Using the National Academies report, {\em Data Science for Undergraduates: Opportunities and Options}, we connect data science curricula to the more familiar pedagogy used by many mathematical scientists. We use their list of ``data acumen" components to ground a discussion, which hopes to connect data science curricula to the more familiar pedagogy used by many mathematical scientists.
Otsuka (2023) argues for a correspondence between data science and traditional epistemology: Bayesian statistics is internalist; classical (frequentist) statistics is externalist, owing to its reliabilist nature; model selection is pragmatist; and machine learning is a version of virtue epistemology. Where he sees diversity, I see an opportunity for unity. In this article, I argue that classical statistics, model selection, and machine learning share a foundation that is reliabilist in an unconventional sense that aligns with internalism. Hence a unification under internalist reliabilism.
The Taylor expansion is a widely used and powerful tool in all branches of Mathematics, both pure and applied. In Probability and Mathematical Statistics, however, a stronger version of Taylor's classical theorem is often needed, but only tacitly assumed. In this note, we provide an elementary proof of this measurable Taylor's theorem, which guarantees that the interpolating point in the Lagrange form of the remainder can be chosen to depend measurably on the independent variable.
It is recommended that teacher-scholars of data science adopt reproducible workflows in their research as scholars and teach reproducible workflows to their students. In this paper, we propose a third dimension to reproducibility practices and recommend that regardless of whether they teach reproducibility in their courses or not, data science instructors adopt reproducible workflows for their own teaching. We consider computational reproducibility, documentation, and openness as three pillars of reproducible teaching framework. We share tools, examples, and recommendations for the three pillars.
In the present paper we construct plans orthogonal through the block factor (POTBs). We describe procedures for adding blocks as well as factors to an initial plan and thus generate a bigger plan. Using these procedures we construct POTBs for symmetrical experiments with factors having three or more levels. We also construct a series of plans inter-class orthogonal through the block factor for two-level factors.
The traditional calculus-based introduction to statistical inference consists of a semester of probability followed by a semester of frequentist inference. Cobb (2015) challenges the statistical education community to rethink the undergraduate statistics curriculum. In particular, he suggests that we should focus on two goals: making fundamental concepts accessible and minimizing prerequisites to research. Using five underlying principles of Cobb, we describe a new calculus-based introduction to statistics based on simulation-based Bayesian computation.
For the estimation of a new energy supply system it is an important to have high-resolution energy load profile. Such a profile is in general either not present or very costly to obtain. We will therefore present a method which synthesizes load profiles from minimal given data, but with maximal resolution. The general initial data setting includes month integrals and load profiles a few days. The resulting time series features all important properties to represent a real energy profile.
In statistical process control, procedures are applied that require relatively strict conditions for their use. If such assumptions are violated, these methods become inefficient, leading to increased incidence of false signals. Therefore, a robust version of control charts is sought to be less sensitive with respect to a breach of normality and independence in measurements. Robust control charts, however, usually increase the delay in the detection of assignable causes. This negative effect can, to some extent, be removed with the aid of an adaptive approach.
Student's theorem is an important result in statistics which states that for normal population, the sample variance is independent from the sample mean and has a chi-square distribution. The existing proofs of this theorem either overly rely on advanced tools such as moment generating functions, or fail to explicitly construct an orthogonal matrix used in the proof. This paper provides an elegant explicit construction of that matrix, making the algebraic proof complete. The constructive algebraic proof proposed here is thus very suitable for being included in textbooks.
Harmonic, Geometric, Arithmetic, Heronian and Contraharmonic means have been studied by many mathematicians. In 2003, H. Evens studied these means from geometrical point of view and established some of the inequalities between them in using a circle and its radius. In 1961, E. Beckenback and R. Bellman introduced several inequalities corresponding to means. In this paper, we will introduce the concept of mean functions and integral means and give bounds on some of these mean functions and integral means.
Inter-Rater quantifies the reliability between multiple raters who evaluate a group of subjects. It calculates the group quantity, Fleiss kappa, and it improves on existing software by keeping information about each user and quantifying how each user agreed with the rest of the group. This is accomplished through permutations of user pairs. The software was written in Python, can be run in Linux, and the code is deposited in Zenodo and GitHub. This software can be used for evaluation of inter-rater reliability in systematic reviews, medical diagnosis algorithms, education applications, and others.
We describe a contest in variable selection which was part of a statistics course for graduate students. In particular, the possibility to create a contest themselves offered an additional challenge for more advanced students. Since working with data is becoming more important in teaching statistics, we greatly encourage other instructors to try the same.
Motivated by the interest of observing the growth of cancer cells among normal living cells and exploring how galaxies and stars are truly formed, the objective of this paper is to introduce a rigorous and effective method for counting point-masses, determining their spatial locations, and computing their attributes. Based on computation of Hermite moments that are Fourier-invariant, our approach facilitates the processing of both spatial and Fourier data in any dimension.
This paper proposes a signature-based approach for solving redundancy allocation problems when component lifetimes are not only heterogeneous but also dependent. The two common schemes for allocations, that is active and standby redundancies, are considered. If the component lifetimes are independent, the proposed approach leads to simple manipulations. Various illustrative examples are also analysed. This method can be implemented for practical complex engineering systems.
Highly Principled Data Science insists on methodologies that are: (1) scientifically justified, (2) statistically principled, and (3) computationally efficient. An astrostatistics collaboration, together with some reminiscences, illustrates the increased roles statisticians can and should play to ensure this trio, and to advance the science of data along the way.
Mark O'Connell, Catherine B. Hurley, Katarina Domijan
The condvis package is for interactive visualization of sections in data space, showing fitted models on the section, and observed data near the section. The primary goal is the interpretation of complex models, and showing how the observed data support the fitted model. There is a video accompaniment to this paper available at https://www.youtube.com/watch?v=rKFq7xwgdX0. This is a preprint version of an article to appear in the Journal of Statistical Software.
Donald Bruce Rubin is John L. Loeb Professor of Statistics at Harvard University. He has made fundamental contributions to statistical methods for missing data, causal inference, survey sampling, Bayesian inference, computing and applications to a wide range of disciplines, including psychology, education, policy, law, economics, epidemiology, public health and other social and biomedical sciences.
In this review article we present different formal frameworks for the description of generalized probabilities in statistical theories. We discuss the particular cases of probabilities appearing in classical and quantum mechanics, possible generalizations of the approaches of A. N. Kolmogorov and R. T. Cox to non-commutative models, and the approach to generalized probabilities based on convex sets.