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DTSTAMP:20260601T084310Z
DESCRIPTION:Bayesian nonparametric inference for discovery probabilities: c
 redible intervals and large sample asymptotics\n\nThe longstanding problem
  of discovery probabilities dates back to World War II with Alan Turing co
 debreaking the Axis forces Enigma machine at Bletchley Park. The problem c
 an be simply sketched as follows. An experimenter sampling units (say anim
 als) from a population and recording their type (say species) asks: What i
 s the probability that the next sampled animal coincides with a species al
 ready observed a given number of times? or that it is a newly discovered s
 pecies? Applications are not limited to ecology but span bioinformatics\, 
 genetics\, machine learning\, multi-armed bandits\, and so on. In this tal
 k I describe a Bayesian nonparametric (BNP) approach to the problem and co
 mpare it to the original and highly popular estimators known as Good-Turin
 g estimators. More specifically\, I start by recalling some basics about t
 he Dirichlet process which is the cornerstone of the BNP paradigm. Then I 
 present a closed form expression for the posterior distribution of discove
 ry probabilities which naturally leads to simple credible intervals. Next 
 I describe asymptotic approximations of the BNP estimators for large sampl
 e size\, and conclude by illustrating the proposed results through a bench
 mark genomic dataset of Expressed Sequence Tags. Joint work with Stefano F
 avaro (University of Torino)\; Bernardo Nipoti (Trinity College\, Dublin)\
 ; Yee Whye Teh (University of Oxford). Manuscript available at https://arx
 iv.org/abs/1506.04915\n\n\n\n
DTSTART:20170525T180000Z
DTEND:20170525T190000Z
LOCATION:Room PK-5115\, CA\, QC\, Montreal\, UQAM\, Pavillon Kennedy
SUMMARY:Julyan Arbel\, INRIA\, Université Grenoble Alpes\, France
URL:/mathstat/channels/event/julyan-arbel-inria-univer
 site-grenoble-alpes-france-268256
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