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SUMMARY:General Bayesian updating and model misspecification - Chris Holme
 s\, University of Oxford
DTSTART:20150508T150000Z
DTEND:20150508T160000Z
UID:TALK58611@talks.cam.ac.uk
CONTACT:20082
DESCRIPTION:Bayesian statistics provides a unified approach to the updatin
 g of beliefs but is challenged by modern applications through the formal r
 equirement to define the true sampling distribution\, or joint likelihood\
 , for the whole data generating process regardless of the study objective.
  So even if the task is inference for a low-dimensional statistic Bayesian
  analysis is required to model the complete data distribution and\, moreov
 er\, assume that the model is ``true''. In this talk we present a coherent
  procedure for general Bayesian inference based on the use of loss functio
 ns to connect information in data to parameters of interest. The updating 
 of a prior belief distribution to a posterior then follows from a decision
  theoretic foundation involving cumulative loss functions and a requiremen
 t for coherency. Sensitivity to model misspecification can be characterise
 d via neighbourhoods in model space around the approximating model. Import
 antly\, the procedure coincides with Bayesian updating when a true likelih
 ood is known\, yet provides coherent subjective inference in much more gen
 eral settings. We demonstrate the approach on examples including model-fre
 e general Bayesian co-clustering of time series.\n
LOCATION:MR12\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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