On the wide applicability of Bayesian hierarchical models

This dissertation attempts to gather the main research topics I engaged during the past four years, in collaboration with several national and international researchers from ``La Sapienza'' and other universities. The primary focus is the application of Bayesian hierarchical models to phenomena in several domains such as economics, environmental health, and epidemiology. One common point is the attention to their fast implementation and results' interpretability. Typically, these two main goals are challenging to be simultaneously achieved in the Bayesian setting for two main reasons: on the one hand, the fast implementation of Bayesian machineries requires an oversimplification of the modeling structure, which does not necessarily reflect the complexity of the analyzed phenomenon; on the other hand, if the estimation of complex models is sought, parameters' interpretation may not be straightforward, especially when intricate dependence structures are present. The reader must be aware that all the presented applications with related solutions stemmed from these premises. The first chapter of this dissertation introduces the advantages of adopting the hierarchical paradigm for the model formulation from a conceptual perspective. Following this conceptual introduction, the second chapter delves more into the technical aspects of hierarchical model formulation and estimation. Far from being exhaustive, it provides all the essential ingredients for a thorough understanding of their theoretical foundations and optimal implementation. These first two chapters pave the road for the four original developments presented thereafter. In particular, the third chapter describes a new statistical protocol aiming at variable selection within a Beta regression model for the estimation of food losses percentages at the country-commodity level. The work has been carried out in collaboration with the Food and Agricultural Organization of the United Nations, which started in 2017 for my Master's thesis and led to the recent publication by Mingione et al. (2021a). The fourth chapter includes an extended version of the work developed during my Visiting Research period at the University of California, Los Angeles. It describes a modeling framework for the fast estimation of temporal Gaussian processes in the presence of high-frequency biometrical sampled data. Nowadays, such data are easily collected using new non-invasive wearable devices (e.g., accelerometers) and generate substantial interest in monitoring human activity. The work is currently under review and is available in Alaimo Di Loro et al. (2021a) as a pre-print. The fifth chapter presents two modeling proposals to estimate epidemiological incidence indicators, typically collected during an epidemic for surveillance purposes. The methodology was applied to the Italian publicly available data for the monitoring of the COVID-19 epidemic. Both proposals consider probability distributions coherent with the nature of the data, which are counts, and adopt a generalized logistic function for the parametrization of the mean term. However, the second proposal allows for a latent component accounting for dependence among geographical units. Notice that, in the first work by Alaimo Di Loro et al. (2021b), the inference is pursued under a likelihood-based framework. This work helps highlighting even more the advantages of using a Bayesian approach, as subsequently described by Mingione et al. (2021b). The last chapter summarizes the main points of the dissertation, underlining the most relevant findings, the original contributions, and stressing out how Bayesian hierarchical models altogether yield a cohesive treatment of many issues