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The aim is to introduce a metric to quantify the relevance of specific subjects within a text and develop a methodology to test whether this relevance is the same or not in various written documents. The proposed metric can be used to track the evolution of a subject in a series of documents or to measure the impact of a given text in related literature. To this aim, text mining tools are combined with Bayesian and frequentist statistical methods innovatively. First, topic modeling based on state-of-the-art techniques is suggested to be employed to identify relevant topics. The derived models are used to quantify the relative importance of a subject defined through a given set of terms, or keywords, by employing Bayesian techniques. Then, a two-sample test statistic is proposed to compare subjects' prevalence in two groups of documents. Given the complexity of the involved parametric distributions, a distribution-free bootstrap approach is suggested. The rationale of the approach will be established. The correctness and consistency of the proposed test are analyzed through simulations. The methodology is used to assess the impact of the EU investment through a project on the related scientific production and for sentiment analysis.1 [ABSTRACT FROM AUTHOR]

A recent study by Social & Scientific Systems Inc. explores the use of Bayesian statistical concepts in rodent toxicology research, comparing them to frequentist statistics commonly used in laboratory data analysis. The researchers advocate for increased adoption of Bayesian methods in laboratory animal research, highlighting their accessibility and advancements in the past 30 years. This research, supported by the National Institute of Environmental Health Sciences, provides valuable insights for practitioners in experimental science. [Extracted from the article]

A recent study conducted by the University of Sydney explores the relationship between musicians' pursuit of expertise-related goals and their regulation of emotions. The research suggests that musicians strategically regulate their emotions during practice in order to prioritize emotions that are conducive to achieving their long-term musical goals, even if those emotions are not necessarily positive. The study found that musicians with higher levels of expertise-related goals demonstrated a nuanced approach to regulating certain negative emotions, indicating a selective and sophisticated emotion regulation behavior. These findings contribute to our understanding of domain-specific emotion regulation and may inform the development of effective musical practice strategies. [Extracted from the article]

Yu and Hoff constructed novel confidence intervals for the treatment means in a one-way layout. They assessed the expected lengths of these intervals using a semi-Bayesian analysis. We provide a revealing assessment of these expected lengths using a fully frequentist analysis. [ABSTRACT FROM AUTHOR]

A recent study conducted by researchers at Southeast University in Nanjing, China, aimed to analyze the safety profiles of rivaroxaban, a factor Xa inhibitor, by examining the Food and Drug Administration Adverse Event Reporting System (FAERS). The study found that rivaroxaban had various suspected adverse reactions, with the most common being gastrointestinal disorders, injury, poisoning, and procedural complications, and nervous system disorders. The researchers concluded that healthcare practitioners should closely monitor these adverse events and continue to assess the associated risks of rivaroxaban in the future. [Extracted from the article]

This article discusses the use of Bayes factors in psychology research to determine the presence or absence of an effect. It highlights two reasons for the low uptake of Bayes factors in psychology: the difficulty in specifying the range of effect sizes and the technical learning curve of implementing Bayes factors. The article presents a case study and simulations to demonstrate a simple method for generating a range of plausible effect sizes. The use of frequentist logistic mixed-effects models and Bayesian hierarchical models is illustrated, and the results obtained from Bayes factors are shown to be reasonable across a range of real effect sizes. [Extracted from the article]

This article discusses the use of Bayes factors in psychology research to determine the presence or absence of an effect. It highlights two reasons for the low uptake of Bayes factors in psychology: the difficulty in specifying the range of effect sizes and the technical learning curve of implementing Bayes factors. The authors present a case study and simulations to demonstrate a simple method for generating a range of plausible effect sizes. The article emphasizes the use of frequentist logistic mixed-effects models and Bayesian hierarchical models to calculate Bayes factors, which provide reasonable results across a range of real effect sizes. However, it is important to note that this preprint has not been peer-reviewed. [Extracted from the article]

A study conducted by a researcher at the University of Padova in Italy explores the use of hierarchical multinomial processing tree models for meta-analysis of diagnostic accuracy studies. The study investigates the applicability of these models in assessing the accuracy of binary classification tools, taking into account the specific disease prevalences of each study. The proposed model is compared to other existing models through simulation studies and is applied to a real meta-analysis on the accuracy of the confusion assessment method as a delirium screening tool. The research provides valuable insights into the evaluation of diagnostic tools in clinical and psychological investigations. [Extracted from the article]

An accurate and efficient statistical method for genetic evaluation is a key requirement for progress in any breeding program. Thus, the present study aimed to evaluate the performance of Frequentist and Bayesian inferences for repeated measures analysis in Jatropha curcas breeding. To this end, 730 individuals from 73 half-sib families were evaluated for grain yield trait, over six crop years. Frequentist and Bayesian analyses were made considering repeatability models with different residual variance structures. Variance components were estimated through restricted maximum likelihood (REML) and Markov Chain Monte Carlo (MCMC). Genetic values were predicted through best linear unbiased prediction (BLUP) and estimated through MCMC. Variance components and genetic and non-genetic parameters estimated by the Frequentist inference presented values similar to those estimated by the Bayesian inference. The selective accuracy presented high magnitude (0.84) by the Frequentist and Bayesian inferences, indicating high reliability. Confidence and highest posterior density (HPD) intervals were similar for the genetic parameters, however the HPD intervals range was slightly short. This study highlighted the importance of testing the residual variance structure and pointed out that the Frequentist and Bayesian inferences presented similar results when using non-informative prior. Then, both inferences can be efficiently applied in Jatropha curcas breeding. [ABSTRACT FROM AUTHOR]

The learning automaton (LA) that simulates the interaction between an intelligent agent and a stochastic environment to learn the optimal action is an important tool in reinforcement learning. Being confronted with an unknown environment, most learning automata have more than one parameters to be tuned during a pretraining process in which the LA interacts with the environment. Only after the parameters are tuned properly, an LA can act most properly during the training procedure to obtain the optimal behavior. The cost of parameter tuning can be enormous, e.g., possibly millions of interactions are required to seek the best parameter configuration. Therefore, the parameter-free LA that uses identical parameters for every environment and saves further tuning has become the hot spot of this research. This article proposes an efficient parameter-free learning automaton (EPFLA) that depends on a separating function (SF). Taking advantage of both frequentist inference and Bayesian inference, the SF plays a dual role in the proposed scheme: 1) evaluating the difference in performance between actions in the environment and 2) exploring actions by coining an action selection strategy. A proof is provided to ensure the $\epsilon $ -optimality of EPFLA. Comprehensive comparisons verify the privileges of EPFLA over both parameter-based schemes and existing parameter-free schemes. [ABSTRACT FROM AUTHOR]

The article discusses the concept of uncertainty. Topics include the debate on the nature of probability and statistics, the so-called frequentist-Bayesian debate, comments from Larry Wasserman of Carnegie Mellon University in Pittsburgh, Pennsylvania on how it affects everyone's life, the differences between can't-know uncertainty and don't-know uncertainty, and the example of a coin flip illustrating the divergent views of frequentists and Bayesians. Also discussed is the advent of Bayesianism, how the advent of quantum theory in the early 20th century re-expressed reality in the language of frequentist probability, the strengths and weaknesses of both approaches, and their use in astrophysics and particle physics research.

Possibility theory is a computationally efficient framework for reasoning with imprecise probabilities. Before performing any possibilistic analysis, however, the (imprecise) probabilistic information about the experiment needs to be expressed in the form of a possibility distribution. In this paper, we propose a novel Imprecise Probability-to-Possibility Transformation. This method unifies many results in quantitative possibility theory concerning information modeling, data analysis, and the construction of joint distributions. Furthermore, we show how it enables new results about possibilistic information aggregation and how it may refine frequentist inference in (im-)precise statistical models. The approach is characterized by a clear distinction between the elementary events' well-known objective possibilities from quantitative possibility theory and the elementary events' subjective plausibilities, a reimagination of qualitative possibility measures, which helps overcome several non-uniqueness issues. [ABSTRACT FROM AUTHOR]

A report from the University of Canberra in Australia discusses the use of Bayesian statistics in veterinary pharmacology. The research highlights the practical utility and interpretability of Bayesian statistics in this field, as well as their ability to generate useful statistics and uncertainty statements. The report includes case studies using simulated data to demonstrate the applications of Bayesian estimation in clinical trials, pharmacodynamics, and pharmacokinetics. The research concludes that this content can serve as a starting point for researchers in veterinary pharmacology interested in using Bayesian estimation in their work. [Extracted from the article]

This article discusses the use of Bayes factors in psychology research to determine the presence or absence of an effect. It highlights two reasons for the low uptake of Bayes factors in psychology: the difficulty in specifying the range of effect sizes and the technical learning curve associated with their implementation. The authors present a case study and simulations that demonstrate a simple method for generating a range of plausible effect sizes, using both frequentist mixed-effects models and Bayesian hierarchical models. This approach provides a solution to the problem of estimating effect sizes in a principled manner. However, it should be noted that this preprint has not undergone peer review. [Extracted from the article]

This article discusses the use of statistical methods in auditing and argues that the frequentist statistical methods commonly used by auditors may not provide the statistical evidence that audit standards require. The article proposes an alternative approach called Bayesian inference, which can quantify audit evidence and align with audit standards. The authors explore the philosophical differences between frequentist and Bayesian inference, address misconceptions in the interpretation of frequentist statistical evidence, and introduce the Bayes factor as a tool for obtaining and interpreting statistical evidence. It is important to note that this preprint has not yet undergone peer review. [Extracted from the article]

Calibration inductive logics are based on accepting estimates of relative frequencies, which are used to generate imprecise probabilities. In turn, these imprecise probabilities are intended to guide beliefs and decisions — a process called "calibration". Two prominent examples are Henry E. Kyburg's system of Evidential Probability and Jon Williamson's version of Objective Bayesianism. There are many unexplored questions about these logics. How well do they perform in the short-run? Under what circumstances do they do better or worse? What is their performance relative to traditional Bayesianism? In this article, we develop an agent-based model of a classic binomial decision problem, including players based on variations of Evidential Probability and Objective Bayesianism. We compare the performances of these players, including against a benchmark player who uses standard Bayesian inductive logic. We find that the calibrated players can match the performance of the Bayesian player, but only with particular acceptance thresholds and decision rules. Among other points, our discussion raises some challenges for characterising "cautious" reasoning using imprecise probabilities. Thus, we demonstrate a new way of systematically comparing imprecise probability systems, and we conclude that calibration inductive logics are surprisingly promising for making decisions. [ABSTRACT FROM AUTHOR]

A software tool, computing observed and expected upper limits on Poissonian process rates using a hybrid frequentist-Bayesian C L s method, is presented. This tool can be used for simple counting experiments where only signal, background and observed yields are provided or for multi-bin experiments where binned distributions of discriminating variables are provided. It allows the combination of several channels and takes into account statistical and systematic uncertainties, as well as correlations of systematic uncertainties between channels. It has been validated against other software tools and analytical calculations, for several realistic cases. Program summary Program Title: OpTHyLiC Program Files doi: http://dx.doi.org/10.17632/2jv8ytrhcg.1 Licensing provisions: GPLv3 Programming language: C++ Supplementary material: http://opthylic.in2p3.fr Nature of problem: computation of limits on Poissonian process rates in presence of background when no signal is observed, taking correctly into account statistical and systematic uncertainties, in particular correlations of systematic uncertainties between samples and channels. Solution method: a C++ library to be used together with the ROOT C++ package, using a hybrid frequentist-Bayesian C L s method; the optimisation of the program typically reduces the limit computation time down to less than a few minutes in realistic cases. Additional comments including Restrictions and Unusual features: the ROOT software is necessary. [ABSTRACT FROM AUTHOR]

Aubrey Clayton B Softcover: b 360 pages B Publisher: b Columbia University Press, 2021 B ISBN: b 978-0-231-19994-0 I Reviewed by Eric-Jan Wagenmakers i If Ed Jaynes were to rise from the grave to lambast frequentist statistics one last time, I Bernoulli's Fallacy i is the kind of book he would want to write. For instance, the author dislikes null-hypothesis testing because, supposedly, the null is never exactly true. Along the way, the author explains the nature of probability, Bayesian reasoning (with its "pathway probabilities"), the birth of frequentism, and more. [Extracted from the article]

For estimating a bounded normal mean with known variance, we exhibit situations of pronounced discrepancy between the credibility of Bayes credible regions and frequentist coverage. Analogously, frequentist confidence intervals are shown to have credibility one in some cases. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the Bayesian inference of the linear hazard rate (LHR) distribution under a progressively censoring scheme. A unified treatment of both Type I and Type II censoring is presented under independent gamma priors for the parameters, that yields the posteriors as mixtures of gamma. The priors are motivated from a probability matching viewpoint. Along with marginal inference and prediction, a joint credible set is constructed utilizing the posterior distribution of certain quantities of interest. The Bayesian inference demonstrates an intimate connection with the frequentist inference results under a Type-II censoring scheme. Bayesian planning strategies are explored that search for the optimal progressive censoring schemes under a variance criterion as well as a criterion based on the length of a credible interval for percentiles. [Copyright &y& Elsevier]

Abstract: In this paper, a new approximation of the marginal posterior distribution function is obtained. Moreover, for the location-scale model, by applying the shrinkage argument, a new approximation of the conditional distribution function of the signed likelihood ratio statistic given an ancillary statistic is derived from the approximated marginal posterior distribution. [Copyright &y& Elsevier]

Abstract: This paper studies generalized linear mixed models (GLMMs) with two components of dispersion. The frequentist analysis of linear mixed model (LMM), and particularly of GLMM, is computationally difficult. On the other hand, the advent of the Markov chain Monte Carlo algorithm has made the Bayesian analysis of LMM and GLMM computationally convenient. The recent introduction of the method of data cloning has made frequentist analysis of mixed models also equally computationally convenient. We use data cloning to conduct frequentist analysis of GLMMs with two components of dispersion based on maximum likelihood estimation (MLE). The resultant estimators of the model parameters are efficient. We discuss the performance of the MLE using the well known salamander mating data, and also through simulation studies. [Copyright &y& Elsevier]

Abstract: Multivariate time series are ubiquitous among a broad array of applications and often include both categorical and continuous series. Further, in many contexts, the continuous variable behaves nonlinearly conditional on a categorical time series. To accommodate the complexity of this structure, we propose a multi-regime smooth transition model where the transition variable is derived from the categorical time series and the degree of smoothness in transitioning between regimes is estimated from the data. The joint model for the continuous and ordinal time series is developed using a Bayesian hierarchical approach and thus, naturally, quantifies different sources of uncertainty. Additionally, we allow a general number of regimes in the smooth transition model and, for estimation, propose an efficient Markov chain Monte Carlo algorithm by blocking the parameters. Moreover, the model can be effectively used to draw inference on the behavior within and between regimes, as well as inference on regime probabilities. In order to demonstrate the frequentist properties of the proposed Bayesian estimators, we present the results of a comprehensive simulation study. Finally, we illustrate the utility of the proposed model through the analysis of two macroeconomic time series. [Copyright &y& Elsevier]

Abstract: In this paper, the reference prior is developed for a truncated model with boundaries of support as two functions of an unknown parameter. It generalizes the result obtained in a recent paper by Berger et al. (2009), in which a rigorous definition of reference priors was proposed and the prior for a uniform distribution with parameter-dependent support was derived. The assumption on the order of the derivatives of these two boundary functions, required by Berger et al. (2009), is removed. In addition, we obtain the frequentist asymptotic distribution of Bayes estimators under the squared error loss function. Comparisons of the Bayesian approach with the frequentist approach are drawn in two examples in detail. Both theoretical and numerical results indicate that the Bayesian approach, especially under the reference prior, is preferable. [Copyright &y& Elsevier]

Abstract: In this paper, objective Bayesian analysis of Pareto distributions under progressive Type-II censoring is considered. Three types of noninformative priors (Jeffreys prior, two reference priors and two general forms of second order probability matching prior) are given. We show that one of the reference priors is also the second order probability matching prior (PMP). However, this reference prior, as well as the Jeffreys prior and PMPs, are related to the censoring scheme of life tests. Thus the other reference prior is preferred, and the proprieties of the posterior are discussed based on it. The simulation shows that the second reference prior leads to the required frequentist property. A real data from is analyzed for the purpose of illustration. [Copyright &y& Elsevier]

The paper focuses on several misconceptions in frequentist inference that undermine the current discussions on replicability and the trustworthiness of empirical evidence, including, (a) the use/abuse of estimation-based effect sizes, (b) (mis)interpreting error probabilities as conditional on hypotheses giving rise to ostensible confusions between P (D | H 0) and P (H 0 | D) , and (c) the questionable nature of noncentrality-based Confidence Intervals (CIs). It is argued that when (a)–(c) are viewed in the context of model-based [ M θ (x) ] frequentist inference can be shown to be grounded in serious misapprehensions. In particular, it is argued that: (i) estimation-based effect sizes are based on the unwarranted claim that a point estimate θ ̂ n (x 0) approximates the 'true' value of the unknown parameter θ , (ii) frequentist error probabilities are not conditional on H 0 and H 1 since the parameters θ , in terms of which they are framed, are unknown constants, rendering both P (D | H 0) and P (H 0 | D) meaningless, and (iii) the cogency of noncentrality CIs, such as Cohen's d , is questionable because they conflate hypothetical (testing) and factual (estimation) reasoning, and as a result they ignore the duality between CIs and hypothesis testing, forfeiting optimality. The paper discusses several additional misconceptions relating to frequentist inference and proposes [i] optimal CIs for Cohen's d , and [ii] cogent testing-based effect sizes originating in the post-data severity evaluation. • Noncentrality-based confidence intervals are ill-thought out because they conflate factual reasoning (presuming θ = θ ∗ — the true value of θ) with hypothetical reasoning (presuming θ = θ 0 — a prespecified value of θ). • Error probabilities cannot be conditional on hypotheses since the latter are framed in terms of the parameter θ , which is an unknown constant in frequentist inference; θ is neither an event nor a random variable. • Estimation-based effect sizes, are based on an unwarranted claim that when θ n ̂ (X) is an optimal estimator of θ , then its estimate θ ̂ (x 0) approximates closely θ ∗ , for a large enough sample size n. • The post-data severity evaluation of testing results provides a more reliable estimate of the 'scientific effect' than estimation-based effect sizes. [ABSTRACT FROM AUTHOR]

The flux of high-energy neutrinos passing through the Earth is attenuated due to their interactions with matter. The interaction rate is determined by the neutrino interaction cross section and affects the flux arriving at the IceCube Neutrino Observatory, a cubic-kilometer neutrino detector embedded in the Antarctic ice sheet. We present a measurement of the neutrino cross section between 60 TeV and 10 PeV using the high-energy starting event (HESE) sample from IceCube with 7.5 years of data. The result is binned in neutrino energy and obtained using both Bayesian and frequentist statistics. We find it compatible with predictions from the Standard Model. While the cross section is expected to be flavor independent above 1 TeV, additional constraints on the measurement are included through updated experimental particle identification (PID) classifiers, proxies for the three neutrino flavors. This is the first such measurement to use a ternary PID observable and the first to account for neutrinos from tau decay. [ABSTRACT FROM AUTHOR]

The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has recently reported strong statistical evidence for a common-spectrum red-noise process for all pulsars, as seen in their 12.5-yr analysis for an isotropic stochastic gravitational-wave signal. However, there is currently very little evidence for quadrupolar spatial correlations across the pulsars in the array, which is needed to make a confident claim of detection of a stochastic gravitational-wave background. In this paper, we provide a "back-of-the-envelope" illustration of the NANOGrav 12.5-yr results for the nonexpert reader, using a very simple signal + noise model and frequentist statistics. We show that the current lack of evidence for spatial correlations is consistent with the magnitude of the correlation coefficients for pairs of Earth-pulsar baselines in the array and the fact that pulsar timing arrays are most likely operating in the intermediate-signal regime. We derive analytic expressions that allow one to compare the expected values of the signal-to-noise ratios for both common-spectrum and cross-correlation estimators. [ABSTRACT FROM AUTHOR]

Psychological theory should guide the method. A method should not dictate theory. Extraneous assumptions entering psychological theories through the backdoor of a method may differentially affect the analysis of different data sets. This introduces noise and jeopardizes successful replication of valid theoretical claims. Auxiliary theoretical assumptions can also bias substantive conclusions (including across replications). It is therefore becoming ever more crucial that theoretical claims genuinely represent the given theory, no more, no less. Recent work has highlighted a disconnect between some theories and their 'predictions,' questioned the scope of theories in the presence of heterogeneity in hypothetical constructs, and developed methods to avoid extraneous assumptions. This tutorial merges these strands of research using a simple, illustrated case study on formulating and testing order-constrained theories. The tutorial applies to empirical paradigms in which scholars can state ordinal constraints on the outcome probabilities for several binary variables such as binary responses or the presence/absence of symptoms, and where the collection of binary variables is associated with a finite set of distinct conditions, such as group membership, treatment condition, or discrete levels of an independent variable. The goal is to let scholars spell out very precise hypotheses that (1) areunadulterated reflections of their theory, (2) provide exceptional theoretical nuance, (3) formally accommodate substantive heterogeneity and (4) offer rigorous and strong quantitative diagnosticity. • Debias scientific hypotheses by removing auxiliary assumptions of standard methods. • Make behavioral hypotheses more replicable by better grounding them in theory. • Provide exceptional theoretical nuance while formally accommodating heterogeneity. • Leverage advanced order-constrained frequentist and Bayesian inference methods. • Make new modeling and methods accessible for a broad range of applications. [ABSTRACT FROM AUTHOR]

This note points some ambiguities in the notation adopted in “Frequentistic approximations to Bayesian prevision of exchangeable random elements” [Int. J. Approx. Reason. 78 (2016) 138–152] and provides the correct way to read those statements and proofs which are affected by the aforesaid ambiguities. [ABSTRACT FROM AUTHOR]

Gerd Gigerenzer, a psychologist and longtime science critic at the Max Planck Institute for Human Development, points to a survey published in 2002, which indicated that most professors of psychology don't know what p-values represent. In a 2004 paper titled Mindless Statistics, Gigerenzer illustrated the crux of the problem with an anecdote from the writings of physicist Richard Feynman. The psychologist didn't get the result he was looking for, but he did notice that the animals alternated directions, right-left-right-left, and asked Feynman if he could calculate the statistical significance of that result. [Extracted from the article]