arXiv subjects

Julio Michael Stern

Publications and source records attributed to Julio Michael Stern.

14 recordsLinked to original sources

arXiv2025

Kullback-Leibler Consistency of $p$-dimensional P\'olya Tree Posteriors and Differential Entropy Estimation

We exploit the multiplicative structure of P\'olya Tree priors to establish novel consistency results on $p$-dimensional trees, conditions to obtain Kullback-Leibler minimax contraction rates for univariate density estimation and a representation theorem of entropy functionals of P\'olya Tree posteriors. These results motivate a novel differential entropy estimator that is consistent under mild conditions on large dimensions.

math.ST↗

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↗

arXiv2022

A Sharper Image: The Quest of Science and Recursive Production of Objective Realities

This article explores the metaphor of Science as provider of sharp images of our environment, using the epistemological framework of Objective Cognitive Constructivism. These sharp images are conveyed by precise scientific hypotheses that, in turn, are encoded by mathematical equations. Furthermore, this article describes how such knowledge is produced by a cyclic and recursive develop, perfection and reinforcement process, leading to the emergence of eigen-solutions characterized by the four essential properties of precision, stability, separability and composability. Finally, this article discusses the role played by ontology and metaphysics in the scientific production process, and in which sense the resulting knowledge can be considered objective.

physics.hist-ph↗

arXiv2020

Randomization and Fair Judgment in Law and Science

Randomization procedures are used in legal and statistical applications, aiming to shield important decisions from spurious influences. This article gives an intuitive introduction to randomization and examines some intended consequences of its use related to truthful statistical inference and fair legal judgment. This article also presents an open-code Java implementation for a cryptographically secure, statistically reliable, transparent, traceable, and fully auditable randomization tool.

stat.OT↗

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

The Full Bayesian Significance Test and the e-value -- Foundations, theory and application in the cognitive sciences

Hypothesis testing is a central statistical method in psychological research and the cognitive sciences. While the problems of null hypothesis significance testing (NHST) have been debated widely, few attractive alternatives exist. In this paper, we provide a tutorial on the Full Bayesian Significance Test (FBST) and the e-value, which is a fully Bayesian alternative to traditional significance tests which rely on p-values. The FBST is an advanced methodological procedure which can be applied to several areas. In this tutorial, we showcase with two examples of widely used statistical methods in psychological research how the FBST can be used in practice, provide researchers with explicit guidelines on how to conduct it and make available R-code to reproduce all results. The FBST is an innovative method which has clearly demonstrated to perform better than frequentist significance testing. However, to our best knowledge, it has not been used so far in the psychological sciences and should be of wide interest to a broad range of researchers in psychology and the cognitive sciences.

stat.ME↗

arXiv2020

A Fair, Traceable, Auditable and Participatory Randomization Tool for Legal Systems

Many real-world scenarios require the random selection of one or more individuals from a pool of eligible candidates. One example of especial social relevance refers to the legal system, in which the jurors and judges are commonly picked according to some probability distribution aiming to avoid biased decisions. In this scenario, ensuring auditability of the random drawing procedure is imperative to promote confidence in its fairness. With this goal in mind, this article describes a protocol for random drawings specially designed for use in legal systems. The proposed design combines the following properties: security by design, ensuring the fairness of the random draw as long as at least one participant behaves honestly; auditability by any interested party, even those having no technical background, using only public information; and statistical robustness, supporting drawings where candidates may have distinct probability distributions. Moreover, it is capable of inviting and engaging as participating stakeholders the main interested parties of a legal process, in a way that promotes process transparency, public trust and institutional resilience. An open-source implementation is also provided as supplementary material.

cs.CR↗

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↗

arXiv2019

Karl Pearson and the Logic of Science: Renouncing Causal Understanding (the Bride) and Inverted Spinozism

Karl Pearson is the leading figure of XX century statistics. He and his co-workers crafted the core of the theory, methods and language of frequentist or classical statistics -- the prevalent inductive logic of contemporary science. However, before working in statistics, K.Pearson had other interests in life, namely, in this order, philosophy, physics, and biological heredity. Key concepts of his philosophical and epistemological system of anti-Spinozism (a form of transcendental idealism) are carried over to his subsequent works on the logic of scientific discovery. This article's main goal is to analyze K.Pearson early philosophical and theological ideas and to investigate how the same ideas came to influence contemporary science, either directly or indirectly -- by the use of variant theories, methods and dialects of statistics, corresponding to variant statistical inference procedures and their specific belief calculi.

stat.OT↗

arXiv2019

Auditable Blockchain Randomization Tool

Randomization is an integral part of well-designed statistical trials, and is also a required procedure in legal systems, see Marcondes et al. (2019) This paper presents an easy to implement randomization protocol that assures, in a formal mathematical setting, a statistically sound, computationally efficient, cryptographically secure, traceable and auditable randomization procedure that is also resistant to collusion and manipulation by participating agents.

cs.CR↗

arXiv2018

Assessing randomness in case assignment: the case study of the Brazilian Supreme Court

Sortition, i.e., random appointment for public duty, has been employed by societies throughout the years, especially for duties related to the judicial system, as a firewall designated to prevent illegitimate interference between parties in a legal case and agents of the legal system. In judicial systems of modern western countries, random procedures are mainly employed to select the jury, the court and/or the judge in charge of judging a legal case, so that they have a significant role in the course of a case. Therefore, these random procedures must comply with some principles, as statistical soundness; complete auditability; open-source programming; and procedural, cryptographical and computational security. Nevertheless, some of these principles are neglected by some random procedures in judicial systems, that are, in some cases, performed in secrecy and are not auditable by the involved parts. The assignment of cases in the Brazilian Supreme Court (Supremo Tribunal Federal) is an example of such procedures, for it is performed by a closed-source algorithm, unknown to the public and to the parts involved in the judicial cases, that allegedly assign the cases randomly to the justice chairs based on their caseload. In this context, this article presents a review of how sortition has been employed historically by societies, and discusses how Mathematical Statistics may be applied to random procedures of the judicial system, as it has been applied for almost a century on clinical trials, for example. Based on this discussion, a statistical model for assessing randomness in case assignment is proposed and applied to the Brazilian Supreme Court in order to shed light on how this assignment process is performed by the closed-source algorithm. Guidelines for random procedures are outlined and topics for further researches presented.

stat.AP↗

arXiv2014

Jacob's Ladder and Scientific Ontologies

The main goal of this article is to use the epistemological framework of a specific version of Cognitive Constructivism to address Piaget's central problem of knowledge construction, namely, the re-equilibration of cognitive structures. The distinctive objective character of this constructivist framework is based on Heinz von Foerster's fundamental metaphor of - objects as tokens for eigen-solutions, and is also supported by formal inference methods of Bayesian statistics. This epistemological perspective is illustrated using some episodes in the history of chemistry concerning the definition or identification of chemical elements. Some of von Foerster's epistemological imperatives provide general guidelines of development and argumentation.

physics.hist-ph↗

arXiv2013

Bayesian test of significance for conditional independence: The multinomial model

Conditional independence tests (CI tests) have received special attention lately in Machine Learning and Computational Intelligence related literature as an important indicator of the relationship among the variables used by their models. In the field of Probabilistic Graphical Models (PGM)--which includes Bayesian Networks (BN) models--CI tests are especially important for the task of learning the PGM structure from data. In this paper, we propose the Full Bayesian Significance Test (FBST) for tests of conditional independence for discrete datasets. FBST is a powerful Bayesian test for precise hypothesis, as an alternative to frequentist's significance tests (characterized by the calculation of the \emph{p-value}).

stat.CO↗