This project is devoted to the probabilistic and statistical investigation of spherical random fields evolving over time, with a view to applications in Cosmology and Astrostatistics.
In an astrophysical context, the analysis of spherical random fields has been strongly motivated in the last few years by satellite missions producing spherical maps of Cosmic Microwave Background (CMB) radiation. In the very near future, other experiments will produce spherical maps depending also on a "time" parameter, so random fields whose domain is the sphere cross time are going to become of the greatest statistical interest. For instance, the LSST observatory will produce over the next decade more than 1000 temporal images of the celestial sphere. Among our objectives, we mention the development of spherical-temporal wavelets and the investigation of their dependence structure; their application to parametric and nonparametric statistical issues; the characterization of Gaussianity, isotropy and stationarity. We aim also at the implementation of some of these new techniques into realistic experimental settings, so that they might become new tools for effective data analysis in this area.
The importance of the objectives of this project for cosmological and astrophysical applications has already been discussed. In brief, we recall here that the techniques we plan to develop are largely motivated by the following ongoing or future experiments:
Spherical data with a time dependence are expected from several major astrophysical collaborations, the most important of which is the Large Synoptic Survey LSST (see https://www.lsst.org/). Statistical techniques on spherical time dependent data are very much in need for the analysis of the (1000) spherical maps which this observatory is expected to produce in the next ten years.
However, a key feature of this project is its truly interdisciplinary nature. While this astrophysical/cosmological data are the primary motivating rationale for the tools that we aim to develop, it is very important to stress that spherical random fields, possibly evolving over time, emerge very naturally in many different frameworks. In particular, previous contributions by Domenico Marinucci (external PhD supervisor of Alessia Caponera) on spherical random fields have been used/quoted in papers on very diverse fields including climate/atmospheric sciences, geophysics and image analysis, while spherical random fields imaging and testing is now very popular even for brain imaging and related disciplines. Many of the topics we consider in this project, for instance those related to spatio-temporal models, have hence in our view a potential for applications which goes much beyond the cosmological/astrophysical environment.