[Forum SIS] Seminari - Collegio Carlo Alberto

[Matteo Ruggiero]

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		                  CICLO DI SEMINARI
          COLLEGIO CARLO ALBERTO - MONCALIERI (TO)
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Nell'ambito del ciclo di seminari organizzato dalla "de Castro Statistics Initiative" (www.carloalberto.org/stats), 
Giovedi' 3 Marzo 2011, presso la Sala Rossa del Collegio Carlo Alberto, 
via Real Collegio 30, 10024, Moncalieri, Torino,

alle ore 11.00

SINEAD WILLIAMSON  (Cambridge University)

terra' un seminario dal titolo 

"DEPENDENT COMPLETELY RANDOM MEASURES VIA POISSON LINE PROCESSES"


ed alle ore 12.00

PETER ORBANZ  (Cambridge University)

terra' un seminario dal titolo 

"PROJECTIVE LIMIT TECHNIQUES IN BAYESIAN NONPARAMETRICS".


Seguono gli abstracts dei seminari.
Tutti gli interessati sono invitati a partecipare.




Sinead Williamson  (Cambridge University)

Dependent completely random measures via poisson line processes

Over recent years, a number of authors have presented dependent nonparametric processes -- distributions over collections of random measures associated with values in some covariate space. While the properties of these random measures are allowed to vary across the covariate space, the marginal distribution at each covariate value is given by a known nonparametric distribution. Such distributions are useful for modelling data that vary with some covariate: in image segmentation, proximal pixels are likely to be assigned to the same segment; in modelling documents, topics are likely to increase and decrease in popularity over time; in modelling neuron spiking, we may wish to account for waveform drift and neuron appearance and disappearance; in financial time series data, the volatility is likely to change over time.
We consider the class of dependent nonparametric processes whose marginals describe completely random measures -- discrete random measures that assign independent masses to disjoint, measurable subsets, such as the gamma process, the Poisson process and the beta process. In this work, we present a very general framework for defining dependent completely random measures. We provide examples based on beta and gamma processes, with applications in survival analysis and modelling time-varying matrix-valued data.

This is joint work with Peter Orbanz and Zoubin Ghahramani.



Peter Orbanz  (Cambridge University)

Projective limit techniques in bayesian nonparametrics

Bayesian nonparametric models can be regarded as Bayesian models on infinite-dimensional spaces. These infinite-dimensional distributions can be constructed from finite-dimensional ones using the projective limit approach familiar from stochastic process theory. I will discuss how this approach can be generalized considerably by applying the projective limit tools available in pure mathematics both to conditional probabilities and to the various mappings associated with a Bayesian model -- the random variables associated with the model, the model's sufficient statistics, and the mapping to the posterior parameters. This allows us to define a nonparametric Bayesian model from parametric Bayesian equations, and to study its properties in terms of the finite-dimensional models. For example, the nonparametric Bayesian model is conjugate if the parametric models in the construction are conjugate, and the sufficient statistics of theparametric models define a sufficient statistic of the nonparametric Bayesian model. I will briefly discuss for which models these constructions follow a generic recipe, and for which cases we have to expect mathematical complications.


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Matteo Ruggiero
Department of Economics and Quantitative Methods
University of Pavia
Via San Felice 5, 27100, Pavia, Italy
Phone:+39.0382.98.6224
Fax:+39.0382.30.4226
Web:http://economia.unipv.it/ruggiero
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