This group has mainly worked with mixture models where the mixing distribution is  a normalized completely random measure (e.g. the Dirichlet process, the normalized  generalized gamma process or the Polya trees process), with a focus on computational issues. For a long time, efforts have been  directed to a particular family of algorithms, called “conditional algorithms based on truncation” in the  specialized literature. These algorithms are based on  finite dimensional approximations of the mixing  distribution, so that computations are simplified  (from infinite to finite dimension) while there is no  need for marginalization, so that the statistical analysis is richer (full Bayesian analysis).

 

Nonparametric mixture models have proved to be very powerful for dealing  with clustering problems.   The group also has  worked on this topic, focusing on data which are  grouped into clusters with   non-standard geometrically shapes. One promising application  concerns a  preliminary study on  seismic events extracted from the catalog of parametric CPTI11 Italian earthquakes, aimed at  identifying a methodology that, through the grouping of data, provides a criterion to associate these  events with the seismogenic source that generated them.

Applications in geophysical field have involved some of the researchers of the group; this activity produced results on estimation of the inter-event time distribution.

Besides Kernel ­based spaces are used to formulate algorithms that connect  geometrical aspects and approximation theory.
 
 

 

People:

Raffaele Argiento Carla Brambilla Licia Lenarduzzi Antonio Pievatolo
Renata Rotondi Fabrizio Ruggeri    

 

References:

R. Argiento, I. Bianchini, A. Guglielmi
A blocked Gibbs sampler for NGG-mixture models via a priori truncation Stat. Comput. (2015) Online First

R. Argiento, A. Cremaschi, A. Guglielmi 
A ``Density-Based'' Algorithm for Cluster Analysis Using Species Sampling Gaussian Mixture Models J. Comp. Graph. Stat.  23 (2013) 1126--1142.

Rotondi R.  
Bayesian nonparametric inference for earthquake recurrence time distributions in different tectonic regimes J. Geophys. Res.  115.B1 (2010)

M. Bozzini. L. Lenarduzzi, M. Rossini, R. Schaback,
Interpolation with variably scaled kernels. IMA J. Numer. Anal. 35 (2015) 199-219

 

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