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SUMMARY:Stable Poisson-Kingman species sampling priors generated by genera
 l ordered size biased generalized gamma mixing distributions  - Prof. Lanc
 elot James (HKUST)
DTSTART:20140508T100000Z
DTEND:20140508T113000Z
UID:TALK52235@talks.cam.ac.uk
CONTACT:Zoubin Ghahramani
DESCRIPTION: Discrete random distribution functions play a central role in
  applications in Bayesian Nonparametrics\, Statistical Machine Learning\, 
 and also in the fields broadly defined as employing Combinatorial Stochast
 ic processes. Arguably the most popular models are the Dirichlet Process a
 nd its two Parameter extension derived from a stable subordinator\, the la
 tter process\nis also known as Pitman-Yor process. \nPerhaps the third mos
 t popular model\, and one which is being used more frequently\, is the  cl
 ass obtained by normalizing a generalized gamma subordinator. The law of a
  generalized gamma random variable is defined by exponentially tilting a s
 table density. \nAs we shall describe\, all models can be considered in a 
 unified way by using the Poisson-Kingman framework applied to a stable sub
 ordinator. This amounts to conditioning on the total mass of a normalized 
 stable process and then mixing over a new distribution of the total mass. 
 \n  The focus of this talk will be based on new classes of models that enc
 ompass the special cases mentioned above. These classes are defined by mix
 ing over random variables based on the expectation of a generalized gamma 
 variable raised to an arbitrary real valued power. \n\nOur results include
  explicit stick-breaking representations derived from a generalized residu
 al allocation scheme for this entire class. Representations in terms of no
 rmalized subordinators. A posterior analysis etc. What is quite interestin
 g is that these results can be seen to arise from mappings that project ra
 ndom variables in a lower ordered class to higher ones. Furthermore this n
 ecessitates randomization of a generalized gamma parameter. If time permit
 s we shall describe how our analysis leads to transparent results related 
 to recent work on species richness estimators.\n  
LOCATION:Engineering Department\, CBL Room BE-438
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