Statistical Concepts Research Articles

Irreversibility in belief dynamics: Unraveling the link to cognitive effort.

The relationship between time irreversibility in neuronal dynamics and cognitive effort is a subject of growing interest in the scientific literature. Although correlations between proxies of both concepts have been experimentally observed, the underlying precise linkage between them remains elusive. Here we investigate the case of learning in decision-making tasks; we do so by introducing a thermodynamically grounded metric-inspired by Landauer's principle-which connects time-irreversible information processing to energy consumption. Equipped with this metric, we investigate the role of macroscopic time-reversal symmetry breaking in belief dynamics for the case of an agent with finite sensitivity while performing a static two-armed bandit task-a standard setup in cognitive neuroscience. To gain insights into the belief dynamics, we analogize it to the dynamics of an active particle subject to state-dependent noise and living in a two-dimensional space. This mapping allows an analytical description of learning-induced biases. We deeply explore the case of Q-learning with forgetting the nonchosen option. In this case, learning-induced risk aversion is formally equivalent to standard thermophoresis, i.e., the net motion towards low-temperature regions. Finally, we quantify the irreversibility of belief dynamics in the steady state for different bandit configurations, sensitivity levels, and exploitative behavior. We found a strong correlation in high-sensitivity learning between heightened irreversibility in belief dynamics and improved decision-making outcomes. Notably, as the task's difficulty increases, a greater degree of irreversibility in belief dynamics becomes necessary for having superior performances; this explicitly unravels a plausible connection between time irreversibility and cognitive effort. In conclusion, our investigation reveals that irreversibility in belief dynamics bridges out-of-equilibrium statistical physics concepts and cognitive neuroscience. In decision-making contexts, this perspective offers insights into the notion of cognitive effort, suggesting a potential mechanism driving the evolution of living systems toward out-of-equilibrium structures.

Fast, approximation-free molecular simulation of the SPC/Fw water model using non-reversible Markov chains

In a world made of atoms, computer simulations of molecular systems such as proteins in water play an enormous role in science. Software packages for molecular simulation have been developed for decades. They all discretize Hamilton’s equations of motion and treat long-range potentials through cutoffs or discretization of reciprocal space. This introduces severe approximations and artifacts that must be controlled algorithmically. Here, we bring to fruition a paradigm for molecular simulation that relies on modern concepts in statistics to explore the thermodynamic equilibrium with an exact and efficient non-reversible Markov process. It is free of all discretizations, approximations, and cutoffs. We explicitly demonstrate that this approach reaches a break-even point with traditional molecular simulation performed at high precision, but without any of its approximations. We stress the potential of our paradigm for crucial applications in biophysics and other fields, and as a practical approach to molecular simulation. We set out a strategy to reach our goal of rigorous molecular simulation.

Applying the anthropological theory of didactics to enhance a multicultural approach to statistics education for engineering students

PurposeThis work aims to introduce basic principles of the Anthropological Theory of Didactics applied to enhance the multicultural sensitivity in engineering statistics classroom. The approach emphasizes understanding learners’ socio-cultural backgrounds to tailor educational practices that resonate more effectively with engineering students.Design/methodology/approachThis paper examines the application of the Anthropological Theory of Didactics within the context of statistics education for engineering students. This study aims to explore how integrating socio-cultural dimensions of learning can make teaching statistics more effective and engaging.FindingsThe application of the Anthropological Theory of Didactics reveals significant potential for enhancing the educational experience in statistics. By acknowledging and incorporating the diverse cultural perspectives of students, educators can develop teaching methods that are not only more inclusive but also more engaging. This methodology encourages a deeper connection between statistical concepts and engineering practices, aiding in the conceptualization of statistics among future engineers.Originality/valueThe paper contributes to the field by providing concrete activities and pedagogical strategies that use the Anthropological Theory of Didactics in a novel context. These activities are designed to foster a better integration of statistical education with engineering, highlighting the theory’s versatility and its relevance to modern educational challenges. This innovative approach promises to enhance how statistics is taught to engineering students, potentially leading to more profound educational outcomes and a stronger grasp of statistical applications in engineering.

Optimizing Learning: Predicting Research Competency via Statistical Proficiency

In higher education, the cultivation of research competency is pivotal for students’ critical thinking development and their subsequent transition into the professional workforce. While statistics plays a fundamental role in supporting the completion of a research project, it is often perceived as challenging, particularly by students in majors outside mathematics or statistics. The connection between students’ statistical proficiency and their research competency remains unexplored despite its significance. To address this gap, we utilize the supervised machine learning approach to predict students’ research competency as represented by their performance in a research methods class, with predictors of students’ proficiency in statistical topics. Predictors relating to students’ learning behavior in a statistics course such as assignment completion and academic dishonesty are also included as auxiliary variables. Results indicate that the three primary categories of statistical skills—namely, the understanding of statistical concepts, proficiency in selecting appropriate statistical methods, and statistics interpretation skills—can be used to predict students’ research competency as demonstrated by their final course scores and letter grades. This study advocates for strategic emphasis on the identified influential topics to enhance efficiency in developing students’ research competency. The findings could inform instructors in adopting a strategic approach to teaching the statistical component of research for enhanced efficiency.

Navigating test accuracy metrics used in diagnostic evaluation

Purpose of review Accurate diagnosis stands as the cornerstone of effective medical practice, influencing treatment decisions and patient outcomes. Additionally, grasping basic statistical concepts behind diagnostic tests is crucial for clinicians to interpret results accurately and make informed clinical judgments. This article discusses the evolution and application of diagnostic indices, using a clinical example to apply fundamental concepts. Recent findings Advances in our understanding of statistical methods are giving rise to new interpretations of diagnostic indices, altering how we relate them to test performance. These new metrics reveal previously unnoticed details within existing diagnostic measures. Consequently, these developments have been discussed and will help to increase understanding of their interpretation and utility in clinical settings. Summary This article provides a concise overview of the latest updates on diagnostic indices and stresses the importance of an updated understanding of their inter-connectedness and interpretation for optimal application to evidence-based care.

Probabilistic Models and Statistics for Electronic Financial Markets in the Digital Age

The scope of this manuscript is to review some recent developments in statistics for discretely observed semimartingales which are motivated by applications for financial markets. Our journey through this area stops to take closer looks at a few selected topics discussing recent literature. We moreover highlight and explain the important role played by some classical concepts of probability and statistics. We focus on three main aspects: Testing for jumps; rough fractional stochastic volatility; and limit order microstructure noise. We review jump tests based on extreme value theory and complement the literature proposing new statistical methods. They are based on asymptotic theory of order statistics and the Rényi representation. The second stage of our journey visits a recent strand of research showing that volatility is rough. We further investigate this and establish a minimax lower bound exploring frontiers to what extent the regularity of latent volatility can be recovered in a more general framework. Finally, we discuss a stochastic boundary model with one-sided microstructure noise for high-frequency limit order prices and its probabilistic and statistical foundation.

Revealing gene function with statistical inference at single-cell resolution.

Single-cell and spatial molecular profiling assays have shown large gains in sensitivity, resolution and throughput. Applying these technologies to specimens from human and model organisms promises to comprehensively catalogue cell types, reveal their lineage origins in development and discern their contributions to disease pathogenesis. Moreover, rapidly dropping costs have made well-controlled perturbation experiments and cohort studies widely accessible, illuminating mechanisms that give rise to phenotypes at the scale of the cell, the tissue and the whole organism. Interpreting the coming flood of single-cell data, much of which will be spatially resolved, will place a tremendous burden on existing computational pipelines. However, statistical concepts, models, tools and algorithms can be repurposed to solve problems now arising in genetic and molecular biology studies of development and disease. Here, I review how the questions that recent technological innovations promise to answer can be addressed by the major classes of statistical tools.

Inferring maximum magnitudes from the ordered sequence of large earthquakes.

The largest magnitude earthquake in a sequence is often used as a proxy for hazard estimates, as consequences are often predominately from this single event (in small seismic zones). In this article, the concept of order statistics is adapted to infer the maximum magnitude ([Formula: see text]) of an earthquake catalogue. A suite tools developed here can discern [Formula: see text] influences through hypothesis testing, quantify [Formula: see text] through maximum likelihood estimation (MLE) or select the best [Formula: see text] prediction amongst several models. The efficacy of these tools is benchmarked against synthetic and real-data tests, demonstrating their utility. Ultimately, 13 cases of induced seismicity spanning wastewater disposal, hydraulic fracturing and enhanced geothermal systems are tested for volume-based [Formula: see text]. I find that there is no evidence of volume-based processes influencing any of these cases. On the contrary, all these cases are adequately explained by an unbounded magnitude distribution. This is significant because it suggests that induced earthquake hazards should also be treated as unbounded. On the other hand, if bounded cases exist, then the tools developed here will be able to discern them, potentially changing how an operator mitigates these hazards. Overall, this suite of tools will be important for better-understanding earthquakes and managing their risks. This article is part of the theme issue 'Induced seismicity in coupled subsurface systems'.

A Cross-Sectional Study Evaluating the Basic Course in Biomedical Research Among Medical Postgraduates and Teachers.

Introduction and methodology This study aims to give feedback on the Basic Course in Biomedical Research (BCBR) program, an initiative of the National Medical Council (NMC) in collaboration with the National Institute of Epidemiology (ICMR-NIE) using the SWAYAM ("Study Webs of Active-Learning for Young Aspiring Minds") portal. The objectives of the study areto evaluate the usefulness of BCBR and the content and conduct of the BCBR program using a questionnaire among medical postgraduates and teachers. The study design used was a cross-sectional study and collected data from 392 participants who completed the BCBR program. A validated questionnaire was utilized to gather information on participant demographics, reasons for enrolment, satisfaction with course material, assignments, technical issues during exams, and perceived usefulness of the course. Results The study found a predominance of postgraduate students among participants (65.31%), reflecting their inclination towards research. Primary reasons for enrolment included institutional requirements and eligibility criteria to appear for the final postgraduate examination. Most participants utilized both videos and lecture hand-outs. This course facilitated its participants to improve their ability to conduct research by 89.03%.Feedback suggested a need for improvement in course content, particularly in simplifying statistical concepts and incorporating more interactive sessions and practical demonstrations. Conclusion The findings highlight the effectiveness of the BCBR program to up-skill the ability of participants to perform research. Overall, the study offers valuable feedback about the BCBR course.

Effectivity of the Microsoft Excel Application on Student Understanding in Statistics Courses

This research aims to test the effectiveness of the Microsoft Excel application on students' understanding of statistics courses. This research is quantitative research and descriptive data analysis, aimed at measuring students' level of understanding of various statistical concepts. Because research data is in the form of numbers, while descriptive analysis is statistics which functions to provide an overview of the object being studied. In this research, researchers used a total sampling technique where the entire population was sampled. So a sample of 22 people was obtained. For data collection, researchers used an online questionnaire method using Google form, the data obtained was analyzed using descriptive analysis. Of the 25 participants, 22 students answered the questionnaire. Respondents' answers regarding question 1, How often do students use Microsoft Excel (P1), Students who said they used Microsoft Excel several times a week and students who said they used Microsoft Excel once a month had the same percentage, namely 31.8%. Then 9.1% said they rarely use Microsoft Excel. Several things that can be concluded from this research are that it is still found that some students do not understand how to use Microsoft Excel, so there is a need for training for students to introduce and train students in the Regular B Building Engineering Education Study Program more deeply in applying Microsoft Excel in solving problems and processing data. and make it easier to complete assignments in statistics courses.

Development and application of a comprehensive glossary for the identification of statistical and methodological concepts in peer review reports

The assessment of problems identified by peer researchers during peer review is difficult because the content of these reports is typically confidential. The current study sought to construct and apply a glossary for the identification of methodological and statistical concepts mentioned in peer review reports. Three assessors created a list of 1,036 different terms in 19 categories. The glossary was tested on the confidential PEERE database, a sample of 496,928 peer review reports from various scientific disciplines. The most frequently mentioned terms were related to data presentation (found in 40.3 % of the reports) and parametric descriptive statistics (33.3 %). Review reports suggesting a rejection were more likely to mention methodological issues, whereas statistical issues were raised more frequently in review reports recommending revisions. Across disciplines, methodological issues were more frequently mentioned in social sciences (64.1 %), while health and medical sciences were more predictive for the identification of statistical issues (40.1 %). Female reviewers identified more statistical issues compared to male reviewers. These results indicate that the glossary could be used as an additional tool for the assessment of the content of peer review reports and for understanding what help authors may need in writing research articles.

Extensions of Some Statistical Concepts to the Complex Domain

This paper deals with the extension of principal component analysis, canonical correlation analysis, the Cramer–Rao inequality, and a few other statistical concepts in the real domain to the corresponding complex domain. Optimizations of Hermitian forms under a linear constraint, a bilinear form under Hermitian-form constraints, and similar maxima/minima problems in the complex domain are discussed. Some vector/matrix differential operators are developed to handle the above types of problems. These operators in the complex domain and the optimization problems in the complex domain are believed to be new and novel. These operators will also be useful in maximum likelihood estimation problems, which will be illustrated in the concluding remarks. Detailed steps are given in the derivations so that the methods are easily accessible to everyone.

Development of high school students’ conceptions of sampling distribution in the context of learning significance tests with technology

Sampling distributions are fundamental for statistical inference, yet their abstract nature poses challenges for students. This research investigates the development of high school students’ conceptions of sampling distribution through informal significance tests with the aid of digital technology. The study focuses on how technological tools contribute to forming these conceptions, guided by an emerging theory that describes this process. A workshop for high school students was organized, involving 36 participants working in pairs across four sessions, each with access to a computer. These sessions involved problem-solving activities, with the teacher introducing key concepts in the initial three sessions. The analysis, employing grounded theory, aimed to characterize the nature of students’ conceptions of sampling distribution as evident in their responses. The findings reveal a transition from empirical to informal conceptions of sampling distribution among students, facilitated by computational mediation. This transition is marked by an abstraction process that includes mathematization, processing, uncertainty/randomness, and conditional reasoning. The study underscores the role of digital simulations in teaching statistical concepts, facilitating students’ conceptual shift critical for grasping statistical inference.

Probabilistic fragility assessment of slopes considering uncertainty associated with temporal patterns of rainfall intensity

The temporal patterns of rainfall intensity, characterized by the variability of rainfall intensity over time during a single rainfall event, play a crucial role in landslide triggering and evolution. However, the influence of temporal patterns of rainfall intensity on the fragility and reliability assessment of slope instability has received limited attention. This study presents a novel methodology for probabilistic slope fragility assessment accounting for uncertainty associated with the temporal patterns of rainfall intensity. Hourly-scale random time series for the rainfall event are generated, considering uncertainties in temporal patterns of rainfall intensity, using the statistical concepts of skewness and kurtosis within the Pearson system of distributions. A time-dependent seepage-stability mechanical model coupling the finite element method and limit equilibrium method for the slope under hourly-scale rainfall time series is established. Slope fragility assessment under rainfall is conducted, accounting for uncertainties in temporal patterns of rainfall intensity based on Monte Carlo simulation. An illustrative example is provided, focusing on a hypothetical soil slope in the southeastern coastal area of China, susceptible to rainfall-induced landslides. The impact of skewness and kurtosis of rainfall time series on the slope failure probability and failure time are examined.

Effective temperatures in nonequilibrium statistical physics.

This paper summarizes two related effective-temperature analyses of nonequilibrium phenomena: first, dislocations in deforming crystals and, second, chaotic behaviors of defects in thermally driven Rayleigh-Bénard hydrodynamic systems. The results are encouraging for broader applications of this statistical concept.

Calibrating gravitational-wave search algorithms with conformal prediction

In astronomy, we frequently face the decision problem: does this data contain a signal? Typically, a statistical approach is used, which requires a threshold. The choice of threshold presents a common challenge in settings where signals and noise must be delineated, but their distributions overlap. Gravitational-wave astronomy, which has gone from the first discovery to catalogs of hundreds of events in less than a decade, presents a fascinating case study. For signals from colliding compact objects, the field has evolved from a frequentist to a Bayesian methodology. However, the issue of choosing a threshold and validating noise contamination in a catalog persists. Confusion and debate often arise due to the misapplication of statistical concepts, the complicated nature of the detection statistics, and the inclusion of astrophysical background models. We introduce conformal prediction (CP), a framework developed in machine learning to provide distribution-free uncertainty quantification to point predictors. We show that CP can be viewed as an extension of the traditional statistical frameworks whereby thresholds are calibrated such that the uncertainty intervals are statistically rigorous and the error rate can be validated. Moreover, we discuss how CP offers a framework to optimally build a metapipeline combining the outputs from multiple independent searches. We introduce CP with a toy cosmic-ray detector, which captures the salient features of most astrophysical search problems and allows us to demonstrate the features of CP in a simple context. We then apply the approach to a recent gravitational-wave mock data challenge using multiple search algorithms for compact binary coalescence signals in interferometric gravitational-wave data. Finally, we conclude with a discussion on the future potential of the method for gravitational-wave astronomy. Published by the American Physical Society 2024

Theoretical approach of hydrogen absorption isotherms on C14–Zr(Cr0.5Ni0.5)2 Laves phases

Theoretical studies on the total energy, and hydrogen absorption thermodynamics on Zr(Cr0.5Ni0.5)2 intermetallic compound were performed using absorption models on the most stable sites. In the first stage, Density Functional calculations provide the absorption energies corresponding to hydrogen in different environments. From there, 28 hydrogen absorption locations were found and the corresponding absorption energies were specifically determined. Then, with this information, a theoretical approximation based on the concept of local absorption isotherm and Fermi-Dirac statistics was applied to study the thermodynamics of the system. In this case, and due to the absence of lateral interactions, exact expressions of the thermodynamic functions can be derived. The process was monitored by following the surface coverage as a function of the chemical potential (absorption isotherm), the energy and configurational entropy of the adsorbed phase and the differential heat of absorption. Interesting behaviours were observed and discussed in terms of the absorption microscopic properties (energy distribution of the absorption sites).

High School Students’ Statistical Literacy Changes in a Flipped Classroom Environment: A Quasi-Experimental Study

Statistics in the 2018 Vietnam General Education Curriculum for Mathematics is emphasized from Grade 2 to Grade 12, helping develop students’ competences and qualities. However, students still struggle to connect and apply statistical concepts to real-life situations. This study used a flipped classroom model to teach 10th-graders statistics to develop their statistical literacy. Using a quasi-experimental design, we evaluated how the students’ statistical literacy developed as they participated in the flipped classroom. The results show that the flipped classroom improves students’ statistical literacy. All four categories of statistical literacy increased statistically significantly, including graphical displays, measures of central tendency, measures of variability, and using statistical knowledge to solve problems. The results are explained by the opportunities embedded into the program. Time outside of class was used for the students to review content and access new concepts, along with questions to demonstrate their statistical knowledge and reveal shortcomings. The students spent the most of their interaction time in class on activities to understand concepts and applied them to real-life situations. Some lessons learned from the study are discussed.

The Synergy between Machine Learning and Statistics: A Review

Underscoring the interwoven methodologies and shared objectives of Machine Learning (ML) and Statistics, this paper aims to explore the synergy between the two disciplines with the proliferation of large datasets and advanced computational power. The ability of observing accurate insights for complex datasets and addressing real world applications with sophisticated, hybrid approaches can enhance with the convergence of the ML and Statistics. Although the concepts of both disciplines started with distinct origins, two disciplines increasingly intersect, fostering methodological cross fertilization. To improve the generalization and interpretability of ML concepts, statistical techniques such as model selection and regularization can be used while ensemble methods and neural networks exemplify predictive modeling’s statistical applications. By integrating ML to address the challenges in statistics such as fairness, interpretability, robustness, and scalability, statistician can enhance the key feature of statistics more effectively. Overall, combined concepts of ML and statistics not only address the diverse analytical task but it pave the path for Artificial Intelligence and data science by highlighting the main role of their synergy in modern data exploration.

Durable Benefits of Learning-by-Teaching for Research Question Generation Performance: A Field Experiment

Generating good questions is central to scientific inquiry. How can we improve this skill in classrooms? This field experiment showed that teaching others enhances students’ ability to generate higher-order research questions that create new knowledge. Whereas learning-by-teaching often involves delivering face-to-face or video-recorded lectures, we tested its efficient implementation via writing a verbatim (i.e., word-for-word) teaching script, exactly as how one would orate a lecture. In a research and statistical methods course, 199 undergraduates studied statistical concepts by writing verbatim teaching scripts or study notes. One month later, students’ long-term learning was assessed on a high-stakes test, whereby they explained the concepts, applied them to design a study to test a given hypothesis, and generated create-level research questions about the concepts. Writing teaching scripts enhanced students’ research question generation and concept application more than writing study notes. The teaching advantage for these higher-order outcomes held although both techniques produced comparably high basic understanding when students explained the concepts at test. Further, students displayed greater generative processing, metacognitive monitoring, and social presence when writing teaching scripts than study notes. Learning-by-teaching can be leveraged in an efficient and inexpensive way via writing verbatim teaching scripts to improve meaningful, durable learning in classrooms.