Abstract Shared frailty models, that is, hazard regression models for censored data including random effects acting multiplicatively on the hazard, are commonly used to analyze time-to-event data possessing a hierarchical structure. When the random effects are assumed to be normally distributed, the cluster-specific marginal likelihood has no closed-form expression. A powerful method for approximating

Abstract We introduce a pair of Shiny web applications that allow users to visualize random forest prediction intervals alongside those produced by linear regression models. The apps are designed to help undergraduate students deepen their understanding of the role that assumptions play in statistical modeling by comparing and contrasting intervals produced by regression models with those produced

ABSTRACT Modern wearable monitors and laboratory equipment allow the recording of high-frequency data that can be used to quantify human movement. However, currently, data analysis approaches in these domains remain limited. This paper proposes a new framework to analyze biomechanical patterns in sport training data recorded across multiple training sessions using multilevel functional models. We apply

Abstract We survey a range of popular generalized count distributions, investigating which (if any) can be arbitrarily underdispersed, i.e., its variance can be arbitrarily small compared to its mean. A philosophical implication is that some models failing this simple criterion should not be considered as “statistical models” according to the extendibility criterion of McCullagh (2002). Four practical

Published in The American Statistician (Vol. 76, No. 3, 2022)

Published in The American Statistician (Vol. 76, No. 3, 2022)

Published in The American Statistician (Vol. 76, No. 3, 2022)

Published in The American Statistician (Vol. 76, No. 3, 2022)

Published in The American Statistician (Vol. 76, No. 3, 2022)

Abstract A mixture of a distribution of responses from untreated patients and a shift of that distribution is a useful model for the responses from a group of treated patients. The mixture model accounts for the fact that not all the patients in the treated group will respond to the treatment and consequently their responses follow the same distribution as the responses from untreated patients. The

Hierarchical clustering is one of the standard methods taught for identifying and exploring the underlying structures that may be present within a data set. Students are shown examples in which the...

Abstract As a result of the increased emphasis on mis- and over-use of p-values in scientific research and the rise in popularity of Bayesian statistics, Bayesian education is becoming more important at the undergraduate level. With the advances in computing tools, Bayesian statistics is also becoming more accessible for undergraduates. This study focuses on analyzing Bayesian courses for undergraduates

Abstract In many moderate dimensional applications we have multiple response variables that are associated with a common set of predictors. When the main objective is prediction of the response variables, a natural question is: do multivariate regression models that accommodate dependency among the response variables improve prediction compared to their univariate counterparts? Note that in this paper

Abstract When releasing record-level data containing sensitive information to the public, the data disseminator is responsible for protecting the privacy of every record in the dataset, simultaneously preserving important features of the data for users’ analyses. These goals can be achieved by data synthesis, where confidential data are replaced with synthetic data that are simulated based on statistical

Abstract Best linear unbiased estimators (BLUE’s) are known to be optimal in many respects under normal assumptions. Since variance minimization doesn’t depend on normality and unbiasedness is often considered reasonable, many statisticians have felt that BLUE’s ought to preform relatively well in some generality. The result here considers the general linear model and shows that any measurable estimator

Abstract Kaplan and Meier’s 1958 paper developed a nonparametric estimator of the survivor function from a right-censored data set. Determining the size of the support of the estimator as a function of the sample size provides a challenging exercise for students in an advanced course in mathematical statistics. We devise two algorithms for calculating the support size and calculate the associated probability

(2022). Bayesian Analysis of Infectious Diseases: COVID-19 and Beyond. The American Statistician: Vol. 76, No. 2, pp. 199-199.

(2022). Statistics in Medicine. The American Statistician: Vol. 76, No. 2, pp. 199-200.

Abstract This note examines, at the population-level, the approach of obtaining predictors h˜(X) of a random variable Y, given the joint distribution of (Y,X), by maximizing the mapping h↦κ(Y,h(X)) for a given correlation function κ(·,·). Commencing with Pearson’s correlation function, the class of such predictors is uncountably infinite. The least-squares predictor h* is an element of this class obtained

(2022). Comment on “On Optimal Correlation-Based Prediction,” by Bottai et al. (2022). The American Statistician. Ahead of Print.

Abstract Much literature has focused on statistical inference for misclassified response variables or misclassified covariates. However, misclassification in both the response variable and the covariate has received very limited attention within applied fields and the statistics community. In situations where the response variable and the covariate are simultaneously subject to misclassification errors

Abstract A new transformation is proposed for treated-minus-control matched pair differences that leaves the center of their distribution untouched, but symmetrically and smoothly transforms and shortens the tails. In this way, the center of the distribution is interpretable, undistorted and uncompressed, yet outliers are clear and distinct along the periphery. The transformation of pair differences

Abstract The accumulation of technical knowledge is the central focus of graduate programs in statistics. However, student success does not depend solely on acquiring such knowledge. Rather, students must also understand the rigors of graduate study to complete their degree. And, they need to understand the statistics profession to prepare for a career after graduation. The purpose of the one-credit

Abstract For many decades now, Bayesian Model Averaging (BMA) has been a popular framework to systematically account for model uncertainty that arises in situations when multiple competing models are available to describe the same or similar physical process. The implementation of this framework, however, comes with a multitude of practical challenges including posterior approximation via Markov Chain

Abstract We adapt the social game “Two truths and a lie” to a classroom setting to give an activity that introduces principles of statistical measurement, uncertainty, prediction, and calibration, while giving students an opportunity to meet each other. We discuss how this activity can be used in a range of different statistics courses.

Abstract Double blind randomized controlled trials are traditionally seen as the gold standard for causal inferences as the difference-in-means estimator is an unbiased estimator of the average treatment effect in the experiment. The fact that this estimator is unbiased over all possible randomizations does not, however, mean that any given estimate is close to the true treatment effect. Similarly

Abstract A number of standard textbooks that are followed in a junior/senior level course or in a first-year graduate level course in mathematical statistics and probability, routinely include one single basic illustration, obviously in its variant forms, to highlight an important point: pairwise independence may not imply (mutual) independence. We earnestly believe that beginning students appreciate

Abstract We consider the truncated geometric distribution and analyze the condition under which a nontrivial maximum likelihood (ML) estimator of the parameter p exists. Additionally, the uniqueness criterion of such an ML estimator is also investigated. Our results indicate that in order to ensure the existence of a nontrivial ML estimator, the sample mean should be smaller than the midpoint of the

Abstract Posterior uncertainty is typically summarized as a credible interval, an interval in the parameter space that contains a fixed proportion—usually 95%—of the posterior’s support. For multivariate parameters, credible sets perform the same role. There are of course many potential 95% intervals from which to choose, yet even standard choices are rarely justified in any formal way. In this article

Abstract An important step for any causal inference study design is understanding the distribution of the subjects in terms of measured baseline covariates. However, not all baseline variation is equally important. We propose a set of visualizations that reduce the space of measured covariates into two components of baseline variation important to the design of an observational causal inference study:

Abstract In a celebrated paper, Schervish [1996] showed that, for testing interval null hypotheses, tests typically viewed as optimal can be logically incoherent. Specifically, one may fail to reject a specific interval null, but nevertheless – testing at the same level with the same data – reject a larger null, in which the original one is nested. This result has been used to argue against the widespread

Abstract The power prior and its variations have been proven to be a useful class of informative priors in Bayesian inference due to their flexibility in incorporating the historical information by raising the likelihood of the historical data to a fractional power δ. The derivation of the marginal likelihood based on the original power prior, and its variation, the normalized power prior, introduces

Abstract Although it is a widely used – and misused – discrete distribution, textbooks tend to give the history of the Poisson distribution short shrift, typically deriving it in the abstract as a limiting case of a binomial. The biological and physical scientists who independently derived it using space and time considerations and used it in their work are seldom mentioned. Nor are the difficulties

Abstract Entity resolution (ER), comprising record linkage and de-duplication, is the process of merging noisy databases in the absence of unique identifiers to remove duplicate entities. One major challenge of analysis with linked data is identifying a representative record among determined matches to pass to an inferential or predictive task, referred to as the downstream task. Additionally, incorporating

(2022). The Impact of Application of the Jackknife to the Sample Median. The American Statistician: Vol. 76, No. 2, pp. 201-201.

Abstract Pearson’s correlation coefficient is considered a measure of linear association between bivariate random variables X and Y. It is recommended not to use it for other forms of associations. Indeed, for nonlinear monotonic associations alternative measures like Spearman’s rank and Kendall’s tau correlation coefficients are considered more appropriate. These views or opinions on the estimation

(2022). Do Dice Play God? The Mathematics of Uncertainty, by Ian Stewart. The American Statistician: Vol. 76, No. 1, pp. 85-85.

(2022). Exploratory Data Analysis with MATLAB, 3rd ed., by Wendy L. Martinez, Angel R. Martinez, and Jeffrey L. Solka. The American Statistician: Vol. 76, No. 1, pp. 85-86.

(2022). The Phantom Pattern Problem: The Mirage of Big Data, The American Statistician: Vol. 76, No. 1, pp. 86-87.

(2022). Statistics for Making Decisions, The American Statistician: Vol. 76, No. 1, pp. 87-88.

(2022). A Connection Between Baseball and Clinical Trials Found in “Slugging Percentage is Not a Percentage—And Why That Matters”. The American Statistician: Vol. 76, No. 1, pp. 89-89.

Abstract Evaluation of treatment effects and more general estimands is typically achieved via parametric modeling, which is unsatisfactory since model misspecification is likely. Data-adaptive model building (e.g., statistical/machine learning) is commonly employed to reduce the risk of misspecification. Naïve use of such methods, however, delivers estimators whose bias may shrink too slowly with sample

Abstract When New York City (NYC) became an epicenter of the COVID-19 pandemic in the spring of 2020, statistical consulting centers at academic medical institutions in the area were immediately inundated with requests from hospital leadership and researchers for methodological support to address different aspects of the outbreak. Statisticians suddenly had to pivot from their usual responsibilities

Abstract A Bayes factor is proposed for testing whether the effect of a key predictor variable on a dependent variable is linear or nonlinear, possibly while controlling for certain covariates. The test can be used (i) in substantive research for assessing the nature of the relationship between certain variables based on scientific expectations, and (ii) for statistical model building to infer whether

Abstract This article establishes a statistical basis for an evidence-reporting strategy that interprets strength of evidence in terms of a reduction in the size of a pool of relevant conceptual objects. The strategy is motivated by debates in forensic science, wherein the pool would consist of sources of forensic material. An advantage of using the pool-reduction strategy is that it highlights uncertainty

ABSTRACT Many approaches for solving problems in business and industry are based on analytics and statistical modelling. Analytical problem solving is driven by the modelling of relationships between dependent (Y) and independent (X) variables, and we discuss three frameworks for modelling such relationships: cause-and-effect modelling, popular in applied statistics and beyond, correlational predictive

Abstract Spatial confounding, where the inclusion of a spatial random effect introduces multicollinearity with spatially structured covariates, is a contentious and active area of research in spatial statistics. However, the majority of research into this topic has focused on the case of spatial mixed models. In this article, we demonstrate that spatial confounding can also arise in the setting of

Abstract The exponential and geometric distribution are well-known continuous and discrete family of distributions with the memoryless property, respectively. The memoryless property is emphasized in introductory probability and statistics textbooks even though no distribution beyond these two families of distributions has been explored in detail. By examining the relationship between these two families

Abstract Health inequities are assessed by health departments to identify social groups disproportionately burdened by disease and by academic researchers to understand how social, economic, and environmental inequities manifest as health inequities. To characterize inequities, group-specific small-area health data are often modeled using log-linear generalized linear models (GLM) or generalized linear

ABSTRACT Recently, online-controlled experiments (i.e., A/B tests) have become an extremely valuable tool used by internet and technology companies for purposes of advertising, product development, product improvement, customer acquisition, and customer retention to name a few. The data-driven decisions that result from these experiments have traditionally been informed by null hypothesis significance

Abstract Recent literature has shown that statistically significant results are often not replicated because the “p-value < 0.05” publication rule results in a high false positive rate (FPR) or false discovery rate (FDR) in some scientific communities. While recommendations to address the phenomenon vary, many amount to incorporating additional study summary information, such as prior null hypothesis

ABSTRACT For multiple comparisons in analysis of variance, the practitioners’ handbooks generally advocate standard methods such as Bonferroni, or an F-test followed by Tukey’s honest significant difference method. These methods are known to be suboptimal compared to closed testing procedures, but improved methods can be complex in the general multigroup set-up. In this note, we argue that the case

ABSTRACT Differentiable programming has recently received much interest as a paradigm that facilitates taking gradients of computer programs. While the corresponding flexible gradient-based optimization approaches so far have been used predominantly for deep learning or enriching the latter with modeling components, we want to demonstrate that they can also be useful for statistical modeling per se

Abstract Despite the efficiency and scalability of machine learning systems, recent studies have demonstrated that many classification methods, especially deep neural networks (DNNs), are vulnerable to adversarial examples; i.e., examples that are carefully crafted to fool a well-trained classification model while being indistinguishable from natural data to human. This makes it potentially unsafe

Abstract We consider settings where an analyst of multiply imputed data desires an integer-valued point estimate and an associated interval estimate, for example, a count of the number of individuals with certain characteristics in a population. Even when the point estimate in each completed dataset is an integer, the multiple imputation point estimator, i.e., the average of these completed-data estimators

Abstract We improve students’ understanding of the F-test for linear hypotheses in a linear model by explaining elements that affect the power of the test. Including true restrictions in a joint null hypothesis affects test power in a way that is not generally known. Asking a student whether including the true restrictions in the null hypothesis will increase or decrease power, the student is likely

(2021). Beyond Multiple Linear Regression: Applied Generalized Linear Models and Multilevel Models in R. The American Statistician: Vol. 75, No. 4, pp. 450-451.

(2021). Probability and Statistical Inference: From Basic Principles to Advanced Models. The American Statistician: Vol. 75, No. 4, pp. 451-453.

(2021). Textual Data Science with R. The American Statistician: Vol. 75, No. 4, pp. 453-454.

(2021). Letter to the Editor: Zhang, J. (2021), “The Mean Relative Entropy: An Invariant Measure of Estimation Error,” The American Statistician, 75, 117–123: comment by Vos and Wu. The American Statistician: Vol. 75, No. 4, pp. 455-457.