[Forum SIS] Seminario Papaspiliopoulos

[Matteo Ruggiero]

**************************************************************
                              CICLO DI SEMINARI
       COLLEGIO CARLO ALBERTO - MONCALIERI (TO)
**************************************************************

Giovedi' 28 ottobre 2010, alle ore 12:00, 
presso la sala rossa del Collegio Carlo Alberto, Moncalieri (TO) (http://www.carloalberto.org)


OMIROS PAPASPILIOPOULOS (Universitat Pompeu Fabra, Barcelona, Spain)
	

terra' un seminario dal titolo


BAYESIAN INFERENCE OF COEFFICIENTS OF DIFFUSION PROCESSES USING DATA AUGMENTATION


Abstract: 
We consider estimation of scalar functions which determine the dynamics of diffusion processes. It is known that nonparametric maximum likelihood is ill-posed in this context. We adopt a probabilistic approach to regularize the problem by the adoption of a prior distribution for the unknown functional. Our first result is that a Bayesian Gaussian conjugate analysis for the drift of one-dimensional diffusions  is feasible given high-frequency data. This is achieved by expressing  the log-likelihood as a quadratic function of the drift, with sufficient statistics given by the so-called local time process and the end points of the observed path. We show how to implement such analysis using flexible and amenable to efficient computations Gaussian Markov process priors. We provide a simple estimator of the local time and a finite element method for the numerical derivation of the posterior mean and precision, as well as the posterior simulation of the unknown functional. We embed  this technology in partially observed situations and adopt a data augmentation approach whereby we iteratively generate missing data paths and draws from the (conditionally) Gaussian posterior distribution of the functional given complete data. Our methodology is applied to estimate the drift of models used in molecular dynamics and financial econometrics using high and low frequency, real and simulated, data. We discuss extensions to other partially observed schemes, connections to other types of non/semi-parametric inference, and to estimation of vector-valued functions.



Tutti gli interessati sono invitati a partecipare. 

Il seminario e' organizzato nell'ambito delle attivita' della "de Castro" Statistics Initiative (http://www.carloalberto.org/stats).
L'elenco dei seminari che si terranno presso il Collegio Carlo Alberto nell'autunno 2010 si trova all'indirizzo http://www.carloalberto.org/stats_seminars.html.

Ulteriori informazioni possono essere richieste all'indirizzo stats at carloalberto.org.

---------
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

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://www.stat.unipg.it/pipermail/sis/attachments/20101020/b6bf85fd/attachment.html>