Advances in statistical methods

A) Composite likelihood methods and statistical computing
In many applications that we  envisage, data are  collected on spatial and/or temporal basis and the dimension of the dataset does not allow one to apply traditional inference techniques.
Recently, a methodological proposal, the composite likelihood, has gained popularity. The method  splits a  inferential problem on a huge dataset in many computational feasible problems on ‘small’ datasets, and finally gives an answer combining the single parts. Moreover, it appears more robust to model misspecification since only model assumptions on small dataset instead of the detailed specification of a model for the full data are required. Finally,  computing time can be drastically reduced  by distributing the operations using parallel computing.

B) Misalignment data and combining incompatible spatial data
Nowadays Global positioning systems and GIS have been widely used to collect and synthesize spatial data from a variety of sources and several different types of data may be collected at differing scales and resolutions, at different spatial locations, and in different dimensions. Moreover, in many cases the data appear noisy hence challenging the statistics in order to integrate  such disparate data.

C) Space-time models and extreme events
We want to suggest  stochastic models for data in a  network of wireless sensors using random field theory. The models should capture the space-time behavior of the underlying phenomenon being observed by the network in the attemp to predict  the size and the spatial distribution of the load. In particular we will consider the case when extreme data  are transmitted in the network.

 

Selected bibliography

  • M. Bevilacqua, C. Gaetan, J. Mateu, E. Porcu: Estimating space and space-time covariance functions: a weighted composite likelihood approach, in J. of the Americal Statistical Association, vol. 107, 2012, pp. 268-280
  • A. Marin, S. Rota Bulò, S. Balsamo: A numerical algorithm for the decomposition of cooperating structured Markov processes in Proc. of IEEE 20th Int. Symp. on Modeling, Analysis and Simulation of Computer and Telecommunication Systems, MASCOTS 2012, Washington DC, USA
  • S. Balsamo, P.G. Harrison, A. Marin: Methodological construction of product-form stochastic Petri nets for performance evaluation, in the J. of Systems and Ssoftware, vol. 85, 2012, pp. 1520-1539
  • A. Marin, S. Balsamo, P.G. Harrison: Analysis of stochastic Petri nets with signals, Performance Evaluation, Volume 69, Issue 11, 2012, pp. 551-572
  • J-N. Bacro J-N., C. Gaetan: A review on spatial extreme modelling in Porcu E., Montero J, Schlather M., Advances and Challenges in Space-time Modelling of Natural Events, in Lecture Notes in Statistics, Berlin Heidelberg, Springer-Verlag, vol. 207, pp. 103-124
  • C. Gaetan, X. Guyon: Spatial Statistics and Modeling, New York, Springer
  • S. Balsamo Queueing Networks with Blocking: Analysis, Solution Algorithms and Properties in D. Kouvatsos, Next Generation Internet, in LNCS, Springer, vol. 5233, pp. 233-257, 2011
  • S. Balsamo, P.G. Harrison, A. Marin: A unifying approach to product-forms in networks with finite capacity constraints in V. Misra, P. Barford, M.S. Squillante Eds, ACM SIGMETRICS 2010, in ACM SIGMETRICS Conferences, New York, ACM, vol. ACM SIGMETRICS
  • F. Braz, S. Orlando, R. Orsini, A. Raffaet√†, A. Roncato, C. Silvestri: Approximate Aggregations in Trajectory Data Warehouses, Proceedings of ICDE Workshop on Spatio-Temporal Data Mining, IEEE Computer Society Press, 2007, pp. 536-545
  • A. Marin, M. G. Vigliotti: Algorithmic product-form approximations of interacting stochastic models, Computers & Mathematics with Applications (to appear)