Article
Mathematics
Jose Manuel Gutierrez
Summary: The conditional probability formula accurately updates probability assignments when new information is added. It is proven that this formula is the only transformed probability measure that satisfies the minimum requirement relational assumption, using a non-atomic probability measure. This result is applicable to the standard Bayesian parametric model.
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
(2023)
Article
Mathematics, Interdisciplinary Applications
Sean Chang, James O. Berger
Summary: The problem of testing mutually exclusive hypotheses with dependent test statistics is explored, with the Bayesian approach shown to have excellent frequentist properties, making it the most effective way to achieve frequentist multiplicity control in the presence of significant test statistic dependence.
Article
Computer Science, Artificial Intelligence
Luis G. Esteves, Rafael Izbicki, Julio M. Stern, Rafael B. Stern
Summary: Hypothesis testing is a key component in Statistics, and simultaneous hypothesis testing is a common problem in practice. However, simultaneous hypothesis tests can be logically incoherent. This paper studies the logical coherence of Bayesian simultaneous three-way hypothesis tests and provides guidelines on how to build logically coherent posterior probability three-way hypothesis tests or more general Bayesian three-way hypothesis tests.
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
(2023)
Article
Biochemical Research Methods
Ronald Yurko, Kathryn Roeder, Bernie Devlin, Max G'Sell
Summary: A new algorithm is introduced to address the correlation issue in gene test statistics, enhancing the ability to detect signals in patients. Adaptive -value thresholding and high-dimensional metadata modeling with gradient boosted trees are used to improve analysis power, especially in studies for autism spectrum disorder. The workflow is based on summary statistics.
BRIEFINGS IN BIOINFORMATICS
(2021)
Article
Statistics & Probability
Michael P. Fay, Michael A. Proschan, Erica H. Brittain, Ram Tiwari
Summary: This paper proposes well-calibrated null preference priors for use in one-sided hypothesis tests, achieving agreement between Bayesian and frequentist inferences. The proposed prior assigns nearly 100% of its belief to the null hypothesis and ensures that the resulting posterior beliefs in the alternative hypothesis are not overconfident. This formulation extends the agreement between Bayes and frequentist methods to problems involving discrete distributions and provides valid p-values for null hypothesis belief.
STATISTICAL SCIENCE
(2022)
Article
Computer Science, Artificial Intelligence
Shalev Shaer, Yaniv Romano
Summary: The model-X conditional randomization test is a versatile method for testing conditional independence and controlling type I errors. By introducing novel model-fitting schemes with a new cost function, we aim to improve the power of the test statistic used to measure violations of conditional independence. Our experiments show that this approach consistently increases the number of correct discoveries while maintaining control over type I errors.
Article
Psychology, Multidisciplinary
Martin Schnuerch, Daniel W. Heck, Edgar Erdfelder
Summary: The article introduces a sequential test procedure called Waldian t test, which combines Bayesian t tests with Abraham Wald's sequential probability ratio test. The procedure can control error probabilities while measuring statistical evidence, satisfying both frequentist and Bayesian requirements. The article also discusses the implications of conventional stopping criteria for sequential Bayesian t tests and provides a user-friendly web application for interested researchers.
PSYCHOLOGICAL METHODS
(2022)
Article
Computer Science, Interdisciplinary Applications
Riko Kelter
Summary: This article discusses the importance of hypothesis testing in biomedical sciences and the development of Bayesian hypothesis tests as possible alternatives. Results show that careful calibration of prior parameters is crucial for improving the type I error rates or power of alternative tests. Moreover, choosing the appropriate test method requires consideration of multiple criteria.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2022)
Article
Computer Science, Artificial Intelligence
Glenn Shafer
Summary: This paper compares the notion of event in de Finetti's subjective theory of probability with the more situated notion of event that underlies the theory of probability and causality that I developed in the 1990s.
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
(2022)
Article
Business, Finance
Andrew Y. Chen
Summary: Research suggests that a large amount of data manipulation is needed to produce over 300 published asset pricing factors if they are all spurious. A more complex model leads to an inability to explain some of the published t-statistics using p-hacking, implying that mispricing, risk, and/or frictions play a key role in stock returns.
JOURNAL OF FINANCE
(2021)
Article
Computer Science, Artificial Intelligence
Pekka Laitila, Kai Virtanen
Summary: This paper introduces the use of ranked nodes method (RNM) in Bayesian networks (BNs) to represent probabilistic relationships of continuous quantities. Two novel discretization approaches, called static discretization approach and dynamic discretization approach, are presented to make the representation of continuous quantities more versatile. The new approaches provide an easier and more flexible way of using RNM in depicting probabilistic relationships, enhancing the effectiveness and diversity in using BNs in decision support systems.
DECISION SUPPORT SYSTEMS
(2022)
Article
Engineering, Electrical & Electronic
Berkan Dulek, Sinan Gezici
Summary: This paper re-visits the problem of optimal signal design for coherent detection of binary signals in Gaussian noise under power and secrecy constraints. The goal is to minimize the probability of error at an intended receiver while maintaining a certain threshold value for the probability of error at an eavesdropper and limited signal powers. The optimal solution is shown to exist in the form of antipodal signaling along the eigen-vector corresponding to the solution of a maximum eigenvalue problem, and can be efficiently solved through a semidefinite programming (SDP) relaxation followed by a matrix rank-one decomposition. Numerical examples are provided to illustrate optimal solutions for different cases.
Article
Medicine, Legal
Keith B. Morris, Jamie S. Spaulding, Jennifer N. Ho
Summary: Presumptive tests are crucial tools in forensic investigations, with varying specificities and sensitivities contributing to their overall accuracy. Proper evaluation and validation are necessary for new tests, especially in capturing error rates for accurate results. The interpretation of these tests, including false positive and false negative rates, is essential for investigators in determining the presence or absence of target materials.
JOURNAL OF FORENSIC SCIENCES
(2022)
Review
Psychology, Mathematical
Brent M. Wilson, Christine R. Harris, John T. Wixted
Summary: The fundamental goal of scientific research is to generate true positives. Increasing sample size can enhance replicability, but it can also increase theoretical false positives. The optimal sample size maximizes the positive predictive value at the theoretical level.
PSYCHONOMIC BULLETIN & REVIEW
(2022)
Article
Biodiversity Conservation
Wentong Yang, Liyuan Zhang, Yu Gao
Summary: This study aims to identify drought and flood risks in rainfed agriculture using conditional probabilities and reduce food losses caused by these disasters. The results show that droughts from May to July and floods from January to March have the greatest impact on rainfed crops in the three northeastern provinces of China. Specific cities, such as Huludao, Changchun, Baishan, Baicheng, Yanbian, Hegang, and Jiamusi, face a higher risk of drought in rainfed crops, while Yichun and Suihua face a higher risk of flooding. These findings provide quantitative guidance for food security work in the three northeastern regions of China.
ECOLOGICAL INDICATORS
(2023)
