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SUMMARY:Optimisation and complexity for Gibbs samplers for hierarchical an
 d crossed-effect models - Gareth Roberts (University of Warwick)
DTSTART:20170705T131500Z
DTEND:20170705T140000Z
UID:TALK73158@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We study the convergence properties of the Gibbs Sampler in th
 e context of Gaussian hierarchical and crossed-effect models. We develop a
  novel methodology based on multi-grid decompositions to derive analytic e
 xpressions for the convergence rates of the algorithm\, extending signific
 antly the class of conditionally Gaussian models amenable to direct analys
 is. In the hierarchical context\, our work gives a rather complete underst
 anding of the Gibbs Sampler behaviour for symmetric models (with arbitrary
  depth)\, while providing approximations and bounds for the non-symmetric 
 cases. The theoretical results give rise to simple and easy-to-implement g
 uidelines to optimise practical implementations of the Gibbs samplers on s
 uch models. While the good performances of the Gibbs Sampler in hierarchic
 ally-structured models is renowned\, the context of crossed-effect models 
 is drastically different. Here hierarchical centering is not possible and 
 the convergence of commonly implemented Gibbs Sampler strategies deteriora
 tes as the data-size increases\, resulting in super-linear computational c
 omplexity (potentially even quadratic) in the number of data-points. We sh
 ow how to leverage the negatively-correlated structure of crossed-effect m
 odels to design easy-to-implement collapsed Gibbs Samplers whose complexit
 y matches the one of hierarchical scenarios.&nbsp\;<br><br>This is joint w
 ork with Giacomo Zanella and Omiros Papaspiliopoulos.  &nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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