Statistical learning of random probability measures

The study of random probability measures is a lively research topic that has attracted interest from different fields in recent years. In this thesis, we consider random probability measures in the context of Bayesian nonparametrics, where the law of a random probability measure is used as prior distribution, and in the context of distributional data analysis, where the goal is to perform inference given avsample from the law of a random probability measure. The contributions contained in this thesis can be subdivided according to three different topics: (i) the use of almost surely discrete repulsive random measures (i.e., whose support points are well separated) for Bayesian model-based clustering, (ii) the proposal of new laws for collections of random probability measures for Bayesian density estimation of partially exchangeable data subdivided into different groups, and (iii) the study of principal component analysis and regression models for probability distributions seen as elements of the 2-Wasserstein space. Specifically, for point (i) above we propose an efficient Markov chain Monte Carlo algorithm for posterior inference, which sidesteps the need of split-merge reversible jump moves typically associated with poor performance, we propose a model for clustering high-dimensional data by introducing a novel class of anisotropic determinantal point processes, and study the distributional properties of the repulsive measures, shedding light on important theoretical results which enable more principled prior elicitation and more efficient posterior simulation algorithms. For point (ii) above, we consider several models suitable for clustering homogeneous populations, inducing spatial dependence across groups of data, extracting the characteristic traits common to all the data-groups, and propose a novel vector autoregressive model to study of growth curves of Singaporean kids. Finally, for point (iii), we propose a novel class of projected statistical methods for distributional data analysis for measures on the real line and on the unit-circle.

Micro and Macro essays in Applied Fiscal Policy

This thesis analysis micro and macro aspect of applied fiscal policy issues. The first chapter investigates the extent to which local budget spending composition reacts to fiscal rules variations. I consider the budget of Italian municipalities and exploit specific changes in the Domestic Stability Pact’s rules, to perform a difference-in-discontinuities analysis. The results show that imposing a cap on the total amount of consumption and investment is not as binding as two caps, one for consumption and a different one for investment. More specifically, consumption is triggered by changes in wages and services spending, while investment relies on infrastructure movements. In addition, there is evidence that when an increase in investment is achieved, there is also a higher budget deficit level. The second chapter intends to analyze the extent to which fiscal policy shocks are able to affect macrovariables during business cycle fluctuations, differentiating among three intervention channels: public taxation, consumption and investment. The econometric methodology implemented is a Panel Vector Autoregressive model with a structural characterization. The results show that fiscal shocks have different multipliers in relation to expansion or contraction periods: output does not react during good times while there are significant effects in bad ones. The third chapter evaluates the effects of fiscal policy announcements by the Italian government on the long-term sovereign bond spread of Italy relative to Germany. After collecting data on relevant fiscal policy announcements, we perform an econometric comparative analysis between the three cabinets that followed one another during the period 2009-2013. The results suggest that only fiscal policy announcements made by members of Monti’s cabinet have been effective in influencing significantly the Italian spread in the expected direction, revealing a remarkable credibility gap between Berlusconi’s and Letta’s governments with respect to Monti’s administration.

Vector meson photoproduction in ultra-peripheral heavy ion collisions with ALICE at the LHC

Ultra-relativistic heavy ions generate strong electromagnetic fields which offer the possibility to study γ-γ and γ-nucleus processes at the LHC in the so called ultra-peripheral collisions (UPC). The photoproduction of J/ψ vector mesons in UPC is sensitive to the gluon distribution of the interacting nuclei. In this thesis the study of coherent and incoherent J/ψ production in Pb-Pb collisions at √sNN = 2.76 TeV is described. The J/ψ has been measured via its leptonic decay in the rapidity range -0.9 < y < 0.9. The cross section for coherent and incoherent J/ψ are given. The results are compared to theoretical models for J/ψ production and the coherent cross section is found to be in good agreement with those models which include nuclear gluon shadowing consistent with EPS09 parametrization. In addition the cross section for the process γ γ→ e+e− has been measured and found to be in agreement with the STARLIGHT Monte Carlo predictions. The analysis has been published by the ALICE Collaboration in the European Physical Journal C, with one of its main plot depicted on the cover-front of the November 2013 issue.