EPSRC Reference: 
EP/I026827/1 
Title: 
Projective Limit Techniques and Representation Theorems in Bayesian Nonparametrics 
Principal Investigator: 
Orbanz, Dr P 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Engineering 
Organisation: 
University of Cambridge 
Scheme: 
Postdoc Research Fellowship 
Starts: 
01 May 2011 
Ends: 
30 September 2012 
Value (£): 
289,421

EPSRC Research Topic Classifications: 
Statistics & Appl. Probability 


EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 
Panel Date  Panel Name  Outcome 
15 Feb 2011

PDRF Maths Interview Panel

Announced

01 Feb 2011

PDRF Maths Sift Panel

Announced


Summary on Grant Application Form 
Statistical models provide the mathematical means to make sense of data  to analyze and interpret its contents, and to translate it into decisions and predictions. A recent development is a class of models, called nonparametric Bayesian models in statistics, that are capable both of integrating prior knowledge about the data and of adapting to the complexity of a given data set. My research will contribute to our understanding of the mathematical mechanisms underlying these models, and to our ability to apply them to new problems.My approach builds on two mathematical concepts, projective limits techniques and representation theorems derived from symmetry properties of data. Projective limits are mathematical tools that assemble a complex mathematical object from many simple components. Based on the projective limit tools available in probability theory and other branches of mathematics, I will develop projective limit methods for nonparametric Bayesian models. Such methods will allow us to solve problems involving complex models  studying their mathematical properties, or applying them to data  by solving the corresponding problems for simpler models and reassembling the solutions.A complementary question to the properties and evaluation of a specific model is which model to use for given data  the fundamental question facing every dataanalyst in practice. Representation theorems relate symmetry properties of data to the class of models compatible with these properties. These are deep mathematical results of great practical utility: They translate simple, intuitive properties of data into characterizations of models adequate for such data. The most wellknown example, de Finetti's theorem, has long been a corner stone of Bayesian statistics, but many results have only emerged as recently as the past decade.In my research, I will study (1) the construction and analysis of nonparametric Bayesian models by means of projective limits, (2) the derivation of models from recent results on symmetry principles and representations, and (3) the interplay between these two formalisms.

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Summary 

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Organisation Website: 
http://www.cam.ac.uk 