BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Statistics
SUMMARY:Nonstandard complete class theorems - Daniel Roy (
University of Toronto)
DTSTART;TZID=Europe/London:20151016T160000
DTEND;TZID=Europe/London:20151016T170000
UID:TALK60698AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/60698
DESCRIPTION:For finite parameter spaces under finite loss\, th
ere is a close link between optimal frequentist de
cision procedures and Bayesian procedures: every B
ayesian procedure derived from a prior with full s
upport is admissible\, and every admissible proced
ure is Bayes. This relationship breaks down as we
move beyond finite parameter spaces. There is a lo
ng line of work relating admissible procedures to
Bayesian ones in more general settings. Under some
regularity conditions\, admissible procedures can
be shown to be the limit of Bayesian procedures.
Under additional regularity\, they are generalized
Bayesian\, i.e.\, they minimize the average loss
with respect to an improper prior. In both these c
ases\, one must venture beyond the strict confines
of Bayesian analysis.\n \nUsing methods from math
ematical logic and nonstandard analysis\, we intro
duce the notion of a hyperfinite statistical decis
ion problem defined on a hyperfinite probability s
pace and study the class of nonstandard Bayesian d
ecision procedures---namely\, those whose average
risk with respect to some prior is within an infin
itesimal of the optimal Bayes risk. We show that
if there is a suitable hyperfinite approximation t
o a standard statistical decision problem\, then e
very admissible decision procedure is nonstandard
Bayes\, and so the nonstandard Bayesian procedures
form a complete class. We give some sufficient re
gularity conditions on standard statistical decisi
on problems that imply the existence of hyperfinit
e approximations\, and conditions such that nonsta
ndard Bayes procedures are in fact Bayes ones.\n\n
Joint work with Haosui (Kevin) Duanmu.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberfo
rce Road\, Cambridge.
CONTACT:Quentin Berthet
END:VEVENT
END:VCALENDAR