STA 216 Generalized Linear Models

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STA 216Generalized Linear Models

• Meets 250-405 T/TH (Old Chem 025)
• Instructor David Dunson
• 221 Old Chemistry, 684-8025
• dunson_at_stat.duke.edu
• Teaching Assistant Eric Vance
• 222 Old Chemistry, 684-8840
• ervance_at_stat.duke.edu

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STA 216 Syllabus

• Topics to be covered
• 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)
• Binary categorical response data
• Basics 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)
• Count Data Poisson over-dispersed Poisson
  log-linear models, prior distributions,
  applications

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STA 216 Syllabus

• Topics to be covered (continued)
• 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
• 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
• Multistate stochastic modeling motivating
  examples (epidemiologic studies with periodic
  observations of a disease process), discrete time
  approaches, joint models, computation

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STA 216 Syllabus

• Topics to be covered (continued)
• 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 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

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• Student Responsibilities
• 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)
• Project Students will be expected to write-up
  and present results from a data analysis project
  (30)
• Final Examination The final examination will
  have both in-class (15) out of class problems
  (15)