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PRODID:-//Columba Systems Ltd//NONSGML CPNG/SpringViewer/ICal Output/3.3-
 M3//EN
VERSION:2.0
CALSCALE:GREGORIAN
METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20250312T091411Z
DTSTART:20250319T150000Z
DTEND:20250319T160000Z
SUMMARY:SQUIDS Seminar - Classification of small-ball modes and maximum a
  posteriori estimators on metric spaces
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}g1uh-m85pe5
 v8-4zgeaj
DESCRIPTION:A mode\, or `most likely point'\, for a probability measure $
 \\mu$ can be defined in various ways using the asymptotic behaviour of t
 he $\\mu$-mass of balls of radius $r \\to 0$.  Such points are of intrin
 sic interest in the local theory of measures on metric spaces and also a
 rise naturally in the study of Bayesian inverse problems and diffusion p
 rocesses.  Building upon special cases already proposed in the literatur
 e\, this paper undertakes a systematic study of possible definitions of 
 modes using such small-ball probabilities.  We propose `common-sense' ax
 ioms that such definitions should obey\, e.g.\\ correct handling of disc
 rete and absolutely continuous $\\mu$\, as well as symmetry and invarian
 ce considerations.  We show that there are exactly ten such definitions 
 consistent with these axioms\, and that they are partially but not total
 ly ordered in strength\, forming a complete\, distributive lattice.  We 
 also show how this general system of ten mode types simplifies for well-
 behaved $\\mu$\, e.g.\\ those dominated by a Gaussian measure\, as is co
 mmon in Bayesian inference and diffusion processes.\n \nJoint work with 
 Ilja Klebanov (FU Berlin) and Hefin Lambley (Warwick).\n
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:G.113\, Alan Turing Building\, Manchester
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