Bayesian Statistics Seminar
North Carolina State University
presents
A Sampler of Graduate Students
Department of Statistics, NC State University
Sayantan Banerjee: Fast Bayesian Model Assessment for Nonparametric Additive Regression Abstract: The literature is replete with variable selection techniques for the classical linear regression model. It is only relatively recently that authors have begun to explore variable selection in fully nonparametric and additive regression models. In this talk, we consider a Bayesian approach for nonparametric additive regression models. We expand the functions in the additive model in a B-spline basis and put a multivariate Laplace prior on the coefficients. We approximately calculate posterior probability of models defined by selection of predictors in the working model, using a Laplace approximation method, where we expand the prior times the likelihood around the posterior mode. The posterior mode for this prior is the so called group LASSO, for which a fast computing algorithm exists. Thus we completely avoid Markov Chain Monte Carlo or any other time consuming sampling based method, leading to quick assessment of various posterior model probabilities. We apply this technique to the high-dimensional situation where the number of parameters exceeds the number of observations.
(this is a joint work with S. Mckay Curtis and Subhashis Ghoshal)
Laura Boehm: Bridging Conditional and Marginal Inference for Spatially-referenced Binary Data Abstract: Spatially-referenced binary data are common in epidemiology and public health. Owing to its elegant log-odds interpretation of the regression coefficients, a natural model for these data is logistic regression. In the case of spatially correlated binary response, typical modeling choices are Gaussian random effects models, in which coefficients must be interpreted conditionally, or a range of marginally specified models, each with its own drawbacks. Here we propose a new spatial random eff ects distribution through a copula framework which ensures that the regression coefficients maintain the log-odds interpretation both conditional on and marginally over the spatial random eff ects. We present simulations to assess the robustness of our proposition to various random eff ects, and apply it to an interesting dataset assessing periodontal health of Gullah-speaking African Americans. The proposed methodology is flexible enough to handle areal or geo-statistical datasets and hierarchical models with multiple random intercepts.
(this is a joint work with Brian Reich)
Liwei Wang: A Flexible Class of Models for Longitudinal Data Subject to Data Irregularities Abstract: Analysis of longitudinal data within a mixed model framework becomes a challenging task when observations are subject to data irregularities like censoring and missing values. Often finite dimensional (parametric) models are found inadequate to address the complex relationship between the response and predictors. A majority of the currently available models and associated estimation methodologies are
based on restrictive assumptions on the correlation structure of
longitudinal data. To begin with we develop a flexible class of models based on a sequence of Bernstein polynomials with varying degrees and propose a model fitting mechanism assuming fully observed data. Various simulated data scenarios are used to illustrate the superior performance of the proposed estimation methodology. We then extend the estimation methodology to accommodate the data irregularities using a Markov Chain Monte Carlo based approach. The newly proposed models and associated inference methodologies are illustrated using real data
analysis.
(this a joint work with Sujit Ghosh)