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SUMMARY:Federico Camerlenghi (University of Milano-Bicocca)
DESCRIPTION:14:00 – 15:00 – Federico Camerlenghi (University of Milano-
 Bicocca)\nTitle: Normalized random measures in Bayesian nonparametrics \nA
 bstract: The seminal work of Ferguson (1973)\, who introduced the Dirichle
 t process\, has spurred the definition and investigation of more general c
 lasses of Bayesian nonparametric priors\, with the aim at increasing flexi
 bility while maintaining analytical tractability. Among the numerous gener
 alizations\, a very large class of random probability measures have been i
 ntroduced by Regazzini et al. (2003): this is the class of normalized rand
 om measures with independent increments (NRMIs). NRMIs are random probabil
 ity measures with almost surely discrete realizations\, defined through th
 e specifications of two ingredients: i) a sequence of unnormalized weights
 \, which are the jumps of a Levy process on the positive real line\; ii) a
  sequence of i.i.d. random atoms from a common base measure. The proposed 
 construction is appealing from a mathematical stand- point\, because analy
 tical tractability is preserved\, however NRMIs do not allow interaction a
 mong atoms\, which are supposed to be independent and identically distribu
 ted. In some applied framework\, the i.i.d. assumption could be too restri
 ctive\, for instance\, in model-based clustering\, when they are used as m
 ixing measures in mixture models. To overcome this limitation\, we propose
  a new class of normalized random measures with atoms’ interaction. In o
 ur construction the atoms come from a finite point process\, which is mark
 ed with i.i.d. positive weights. Thus\, a new class of random probability 
 measures is obtained by normalization. The desired interaction among atoms
  is then induced by a suitable choice of the law of the point process\, wh
 ich can create a repulsive or attractive behaviour. By means of Palm calcu
 lus\, we are able to characterize marginal\, predictive and posterior dist
 ributions for the proposed model. We specialize all our results for severa
 l choices of the finite point process\, i.e.\, in the Poisson\, Determinan
 tal\, Gibbs and Shot-Noise Cox case. This talk is based on a joint work wi
 th Raffaele Argiento\, Mario Beraha and Alessandra Guglielmi.\nRefreshment
 s available between 15:00 – 15:30\, Huxley Common Room (HXLY 549)
URL:https://www.imperial.ac.uk/events/170880/federico-camerlenghi-universit
 y-of-milano-bicocca/
DTSTART;TZID=Europe/London:20240209T140000
DTEND;TZID=Europe/London:20240209T150000
LOCATION:BLKT 1004 (10th floor)\, Blackett Building\, South Kensington Camp
 us\, Imperial College London\, London\, SW7 2AZ\, United Kingdom
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