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SUMMARY:New approaches to Bayesian asymptotics - Heather Battey\, Departme
 nt of Economics\, University of Cambridge
DTSTART:20100120T163000Z
DTEND:20100120T180000Z
UID:TALK22435@talks.cam.ac.uk
CONTACT:Richard Samworth
DESCRIPTION:It is now widely agreed that one should assess the performance
  of Bayesian\nestimators of infinite dimensional parameters by the asympto
 tic behaviour of\nthe posterior distribution. A rich literature has develo
 ped over the last 10\nyears\, aimed at establishing weak and easily verifi
 able conditions on the\nprior such that the posterior concentrates almost 
 surely on suitably defined\nneighbourhoods of the true parameter. Establis
 hing tight bounds on the size\nof these shrinking neighbourhoods under var
 ious nonparametric priors has\nalso been a concern. Omitting technical det
 ails\, I will briefly outline the\ndensity estimation problem and the usua
 l sieve constructions that\, together\nwith a well known support condition
 \, provide sufficient conditions for\nstrong consistency of the posterior.
  I will then present alternative\napproaches due to Walker (2004)\, which 
 do not rely on the challenging sieve\nconstructions of previous work\, but
  rather on a simple and elegant\nmartingale argument. I will set the paper
  in the context of subsequent work\,\nhighlighting - among others - the pa
 per of Walker\, Lijoi and Prunster\n(2007)\, which develops one of Walker'
 s arguments in order to improve the\npreviously known convergence rates un
 der two popular priors.\n\nLinks to relevent papers:\n\n"Walker. Ann. Stat
 ist. 32 (2004)\, no. 5\, 2028--2043.":http://www.ams.org/mathscinet/search
 /publdoc.html?pg1=IID&s1=611731&vfpref=html&r=49&mx-pid=2102501\n\n"Walker
  et. al. Ann. Statist. 35 (2007)\, no. 2\, 738--746.":http://www.ams.org/m
 athscinet/search/publdoc.html?pg1=IID&s1=611731&vfpref=html&r=27&mx-pid=23
 36866\n\n"Ghosal and Tang. J. Statist. Plann. Inference 137 (2007)\, no. 6
 \, 1711--1726.":http://www.ams.org/mathscinet/search/publdoc.html?arg3=&co
 4=AND&co5=AND&co6=AND&co7=AND&dr=all&pg4=AUCN&pg5=AUCN&pg6=AUCN&pg7=ALLF&p
 g8=ET&review_format=html&s4=ghosal&s5=tang&s6=&s7=&s8=All&vfpref=html&year
 RangeFirst=&yearRangeSecond=&yrop=eq&r=4&mx-pid=2323858\n
LOCATION:MR5\, CMS
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