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.
|Raffaele Argiento||Carla Brambilla||Licia Lenarduzzi||Antonio Pievatolo|
|Renata Rotondi||Fabrizio Ruggeri|
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.
Bayesian nonparametric inference for earthquake recurrence time distributions in different tectonic regimes J. Geophys. Res. 115.B1 (2010)