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SUMMARY:Likelihood Inference and Bayesian MCMC - Don Pierce (Oregon State 
 University)
DTSTART:20110506T150000Z
DTEND:20110506T160000Z
UID:TALK30794@talks.cam.ac.uk
CONTACT:Richard Nickl
DESCRIPTION:Much of Bayesian MCMC aims to be “objective” and hence is 
 often strongly related to likelihood inference. A primary distinction betw
 een the two approaches involves whether nuisance parameters are maximized 
 or integrated out of likelihood functions. This distinction has also been 
 of interest in frequentist higher-order likelihood theory. In particular\,
  there are various forms of adjustments to profile likelihood\, aimed at r
 educing undesirable effects of fitting nuisance parameters. These adjustme
 nts are closely related to the distinction between profile likelihood and 
 marginal posterior distributions under diffuse priors. We have explored us
 ing MCMC posterior samples on nuisance parameters to adjust posterior dist
 ributions for approximating profile likelihood\, which differs from using 
 special non-Bayesian MCMC methods to calculate the likelihood. However\, t
 he best of frequentist modified profile likelihoods can improve on the pro
 file\, and we also explore using MCMC to approximate these. This involves 
 representing nuisance parameters orthogonally to interest parameters\, in 
 a sense stronger than usual. These issues seem also related to marginaliza
 tion difficulties in fiducial inference.\n\n\nDonald A. Pierce\, Oregon He
 alth & Science University\nRuggero Bellio\, Udine University\, Italy\n\n\n
 http://www.ohsu.edu/xd/education/schools/school-of-medicine/departments/cl
 inical-departments/public-health/people/pierce.cfm\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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