Critical Points, Multiple Testing and Point Source Detection for Cosmological Data
Over the last two decades, Cosmology has experienced a sort of revolution, where a flood of data of unprecedented accuracy has become available by means of a number of different ground-based and satellite experiments. The analysis of these maps raises a number of extremely interesting statistical questions, mostly related to the geometry of spherical random fields. In this talk, we shall be concerned in particular with issues related to detection of point sources (Galaxies) in Cosmic Microwave Background radiation (CMB) Data; we shall discuss the connections with spherical wavelets, distribution of critical points for spherical random fields, and multiple testing procedures.
In regression problems, we are interested in some aspects of the distribution of a response variable conditional on a set of predictors, e.g., conditional means, probabilities, or quantiles.
Copulas characterize the dependence of a random vector. In particular, we can use them to model the dependence between a response and predictors. In this talk, I give a brief introduction to copula models, discuss how they can be used in a regression context, and present a some general asymptotic results for inference in such models.