May 31, June 7 - 9, 2011

EURANDOM CHAIR

Mini course:

An Invitation to Bayesian Nonparametrics

Subhasis Ghoshal

VENUE 

EURANDOM, Green Room, LG 1.105

May 31, 14.30 - 16.30 h.

June  7, 14.30 - 16.30 h.

June  9, 14.30 - 16.30 h.

SPEAKER

Subhasis Ghoshal - North Carolina State University - USA

Classified Research Topics:

• Nonparametric Bayesian Analysis
• Nonparametric Curve Estimation and Testing
• Bayesian Asymptotics
• Nonregularity
• Default prior
• Limit Theorems in Probability

Homepage

ABSTRACT

Theoretical breakthroughs, computation developments and successful applications in many areas in the recent years have made Bayesian approach to nonparametric problems a popular paradigm of inference.
The short course will discuss methods of construction of priors on infinite dimensional spaces, computational techniques, asymptotic properties of the resulting posterior distribution and applications.

PRESENTATION

Tentative course material:


Examples of nonparametric and semiparametric problems
Prior construction
    Issues
    Methods
    A. Prior on space of functions
        -Random basis expansion
        -Use of link function
        -Gaussian processes
    B. Prior on space of measures
        -Completely random meaasures
        -Levy processes
    C. Prior on space of probability measures
        -Random discrete distributions
        -Stick-breaking
        -Normalized Levy processes
        -Partitioning method
        -Tail-free processes
            Moments, Conjugacy, Full support, Kraft's theorem, zero-one laws
        -Polya trees
            Moments, Conjugacy, Full support, Polya urn scheme, variants
        -Dirichlet processs
    D. Prior on density functions
        -Kernel smoothing
        -Spline or other basis expansions
        -Gaussian processes
       
Dirichlet process
    -Properties (moments, conjugacy, self-similarity, discreteness, support,     convergence, approximation, marginal and conditionals, clustering property, mutual singularity, behavior of tail, distribution of median and mean)
    -Constructions
    -Variants
    -Mixtures of Dirichlet process
    -Dirichlet mixtures process
      Markov chain Monte-Carlo techniques, Variational methods, Choice of kernel
    -Bayesian bootstrap
   
 
Posterior consistency
    -Why consistency matters?
    -Examples of inconsistency
    -Doob's consistency theorem
    -Schwartz theory
      Role of tests, Kullback-Leibler property
    -Density estimation, sieves and the role of entropy
    -Applications using Dirichlet mixtures and Polya trees
    -Non-i.i.d. extensions
   
Convergence rates
    -Rate theorems
    -Applications using log-splines, bracketing and Dirichlet mixtures
    -Non-i.i.d. extensions and examples
    -Convergence rate under misspecification
 
Bayesian adaptation
    -Infinite dimensional normal model
    -Density estimation
    -Adaptation using log-spline
    -Model selection consistency
   
Convergence rate for Gaussian processes
     -Examples of common Gaussian processes
     -Role of RKHS
     -Rate theorems with illustrations
     -Lower bounds
     -Rescaling technique and adaptive estimation

Bernstein-von Mises theorems
     -Nonparametric examples
     -Semiparametric example
     -Failures of Bernstein-von Mises theorem
     -Recent progresses
    
Bayesian Survival analysis
    -Dirichlet process non-conjugacy under censored data
    -Neutral-to-the-right processes
    -Levy processes
      Examples, conjugacy, consistency, Bernstein-von Mises theorem
    -Proportional hazard model
    -Smooth hazard process
   
Complex random structures 
    -Chinese restaurant process
    -Indian buffet process
    -Exchangeable partitions
      Pitman-Yor process, species sampling process
    -Dependent Dirichlet processes
     

Prerequisite:

Familiarity with the basic concepts of mathematical analysis, probability and statistics is required. Some knowledge of measure theory is helpful but not essential. Familiarity with classical nonparametric statistics and parametric Bayesian analysis is desirable, but is not necessary.

PRACTICAL INFORMATION

Conference Location
The workshop location is EURANDOM,  Den Dolech 2, 5612 AZ Eindhoven, Laplace Building, 1st floor, LG 1.105.

EURANDOM is located on the campus of Eindhoven University of Technology, in the 'Laplacegebouw' building' (LG on the map). The university is located at 10 minutes walking distance from Eindhoven railway station (take the exit north side and walk towards the tall building on the right with the sign TU/e).

For all information on how to come to Eindhoven, please check http://www.eurandom.tue.nl/contact.htm

Contact
For more information please contact Mrs. Patty Koorn,
Workshop officer of  EURANDOM

Sponsored by:

Last updated 06-06-11,
by PK