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UID:8724@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20251006T140000
DTEND;TZID=Europe/Paris:20251006T160000
DTSTAMP:20250903T152832Z
URL:https://www.i2m.univ-amu.fr/evenements/paul-gauthier-noe/
SUMMARY:Paul-Gauthier Noé ( Laboratoire d'informatique et systèmes): The 
 distribution of calibrated likelihood functions on the probability-likelih
 ood simplex
DESCRIPTION:Paul-Gauthier Noé: While calibration of probabilistic predicti
 ons has been widely studied\nin the fields of weather forecasting\, biomet
 rics\, statistics\, and\nmachine learning\; this presentation will rather 
 address calibration of\nlikelihood functions. This has been discussed\, es
 pecially in biometrics\,\nin cases with only two exhaustive and mutually e
 xclusive hypotheses (or\nclasses) where likelihood functions can be writte
 n as\nlog-likelihood-ratios (LLRs). After defining calibration for LLRs an
 d\nits connection with the concept of weight-of-evidence (log Bayes\nfacto
 r)\, We will present the idempotence property and how it leads to a\nconst
 raint on their distribution. Especially\, if calibrated LLRs are\nnormally
  distributed under one hypothesis\, they are also normally\ndistributed un
 der the other hypothesis\, with an opposite mean\, and a\nshared variance 
 equal to twice the mean. Although these results have\nbeen known for decad
 es\, they have been limited to the binary case.\n\nIn this presentation\, 
 we will extend these results to cases with more\nthan two hypotheses by us
 ing the Aitchison geometry of the simplex. The\nlatter allows us to recove
 r\, in a vector form\, the additive form of the\nBayes' rule\; extending t
 herefore the concepts of LLR and\nweight-of-evidence to any number of hypo
 theses. Especially\, we will\nextend the definition of calibration\, the i
 dempotence\, and the\nconstraint on the distribution of likelihood functio
 ns to the multiple\nhypotheses and multiclass counterpart of the LLR: the\
 nisometric-log-ratio transformed likelihood function. This work is mainly\
 nconceptual\, but if time permits\, we will see one application of these\n
 results by presenting a non-linear discriminant analysis where the\ndiscri
 minant components form a calibrated likelihood function over the\nclasses\
 , improving therefore the interpretability and the reliability of\nthe met
 hod.
CATEGORIES:Séminaire,Statistique
LOCATION:I2M Saint-Charles - Salle de séminaire\, Université Aix-Marseill
 e\, Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, Franc
 e
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Université Aix-Marseille\,
  Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, France;X
 -APPLE-RADIUS=100;X-TITLE=I2M Saint-Charles - Salle de séminaire:geo:0,0
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