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Previous results show that standard two-way hypothesis tests cannot be logically coherent. This paper studies whether Bayesian simultaneous three-way hypothesis tests can be logically coherent. Specifically, under the GFBST loss, the Bayes test is logically coherent.

In dynamic learning, a rational agent must revise their credence about a question of interest in accordance with the total evidence available between the earlier and later times. We discuss situations in which an observable event F that is sufficient for the total evidence can be identified, yet its probabilistic modeling cannot be performed in a precise manner. The agent may employ imprecise (IP) models of reasoning to account for the identified sufficient event, and perform change of credence or sequential decisions accordingly.

Conformal methods create prediction bands that control average coverage assuming solely i.i.d. data. We introduce CD-split and HPD-split, which yield general prediction regions and converge to the optimal highest predictive density set.

O artigo descreve a dinâmica do processo decisório do STF no período de transição democrática, observando como os ministros que integraram o tribunal entre os anos de 1978 e 1988 se compuseram para decidir casos de controle abstrato de constitucionalidade. Nosso objetivo é identificar a formação de coalizões, e verificar se, e em que medida, as nomeações presidenciais e as trajetórias de carreira pregressas dos ministros ajudam a explicar essas coalizões, a partir do emprego do método de escalonamento multidimensional de votos W-Nominate.

A familiar defense of Personalist or Subjective Bayesian theory is that, under a variety of sufficient conditions, asymptotically – with increasing shared evidence – almost surely, each non-extreme, countably additive Bayesian opinion, when updated by conditionalization, converges to certainty that is veridical about the truth/falsity of hypotheses of interest. Then, with probability 1 over possible evidential histories, personal probabilities track the truth. In this note we examine varieties of failures of these asymptotics. In an extreme case, conditional probabilities are deceptive when they converge to certainty for a false hypothesis. We establish that proposals for so-called “modest” credences, offered by Elga (2016) and by Nielsen and Stewart (2019) in response to a concern about Bayesian orgulity raised by Belot (2013), instead support deceptive credences. We argue that deceptive credences are not modest, but for a reason different than Belot adduces.

We examine general decision problems with loss functions that are bounded below. We allow the loss function to assume the value infinity. No other assumptions are made about the action space, the types of data available, the types of non-randomized decision rules allowed, or the parameter space. By allowing prior distributions and the randomizations in randomized rules to be finitely-additive, we prove very general complete class and minimax theorems. Specifically, under the sole assumption that the loss function is bounded below, we show that every decision problem has a minimal complete class and all admissible rules are Bayes rules. We also show that every decision problem has a minimax rule and a least-favorable distribution and that every minimax rule is Bayes with respect to the least-favorable distribution. Some special care is required to deal properly with infinite-valued risk functions and integrals taking infinite values.

Este artigo estuda as causas de desaparecimento no estado de São Paulo por idade e sexo dos desaparecidos. Para tanto, utiliza algoritmos de aprendizado de máquina para avaliar automaticamente o texto de boletins de ocorrência.

Despite its common practice, statistical hypothesis testing presents challenges in interpretation. For instance, in the standard frequentist framework there is no control of the type II error. As a result, the non-rejection of the null hypothesis (H0) cannot reasonably be interpreted as its acceptance. We propose that this dilemma can be overcome by using agnostic hypothesis tests, since they can control the type I and II errors simultaneously. In order to make this idea operational, we show how to obtain agnostic hypothesis in typical models. For instance, we show how to build (unbiased) uniformly most powerful agnostic tests and how to obtain agnostic tests from standard p-values. Also, we present conditions such that the above tests can be made logically coherent. Finally, we present examples of consistent agnostic hypothesis tests.

People with Parkinsons disease (PD) display poorer gait performance when walking under complex conditions than under simple conditions. Screening tests that evaluate gait performance changes under complex walking conditions may be valuable tools for early intervention, especially if allowing for massive data collection. To investigate the use of the Goalkeeper Game (GG) to predict impairment in gait performance under complex conditions in people with Parkinsons disease (PPD) and compare its predictive power with the one of the Montreal Cognitive Assessment (MoCA) test. 74 PPD (HY stages: 23 in stage 1; 31 in stage 2; 20 in stage 3), without dementia (MoCA cut-off 21), tested in ON period with dopaminergic medication were submitted to single individual cognitive/motor evaluation sessions. MoCA and GG were used to assess cognition, and the dynamic gait index (DGI) test was used to assess gait performance under complex condition. GG test resulted in 9 measures extracted via a statistical model. The predictive power of the GG measures and the MoCA score with respect to gait performance, as assessed by DGI, were compared. The predictive models based on GG obtained a better score of prediction (65%) then MoCA (56%) for DGI scores (at a 50% specificity). GG is a novel tool for noninvasive screening that showed a superior predictive power in assessing gait performance under complex condition in people with PD than the well-established MoCa test.

We present two different proofs that positive polynomials on closed boxes of the plane can be written as bivariate Bernstein …