https://repositorio.ufba.br/handle/ri/2093 2026-05-03T11:23:14Z https://repositorio.ufba.br/handle/ri/17184 Título: Gaussian distributions, Jacobi group, and Siegel-Jacobi space Autor(es): Molitor, Mathieu Abstract: Let N be the space of Gaussian distribution functions over ℝ, regarded as a 2-dimensional statistical manifold parameterized by the mean μ and the deviation σ. In this paper, we show that the tangent bundle of N , endowed with its natural Kähler structure, is the Siegel-Jacobi space appearing in the context of Number Theory and Jacobi forms. Geometrical aspects of the Siegel-Jacobi space are discussed in detail (completeness, curvature, group of holomorphic isometries, space of Kähler functions, and relationship to the Jacobi group), and are related to the quantum formalism in its geometrical form, i.e., based on the Kähler structure of the complex projective space. This paper is a continuation of our previous work [M. Molitor, “Remarks on the statistical origin of the geometrical formulation of quantum mechanics,” Int. J. Geom. Methods Mod. Phys. 9(3), 1220001, 9 (2012); M. Molitor, “Information geometry and the hydrodynamical formulation of quantum mechanics,” e-print arXiv (2012); M. Molitor, “Exponential families, Kähler geometry and quantum mechanics,” J. Geom. Phys. 70, 54–80 (2013)], where we studied the quantum formalism from a geometric and information-theoretical point of view. Tipo: Artigo de Periódico 2014-01-01T00:00:00Z https://repositorio.ufba.br/handle/ri/15724 Título: Non-uniform Specification and Large Deviations for Weak Gibbs Measures Autor(es): Varandas, Paulo César Rodrigues Pinto Abstract: We establish bounds for the measure of deviation sets associated to continuous observables with respect to not necessarily invariant weak Gibbs measures. Under some mild assumptions, we obtain upper and lower bounds for the measure of deviation sets of some non-uniformly expanding maps, including quadratic maps and robust multidimensional non-uniformly expanding local diffeomorphisms. For that purpose, a measure theoretical weak form of specification is introduced and proved to hold for the robust classes of multidimensional non-uniformly expanding local diffeomorphisms and Viana maps. Tipo: Artigo de Periódico 2012-01-01T00:00:00Z https://repositorio.ufba.br/handle/ri/15600 Título: Robust Exponential Decay of Correlations for Singular-Flows Autor(es): Araujo, Vitor; Varandas, Paulo César Rodrigues Pinto Abstract: We construct open sets of C k (k ≥ 2) vector fields with singularities that have robust exponential decay of correlations with respect to the unique physical measure. In particular we prove that the geometric Lorenz attractor has exponential decay of correlations with respect to the unique physical measure. Tipo: Artigo de Periódico 2012-01-01T00:00:00Z https://repositorio.ufba.br/handle/ri/15571 Título: Bayesian inference for power law processes with applications in repairable systems Autor(es): Oliveira, Maristela Dias de; Colosimo, Enrico A.; Gilardoni, Gustavo L. Abstract: Statistical models for recurrent events are of great interest in repairable systems reliability and maintenance. The adopted model under minimal repair maintenance is frequently a nonhomogeneous Poisson process with the power law process (PLP) intensity function. Although inference for the PLP is generally based on maximum likelihood theory, some advantages of the Bayesian approach have been reported in the literature. In this paper it is proposed that the PLP intensity be reparametrized in terms of (β,η)(β,η), where ββ is the elasticity of the mean number of events with respect to time and ηη is the mean number of events for the period in which the system was actually observed. It is shown that ββ and ηη are orthogonal and that the likelihood becomes proportional to a product of gamma densities. Therefore, the family of natural conjugate priors is also a product of gammas. The idea is extended to the case that several realizations of the same PLP are observed along overlapping periods of time. Some Monte Carlo simulations are provided to study the frequentist behavior of the Bayesian estimates and to compare them with the maximum likelihood estimates. The results are applied to a real problem concerning the determination of the optimal periodicity of preventive maintenance for a set of power transformers. Prior distributions are elicited for ββ and ηη based on their operational interpretation and engineering expertise. Tipo: Artigo de Periódico 2012-01-01T00:00:00Z