Multilevel Analysis in Household Survey: An Application to Health Condition Data

The aim of this thesis is to apply multilevel regression model in context of household surveys. Hierarchical structure in this type of data is characterized by many small groups. In last years comparative and multilevel analysis in the field of perceived health have grown in size. The purpose of this thesis is to develop a multilevel analysis with three level of hierarchy for Physical Component Summary outcome to: evaluate magnitude of within and between variance at each level (individual, household and municipality); explore which covariates affect on perceived physical health at each level; compare model-based and design-based approach in order to establish informativeness of sampling design; estimate a quantile regression for hierarchical data. The target population are the Italian residents aged 18 years and older. Our study shows a high degree of homogeneity within level 1 units belonging from the same group, with an intraclass correlation of 27% in a level-2 null model. Almost all variance is explained by level 1 covariates. In fact, in our model the explanatory variables having more impact on the outcome are disability, unable to work, age and chronic diseases (18 pathologies). An additional analysis are performed by using novel procedure of analysis :"Linear Quantile Mixed Model", named "Multilevel Linear Quantile Regression", estimate. This give us the possibility to describe more generally the conditional distribution of the response through the estimation of its quantiles, while accounting for the dependence among the observations. This has represented a great advantage of our models with respect to classic multilevel regression. The median regression with random effects reveals to be more efficient than the mean regression in representation of the outcome central tendency. A more detailed analysis of the conditional distribution of the response on other quantiles highlighted a differential effect of some covariate along the distribution.

Development of new tools and devices for CMB and foreground data analysis and future experiments

The discovery of the Cosmic Microwave Background (CMB) radiation in 1965 is one of the fundamental milestones supporting the Big Bang theory. The CMB is one of the most important source of information in cosmology. The excellent accuracy of the recent CMB data of WMAP and Planck satellites confirmed the validity of the standard cosmological model and set a new challenge for the data analysis processes and their interpretation. In this thesis we deal with several aspects and useful tools of the data analysis. We focus on their optimization in order to have a complete exploitation of the Planck data and contribute to the final published results. The issues investigated are: the change of coordinates of CMB maps using the HEALPix package, the problem of the aliasing effect in the generation of low resolution maps, the comparison of the Angular Power Spectrum (APS) extraction performances of the optimal QML method, implemented in the code called BolPol, and the pseudo-Cl method, implemented in Cromaster. The QML method has been then applied to the Planck data at large angular scales to extract the CMB APS. The same method has been applied also to analyze the TT parity and the Low Variance anomalies in the Planck maps, showing a consistent deviation from the standard cosmological model, the possible origins for this results have been discussed. The Cromaster code instead has been applied to the 408 MHz and 1.42 GHz surveys focusing on the analysis of the APS of selected regions of the synchrotron emission. The new generation of CMB experiments will be dedicated to polarization measurements, for which are necessary high accuracy devices for separating the polarizations. Here a new technology, called Photonic Crystals, is exploited to develop a new polarization splitter device and its performances are compared to the devices used nowadays.

Statistical Analysis and Modelling Aspects of Thermally Driven Turbulence

The present work aims to provide a deeper understanding of thermally driven turbulence and to address some modelling aspects related to the physics of the flow. For this purpose, two idealized systems are investigated by Direct Numerical Simulation: the rotating and non-rotating Rayleigh-Bénard convection. The preliminary study of the flow topologies shows how the coherent structures organise into different patterns depending on the rotation rate. From a statistical perspective, the analysis of the turbulent kinetic energy and temperature variance budgets allows to identify the flow regions where the production, the transport, and the dissipation of turbulent fluctuations occur. To provide a multi-scale description of the flows, a theoretical framework based on the Kolmogorov and Yaglom equations is applied for the first time to the Rayleigh-Bénard convection. The analysis shows how the spatial inhomogeneity modulates the dynamics at different scales and wall-distances. Inside the core of the flow, the space of scales can be divided into an inhomogeneity-dominated range at large scales, an inertial-like range at intermediate scales and a dissipative range at small scales. This classic scenario breaks close to the walls, where the inhomogeneous mechanisms and the viscous/diffusive processes are important at every scale and entail more complex dynamics. The same theoretical framework is extended to the filtered velocity and temperature fields of non-rotating Rayleigh-Bénard convection. The analysis of the filtered Kolmogorov and Yaglom equations reveals the influence of the residual scales on the filtered dynamics both in physical and scale space, highlighting the effect of the relative position between the filter length and the crossover that separates the inhomogeneity-dominated range from the quasi-homogeneous range. The assessment of the filtered and residual physics results to be instrumental for the correct use of the existing Large-Eddy Simulation models and for the development of new ones.

Frequency domain analysis of stationary time series

This thesis provides a necessary and sufficient condition for asymptotic efficiency of a nonparametric estimator of the generalised autocovariance function of a Gaussian stationary random process. The generalised autocovariance function is the inverse Fourier transform of a power transformation of the spectral density, and encompasses the traditional and inverse autocovariance functions. Its nonparametric estimator is based on the inverse discrete Fourier transform of the same power transformation of the pooled periodogram. The general result is then applied to the class of Gaussian stationary ARMA processes and its implications are discussed. We illustrate that for a class of contrast functionals and spectral densities, the minimum contrast estimator of the spectral density satisfies a Yule-Walker system of equations in the generalised autocovariance estimator. Selection of the pooling parameter, which characterizes the nonparametric estimator of the generalised autocovariance, controlling its resolution, is addressed by using a multiplicative periodogram bootstrap to estimate the finite-sample distribution of the estimator. A multivariate extension of recently introduced spectral models for univariate time series is considered, and an algorithm for the coefficients of a power transformation of matrix polynomials is derived, which allows to obtain the Wold coefficients from the matrix coefficients characterizing the generalised matrix cepstral models. This algorithm also allows the definition of the matrix variance profile, providing important quantities for vector time series analysis. A nonparametric estimator based on a transformation of the smoothed periodogram is proposed for estimation of the matrix variance profile.