Competing regression models for longitudinal data

The choice of an appropriate family of linear models for the analysis of longitudinal data is often a matter of concern for practitioners. To attenuate such difficulties, we discuss some issues that emerge when analyzing this type of data via a practical example involving pretestposttest longitudinal data. In particular, we consider log-normal linear mixed models (LNLMM), generalized linear mixed models (GLMM), and models based on generalized estimating equations (GEE). We show how some special features of the data, like a nonconstant coefficient of variation, may be handled in the three approaches and evaluate their performance with respect to the magnitude of standard errors of interpretable and comparable parameters. We also show how different diagnostic tools may be employed to identify outliers and comment on available software. We conclude by noting that the results are similar, but that GEE-based models may be preferable when the goal is to compare the marginal expected responses.

Robust statistical modeling using the Birnbaum-Saunders-t distribution applied to insurance

In this paper, we carry out robust modeling and influence diagnostics in Birnbaum-Saunders (BS) regression models. Specifically, we present some aspects related to BS and log-BS distributions and their generalizations from the Student-t distribution, and develop BS-t regression models, including maximum likelihood estimation based on the EM algorithm and diagnostic tools. In addition, we apply the obtained results to real data from insurance, which shows the uses of the proposed model. Copyright (c) 2011 John Wiley & Sons, Ltd.

Influence of the initial condition in equilibrium last-passage percolation models

In this paper we consider an equilibrium last-passage percolation model on an environment given by a compound two-dimensional Poisson process. We prove an L-2-formula relating the initial measure with the last-passage percolation time. This formula turns out to be a useful tool to analyze the fluctuations of the last-passage times along non-characteristic directions.

PXRF and multivariate statistics analysis of pre-colonial pottery from northeast of Brazil

Portable system of energy dispersive X-ray fluorescence was used to determine the elemental composition of 68 pottery fragments from Sambaqui do Bacanga, an archeological site in Sao Luis, Maranhao, Brazil. This site was occupied from 6600 BP until 900 BP. By determining the element chemical composition of those fragments, it was possible to verify the existence of engobe in 43 pottery fragments. Obtained from two-dimensional graphs and hierarchical cluster analysis performed in fragments of stratigraphies from surface and 113-cm level, and 10 to 20, 132 and 144-cm level, it was possible to group these fragments in five distinct groups, according to their stratigraphies. The results of data grouping (two-dimensional graphics) are in agreement with hierarchical cluster analysis by Ward method. Copyright (C) 2011 John Wiley & Sons, Ltd.

Polynomial and Poisson dependence in free Poisson algebras and free Poisson fields

We prove that any two Poisson dependent elements in a free Poisson algebra and a free Poisson field of characteristic zero are algebraically dependent, thus answering positively a question from Makar-Limanov and Umirbaev (2007) [8]. We apply this result to give a new proof of the tameness of automorphisms for free Poisson algebras of rank two (see Makar-Limanov and Umirbaev (2011) [9], Makar-Limanov et al. (2009) [10]). (C) 2011 Elsevier Inc. All rights reserved.

Spatio-temporal patterns of tuberculosis incidence in Ribeirão Preto, State of São Paulo, southeast Brazil, and their relationship with social vulnerability: a Bayesian analysis

INTRODUCTION: The purpose of this ecological study was to evaluate the urban spatial and temporal distribution of tuberculosis (TB) in Ribeirão Preto, State of São Paulo, southeast Brazil, between 2006 and 2009 and to evaluate its relationship with factors of social vulnerability such as income and education level. METHODS: We evaluated data from TBWeb, an electronic notification system for TB cases. Measures of social vulnerability were obtained from the SEADE Foundation, and information about the number of inhabitants, education and income of the households were obtained from Brazilian Institute of Geography and Statistics. Statistical analyses were conducted by a Bayesian regression model assuming a Poisson distribution for the observed new cases of TB in each area. A conditional autoregressive structure was used for the spatial covariance structure. RESULTS: The Bayesian model confirmed the spatial heterogeneity of TB distribution in Ribeirão Preto, identifying areas with elevated risk and the effects of social vulnerability on the disease. We demonstrated that the rate of TB was correlated with the measures of income, education and social vulnerability. However, we observed areas with low vulnerability and high education and income, but with high estimated TB rates. CONCLUSIONS: The study identified areas with different risks for TB, given that the public health system deals with the characteristics of each region individually and prioritizes those that present a higher propensity to risk of TB. Complex relationships may exist between TB incidence and a wide range of environmental and intrinsic factors, which need to be studied in future research.

Aplicación del análisis isogeométrico a un problema bidimensional de Poisson

Máster Universitario en Sistemas Inteligentes y Aplicaciones Numéricas en Ingeniería (SIANI)

Statistical analysis and simulation techniques in wall-bounded turbulence

The present work is devoted to the assessment of the energy fluxes physics in the space of scales and physical space of wall-turbulent flows. The generalized Kolmogorov equation will be applied to DNS data of a turbulent channel flow in order to describe the energy fluxes paths from production to dissipation in the augmented space of wall-turbulent flows. This multidimensional description will be shown to be crucial to understand the formation and sustainment of the turbulent fluctuations fed by the energy fluxes coming from the near-wall production region. An unexpected behavior of the energy fluxes comes out from this analysis consisting of spiral-like paths in the combined physical/scale space where the controversial reverse energy cascade plays a central role. The observed behavior conflicts with the classical notion of the Richardson/Kolmogorov energy cascade and may have strong repercussions on both theoretical and modeling approaches to wall-turbulence. To this aim a new relation stating the leading physical processes governing the energy transfer in wall-turbulence is suggested and shown able to capture most of the rich dynamics of the shear dominated region of the flow. Two dynamical processes are identified as driving mechanisms for the fluxes, one in the near wall region and a second one further away from the wall. The former, stronger one is related to the dynamics involved in the near-wall turbulence regeneration cycle. The second suggests an outer self-sustaining mechanism which is asymptotically expected to take place in the log-layer and could explain the debated mixed inner/outer scaling of the near-wall statistics. The same approach is applied for the first time to a filtered velocity field. A generalized Kolmogorov equation specialized for filtered velocity field is derived and discussed. The results will show what effects the subgrid scales have on the resolved motion in both physical and scale space, singling out the prominent role of the filter length compared to the cross-over scale between production dominated scales and inertial range, lc, and the reverse energy cascade region lb. The systematic characterization of the resolved and subgrid physics as function of the filter scale and of the wall-distance will be shown instrumental for a correct use of LES models in the simulation of wall turbulent flows. Taking inspiration from the new relation for the energy transfer in wall turbulence, a new class of LES models will be also proposed. Finally, the generalized Kolmogorov equation specialized for filtered velocity fields will be shown to be an helpful statistical tool for the assessment of LES models and for the development of new ones. As example, some classical purely dissipative eddy viscosity models are analyzed via an a priori procedure.

On the geometry of the spin-statistics connection in quantum mechanics

The Spin-Statistics theorem states that the statistics of a system of identical particles is determined by their spin: Particles of integer spin are Bosons (i.e. obey Bose-Einstein statistics), whereas particles of half-integer spin are Fermions (i.e. obey Fermi-Dirac statistics). Since the original proof by Fierz and Pauli, it has been known that the connection between Spin and Statistics follows from the general principles of relativistic Quantum Field Theory. In spite of this, there are different approaches to Spin-Statistics and it is not clear whether the theorem holds under assumptions that are different, and even less restrictive, than the usual ones (e.g. Lorentz-covariance). Additionally, in Quantum Mechanics there is a deep relation between indistinguishabilty and the geometry of the configuration space. This is clearly illustrated by Gibbs' paradox. Therefore, for many years efforts have been made in order to find a geometric proof of the connection between Spin and Statistics. Recently, various proposals have been put forward, in which an attempt is made to derive the Spin-Statistics connection from assumptions different from the ones used in the relativistic, quantum field theoretic proofs. Among these, there is the one due to Berry and Robbins (BR), based on the postulation of a certain single-valuedness condition, that has caused a renewed interest in the problem. In the present thesis, we consider the problem of indistinguishability in Quantum Mechanics from a geometric-algebraic point of view. An approach is developed to study configuration spaces Q having a finite fundamental group, that allows us to describe different geometric structures of Q in terms of spaces of functions on the universal cover of Q. In particular, it is shown that the space of complex continuous functions over the universal cover of Q admits a decomposition into C(Q)-submodules, labelled by the irreducible representations of the fundamental group of Q, that can be interpreted as the spaces of sections of certain flat vector bundles over Q. With this technique, various results pertaining to the problem of quantum indistinguishability are reproduced in a clear and systematic way. Our method is also used in order to give a global formulation of the BR construction. As a result of this analysis, it is found that the single-valuedness condition of BR is inconsistent. Additionally, a proposal aiming at establishing the Fermi-Bose alternative, within our approach, is made.

Existence of solutions and asymtptotic limits of the Euler-Poisson and the quantum drift-diffusion systems

My work concerns two different systems of equations used in the mathematical modeling of semiconductors and plasmas: the Euler-Poisson system and the quantum drift-diffusion system. The first is given by the Euler equations for the conservation of mass and momentum, with a Poisson equation for the electrostatic potential. The second one takes into account the physical effects due to the smallness of the devices (quantum effects). It is a simple extension of the classical drift-diffusion model which consists of two continuity equations for the charge densities, with a Poisson equation for the electrostatic potential. Using an asymptotic expansion method, we study (in the steady-state case for a potential flow) the limit to zero of the three physical parameters which arise in the Euler-Poisson system: the electron mass, the relaxation time and the Debye length. For each limit, we prove the existence and uniqueness of profiles to the asymptotic expansion and some error estimates. For a vanishing electron mass or a vanishing relaxation time, this method gives us a new approach in the convergence of the Euler-Poisson system to the incompressible Euler equations. For a vanishing Debye length (also called quasineutral limit), we obtain a new approach in the existence of solutions when boundary layers can appear (i.e. when no compatibility condition is assumed). Moreover, using an iterative method, and a finite volume scheme or a penalized mixed finite volume scheme, we numerically show the smallness condition on the electron mass needed in the existence of solutions to the system, condition which has already been shown in the literature. In the quantum drift-diffusion model for the transient bipolar case in one-space dimension, we show, by using a time discretization and energy estimates, the existence of solutions (for a general doping profile). We also prove rigorously the quasineutral limit (for a vanishing doping profile). Finally, using a new time discretization and an algorithmic construction of entropies, we prove some regularity properties for the solutions of the equation obtained in the quasineutral limit (for a vanishing pressure). This new regularity permits us to prove the positivity of solutions to this equation for at least times large enough.

"Making Sense of Figures": Statistics, Computing and Information Technologies in Agriculture and Biology in Britain, 1920s-1960s

Throughout the twentieth century statistical methods have increasingly become part of experimental research. In particular, statistics has made quantification processes meaningful in the soft sciences, which had traditionally relied on activities such as collecting and describing diversity rather than timing variation. The thesis explores this change in relation to agriculture and biology, focusing on analysis of variance and experimental design, the statistical methods developed by the mathematician and geneticist Ronald Aylmer Fisher during the 1920s. The role that Fisher’s methods acquired as tools of scientific research, side by side with the laboratory equipment and the field practices adopted by research workers, is here investigated bottom-up, beginning with the computing instruments and the information technologies that were the tools of the trade for statisticians. Four case studies show under several perspectives the interaction of statistics, computing and information technologies, giving on the one hand an overview of the main tools – mechanical calculators, statistical tables, punched and index cards, standardised forms, digital computers – adopted in the period, and on the other pointing out how these tools complemented each other and were instrumental for the development and dissemination of analysis of variance and experimental design. The period considered is the half-century from the early 1920s to the late 1960s, the institutions investigated are Rothamsted Experimental Station and the Galton Laboratory, and the statisticians examined are Ronald Fisher and Frank Yates.