STA 216 Generalized Linear Models Meets: 2:50-4:05 T/TH (Old Chem 025) Instructor: David Dunson 219A Old Chemistry, Teaching Assistant: Dawn Barnard 112 Old Chemistry,

STA 216 Syllabus  Topics to be covered: GLM Basics: components, exponential family, model fitting, frequent inference: analysis of deviance, stepwise selection, goodness of fit GLM Basics: components, exponential family, model fitting, frequent inference: analysis of deviance, stepwise selection, goodness of fit Bayesian Inference in GLMs (basics): priors, posterior, comparison with frequentist approach, posterior computation, MCMC strategies (Gibbs, Metropolis-Hastings) Bayesian Inference in GLMs (basics): priors, posterior, comparison with frequentist approach, posterior computation, MCMC strategies (Gibbs, Metropolis-Hastings) Binary & categorical response data: Binary & categorical response data: Basics: link functions, form of posterior, approximations, Gibbs sampling via adaptive rejectionBasics: link functions, form of posterior, approximations, Gibbs sampling via adaptive rejection Latent variable models: Threshold formulations, probit models, discrete choice models, logistic regression & generalizations, data augmentation algorithms (Albert & Chib + other forms)Latent variable models: Threshold formulations, probit models, discrete choice models, logistic regression & generalizations, data augmentation algorithms (Albert & Chib + other forms) Count Data : Poisson & over-dispersed Poisson log-linear models, prior distributions, applications Count Data : Poisson & over-dispersed Poisson log-linear models, prior distributions, applications

STA 216 Syllabus  Topics to be covered (continued): Bayesian Variable Selection : problem formulation, mixture priors, stochastic search algorithms, examples, approximations Bayesian Variable Selection : problem formulation, mixture priors, stochastic search algorithms, examples, approximations Bayesian hypothesis testing in GLMs : one- and two-sided alternatives, basic decision theoretic approaches, mixture priors, computation, order restricted inference Bayesian hypothesis testing in GLMs : one- and two-sided alternatives, basic decision theoretic approaches, mixture priors, computation, order restricted inference Survival analysis : censoring definitions, form of likelihood, parametric models, discrete-time & continuous time formulations, proportional hazards, priors for hazard functions, computation Survival analysis : censoring definitions, form of likelihood, parametric models, discrete-time & continuous time formulations, proportional hazards, priors for hazard functions, computation Missing data : problem formulation, selection & pattern mixture models, shared variable approaches, examples Missing data : problem formulation, selection & pattern mixture models, shared variable approaches, examples Multistate & stochastic modeling : motivating examples (epidemiologic studies with periodic observations of a disease process), discrete time approaches, joint models, computation Multistate & stochastic modeling : motivating examples (epidemiologic studies with periodic observations of a disease process), discrete time approaches, joint models, computation

STA 216 Syllabus  Topics to be covered (continued): Correlated data (basics) : mixed models for longitudinal, frequentist alternatives (marginal models, GEEs, etc) Correlated data (basics) : mixed models for longitudinal, frequentist alternatives (marginal models, GEEs, etc) Generalized linear mixed models (GLMM): definition, examples, normal linear case - induced correlation structure, priors, computation, multi-level models, covariance selection Generalized linear mixed models (GLMM): definition, examples, normal linear case - induced correlation structure, priors, computation, multi-level models, covariance selection Generalized additive models : definition, frequentist approaches for inference & computation (Hastie & Tibshirani), Bayesian approaches using basis functions, priors, computation Generalized additive models : definition, frequentist approaches for inference & computation (Hastie & Tibshirani), Bayesian approaches using basis functions, priors, computation Factor analytic models : Underlying normal formulations, mixed discrete & continuous outcomes, generalized factor models, joint models for longitudinal and event time data, covariance selection, model identifiability issues, computation Factor analytic models : Underlying normal formulations, mixed discrete & continuous outcomes, generalized factor models, joint models for longitudinal and event time data, covariance selection, model identifiability issues, computation

 Student Responsibilities: Assignments: Outside reading and problems sets will typically be assigned after each class (10%) Assignments: Outside reading and problems sets will typically be assigned after each class (10%) Mid-term Examination: An in-class closed-book mid term examination will be given (30%) Mid-term Examination: An in-class closed-book mid term examination will be given (30%) Project: Students will be expected to write-up and present results from a data analysis project (30%) Project: Students will be expected to write-up and present results from a data analysis project (30%) Final Examination: The final examination be out of class (30%) Final Examination: The final examination be out of class (30%)

Comments on Computing  Course will have an applied emphasis  Students will be expected to implement frequentist & Bayesian analyses of real and simulated data examples  It is not required that students use a particular computing package  However, emphasis will be given to R/S-PLUS & Matlab, with code sometimes provided