and also selects features which show less correlation with the confounding factors.Comment: Published version, 21 pages, 6 figure

Generalized structured additive regression based on Bayesian P-splines

Generalized additive models (GAM) for modelling nonlinear effects of continuous covariates are now well established tools for the applied statistician. In this paper we develop Bayesian GAM's and extensions to generalized structured additive regression based on one or two dimensional P-splines as the main building block. The approach extends previous work by Lang und Brezger (2003) for Gaussian responses. Inference relies on Markov chain Monte Carlo (MCMC) simulation techniques, and is either based on iteratively weighted least squares (IWLS) proposals or on latent utility representations of (multi)categorical regression models. Our approach covers the most common univariate response distributions, e.g. the Binomial, Poisson or Gamma distribution, as well as multicategorical responses. For the first time, we present Bayesian semiparametric inference for the widely used multinomial logit models. As we will demonstrate through two applications on the forest health status of trees and a space-time analysis of health insurance data, the approach allows realistic modelling of complex problems. We consider the enormous flexibility and extendability of our approach as a main advantage of Bayesian inference based on MCMC techniques compared to more traditional approaches. Software for the methodology presented in the paper is provided within the public domain package BayesX

Non-Gaussian Discriminative Factor Models via the Max-Margin Rank-Likelihood

We consider the problem of discriminative factor analysis for data that are in general non-Gaussian. A Bayesian model based on the ranks of the data is proposed. We first introduce a new {\em max-margin} version of the rank-likelihood. A discriminative factor model is then developed, integrating the max-margin rank-likelihood and (linear) Bayesian support vector machines, which are also built on the max-margin principle. The discriminative factor model is further extended to the {\em nonlinear} case through mixtures of local linear classifiers, via Dirichlet processes. Fully local conjugacy of the model yields efficient inference with both Markov Chain Monte Carlo and variational Bayes approaches. Extensive experiments on benchmark and real data demonstrate superior performance of the proposed model and its potential for applications in computational biology.Comment: 14 pages, 7 figures, ICML 201

Measurement error caused by spatial misalignment in environmental epidemiology

Copyright @ 2009 Gryparis et al - Published by Oxford University Press.In many environmental epidemiology studies, the locations and/or times of exposure measurements and health assessments do not match. In such settings, health effects analyses often use the predictions from an exposure model as a covariate in a regression model. Such exposure predictions contain some measurement error as the predicted values do not equal the true exposures. We provide a framework for spatial measurement error modeling, showing that smoothing induces a Berkson-type measurement error with nondiagonal error structure. From this viewpoint, we review the existing approaches to estimation in a linear regression health model, including direct use of the spatial predictions and exposure simulation, and explore some modified approaches, including Bayesian models and out-of-sample regression calibration, motivated by measurement error principles. We then extend this work to the generalized linear model framework for health outcomes. Based on analytical considerations and simulation results, we compare the performance of all these approaches under several spatial models for exposure. Our comparisons underscore several important points. First, exposure simulation can perform very poorly under certain realistic scenarios. Second, the relative performance of the different methods depends on the nature of the underlying exposure surface. Third, traditional measurement error concepts can help to explain the relative practical performance of the different methods. We apply the methods to data on the association between levels of particulate matter and birth weight in the greater Boston area.This research was supported by NIEHS grants ES012044 (AG, BAC), ES009825 (JS, BAC), ES007142 (CJP), and ES000002 (CJP), and EPA grant R-832416 (JS, BAC)