STA 941: Bayesian Nonparametrics
Fall 2018 TTh 11:45 AM-1:00 PM Language 211

Instructor: Surya T Tokdar
Associate Professor, Department of Statistical Science
219A Old Chem Bldg, (919) 684 2152, surya.tokdar AT duke.edu
Office Hour: By Appointment

Grader: Erika Cunningham
Books:
[Recommended] Hjort, Holmes, Müller & Walker. Bayesian Nonparametrics. (Cambridge, Amazon)
[Others] Ghosh & Ramamoorthi. Bayesian Nonparametrics. (Springer, Amazon)
Rasmussen & Williams. Gaussian Processes for Machine Learning. (Book web)
Ghosal & van der Vaart. Fundamentals of Nonparametric Bayesian Inference. (Amazon)
Web:
Yee Whye Teh's npbayes. Peter Orbanz's BNP. Also, The GP Web
Logistics: Read syllabus. Download and install R. Find grades on Sakai.
Assessment: Rolling sets of homework assignment. No exams


Tentative Schedule
8/28 Introduction: overview of classical nonparametrics
8/30 - 9/13 Mixture models: The Dirichlet process prior
  • Ferguson's definition
  • Dirichlet-multinomial conjugacy: infinite version
  • Sethuraman's stick-breaking construction
  • Dirichlet mixture models and posterior computation
  • Applications to random effects modeling
  • 9/18 - 10/02 Smoothing with Gaussian process priors
  • Definitions, properties, RKHS
  • Smoothness, differentiabiilty, non-stationarity
  • Regression models and posterior computation
  • Application to causal inference
  • Approximate computation for large data
  • 10/04 Application to second order stochasticity of neural activity
    10/09 Fall Break: No Class
    10/11 - 10/25 Theoretical properties
  • Doob's consistency theorem and limitations
  • Inconsistency and the role of prior
  • Prior thickness and near compacness
  • Efficient and adaptive function estimation
  • Other theoretical results
  • 10/30 - 11/08 Special models and applications
  • Semiparametric density estimation and extremes
  • Quantile regression
  • Bayesian emulation and optimization
  • 11/13 - 11/15 Partition models based on random trees
    11/20 TBD
    11/22 Thanksgiving Break: No Class
    11/27 - 11/29 Hierarchical learning via clustering
  • Chinese restaurant/franchise models
  • Indian buffet process models
  • Probit stick-breaking process models
  • Applications