arXiv subjects

Carlos Alberto de Braganca Pereira

Publications and source records attributed to Carlos Alberto de Braganca Pereira.

7 recordsLinked to original sources

arXiv2024

The e-value and the Full Bayesian Significance Test: Logical Properties and Philosophical Consequences

This article gives a conceptual review of the e-value, ev(H|X) -- the epistemic value of hypothesis H given observations X. This statistical significance measure was developed in order to allow logically coherent and consistent tests of hypotheses, including sharp or precise hypotheses, via the Full Bayesian Significance Test (FBST). Arguments of analysis allow a full characterization of this statistical test by its logical or compositional properties, showing a mutual complementarity between results of mathematical statistics and the logical desiderata lying at the foundations of this theory.

math.ST↗

arXiv2020

Cointegration and unit root tests: A fully Bayesian approach

To perform statistical inference for time series, one should be able to assess if they present deterministic or stochastic trends. For univariate analysis one way to detect stochastic trends is to test if the series has unit roots, and for multivariate studies it is often relevant to search for stationary linear relationships between the series, or if they cointegrate. The main goal of this article is to briefly review the shortcomings of unit root and cointegration tests proposed by the Bayesian approach of statistical inference and to show how they can be overcome by the fully Bayesian significance test (FBST), a procedure designed to test sharp or precise hypothesis. We will compare its performance with the most used frequentist alternatives, namely, the Augmented Dickey-Fuller for unit roots and the maximum eigenvalue test for cointegration. Keywords: Time series; Bayesian inference; Hypothesis testing; Unit root; Cointegration.

math.ST↗

arXiv2020

Otimizacao e Processos Estocasticos Aplicados a Economia e Financas

Optimization and Stochastic Processes Applied to Economy and Finance -- is the name of this book translated to English; It has been used at the IME-USP - The Institute of Mathematics and Statistics of the University of Sao Paulo, since 1993. Contents: Ch.1: Linear Programming; Ch.2: Non-Linear Programming; Ch.3: Quadratic Programming; Ch.4: Markowitz Model; Ch.5: Dynamic Programming; Ch.6: LQG Estimation and Control; Ch.7: Decision Trees; Ch.8: Pension Funds; Ch.9: Mixed Portfolios Including Derivative Contracts; Appendices: App.A: Matlab; App.B: Critical-Point Software; App.C: Computational Linear Algebra; App.D: Probability; App.E: Computer Codes. This book is written in Portuguese language.

cs.CE↗

arXiv2020

The e-value: A Fully Bayesian Significance Measure for Precise Statistical Hypotheses and its Research Program

This article gives a survey of the e-value, a statistical significance measure a.k.a. the evidence rendered by observational data, X, in support of a statistical hypothesis, H, or, the other way around, the epistemic value of H given X. The $e$-value and the accompanying FBST, the Full Bayesian Significance Test, constitute the core of a research program that was started at IME-USP, is being developed by over 20 researchers worldwide, and has, so far, been referenced by over 200 publications. The e-value and the FBST comply with the best principles of Bayesian inference, including the likelihood principle, complete invariance, asymptotic consistency, etc. Furthermore, they exhibit powerful logic or algebraic properties in situations where one needs to compare or compose distinct hypotheses that can be formulated either in the same or in different statistical models. Moreover, they effortlessly accommodate the case of sharp or precise hypotheses, a situation where alternative methods often require ad hoc and convoluted procedures. Finally, the FBST has outstanding robustness and reliability characteristics, outperforming traditional tests of hypotheses in many practical applications of statistical modeling and operations research.

stat.ME↗

arXiv2018

Odds for the Brazilian 2018 president elections: An application of Bayesian statistics in contingency tables

The purpose of these notes is to present an assessment of the probability of a candidate be elected in a two-round presidential election. In the first round, all candidates can be voted on. If one of them has more than 50% of the vote (s)he is elected and there is no second round. If none of the candidates obtain more than 50% of the votes, then the top two candidates will be selected for a second round. In this second round, the most voted candidate is elected. This is the scenario of the Brazilian elections that are taking place at the moment. We are calculating the odds associated with the 2018 presidential elections in Brazil. The first round is on October 7, and the second round is on October 28, 2018.

stat.AP↗

arXiv2018

Reliability of components of coherent systems: estimates in presence of masked data

The reliability of a system of components depends on reliability of each component. Thus, the initial statistical work should be the estimation of the reliability of each component of the system. This is not an easy task because when the system fails, the failure time of a given component can not be observed, that is, censored data. Rodrigues et al. (2017) presented a solution for reliability estimation of components when it is avaliable the system failure time and the status of each component at the time of system failure (if it had failed before, after or it is responsible for system failure). However, there are situations it may be difficult to identify the status of components at the moment of system failure. Such cases are systems with masked causes of failure. Since parallel and series systems are the simplest systems, innumerous alternative solutions for these two systems have been appeared in the literature. To the best of our knowledge, this seems to be the first work that considers the general case of coherent systems. The three-parameter Weibull distribution is considered as the component failure time model. Identically distributed failure times is not required restrictions. Furthermore, there is no restriction on the subjective choice of prior distributions but preference has been given to continuous prior distributions; these priors represent well the nuances of the environment that the system operates. The statistical work of obtaining quantities of the posterior distribution is supported by the Metropolis within Gibbs algorithm. With several simulations, the excellent performance of the model was evaluated. We also consider a computer hard-drives real dataset in order to present the practical relevance of the proposed model.

stat.ME↗

arXiv2017

Estimation of Component Reliability in Coherent Systems

The first step in statistical reliability studies of coherent systems is the estimation of the reliability of each system component. For the cases of parallel and series systems the literature is abundant. It seems that the present paper is the first that presents the general case of component inferences in coherent systems. The failure time model considered here is the three-parameter Weibull distribution. Furthermore, neither independence nor identically distributed failure times are required restrictions. The proposed model is general in the sense that it can be used for any coherent system, from the simplest to the more complex structures. It can be considered for all kinds of censored data; including interval-censored data. An important property obtained for the Weibull model is the fact that the posterior distributions are proper, even for non-informative priors. Using several simulations, the excellent performance of the model is illustrated. As a real example, boys first use of marijuana is considered to show the efficiency of the solution even when censored data occurs.

stat.ME↗