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Probabilistic models such as logistic regression, Bayesian classification, neural networks, and models for natural language processing, are increasingly more present in both undergraduate and graduate statistics and data science curricula due to their wide range of applications. In this article, we present a one-week course module for students in advanced undergraduate and applied graduate courses on variational inference, a popular optimization-based approach for approximate inference with probabilistic models. Our proposed module is guided by active learning principles: In addition to lecture materials on variational inference, we provide an accompanying class activity, an R shiny app, and guided labs based on real data applications of logistic regression and clustering documents using Latent Dirichlet Allocation with R code. The main goal of our module is to expose students to a method that facilitates statistical modeling and inference with large datasets. Using our proposed module as a foundation, instructors can adopt and adapt it to introduce more realistic case studies and applications in data science, Bayesian statistics, multivariate analysis, and statistical machine learning courses. [ABSTRACT FROM AUTHOR]

Epistemic bootstrap is a resampling algorithm that generates bootstrap real-valued samples based on some epistemic fuzzy data input. We apply this method as a universal basis for various statistical tests which can be then directly used for fuzzy random variables. Two classical goodness-of-fit tests are considered as an example to examine the suggested methodology for both synthetic and real data. The proposed approach is also compared with two other goodness-of-fit tests dedicated directly to fuzzy data.

The road passenger transportation enterprise is a complex system, requiring a clear understanding of their active safety situation (ASS), trends, and influencing factors. This facilitates transportation authorities to promptly receive signals and take effective measures. Through exploratory factor analysis and confirmatory factor analysis, we delved into potential factors for evaluating ASS and extracted an ASS index. To predict obtaining a higher ASS information rate, we compared multiple time series models, including GRU (gated recurrent unit), LSTM (long short-term memory), ARIMA, Prophet, Conv_LSTM, and TCN (temporal convolutional network). This paper proposed the WDA-DBN (water drop algorithm-Deep Belief Network) model and employed DEEPSHAP to identify factors with higher ASS information content. TCN and GRU performed well in the prediction. Compared to the other models, WDA-DBN exhibited the best performance in terms of MSE and MAE. Overall, deep learning models outperform econometric models in terms of information processing. The total time spent processing alarms positively influences ASS, while variables such as fatigue driving occurrences, abnormal driving occurrences, and nighttime driving alarm occurrences have a negative impact on ASS. [ABSTRACT FROM AUTHOR]

We propose a non‐stationary spatial model based on a normal‐inverse‐Wishart framework, conditioning on a set of nearest‐neighbors. The model, called nearest‐neighbor Gaussian process with random covariance matrices is developed for both univariate and multivariate spatial settings and allows for fully flexible covariance structures that impose no stationarity or isotropic restrictions. In addition, the model can handle duplicate observations and missing data. We consider an approach based on integrating out the spatial random effects that allows fast inference for the model parameters. We also consider a full hierarchical approach that leverages the sparse structures induced by the model to perform fast Monte Carlo computations. Strong computational efficiency is achieved by leveraging the adaptive localized structure of the model that allows for a high level of parallelization. We illustrate the performance of the model with univariate and bivariate simulations, as well as with observations from two stationary satellites consisting of albedo measurements. [ABSTRACT FROM AUTHOR]

Nesterov’s accelerated gradient (AG) is a popular technique to optimize objective functions comprising two components: a convex loss and a penalty function. While AG methods perform well for convex penalties, such as the LASSO, convergence issues may arise when it is applied to nonconvex penalties, such as SCAD. A recent proposal generalizes Nesterov’s AG method to the nonconvex setting. The proposed algorithm requires specification of several hyperparameters for its practical application. Aside from some general conditions, there is no explicit rule for selecting the hyperparameters, and how different selection can affect convergence of the algorithm. In this article, we propose a hyperparameter setting based on the complexity upper bound to accelerate convergence, and consider the application of this nonconvex AG algorithm to high-dimensional linear and logistic sparse learning problems. We further establish the rate of convergence and present a simple and useful bound to characterize our proposed optimal damping sequence. Simulation studies show that convergence can be made, on average, considerably faster than that of the conventional proximal gradient algorithm. Our experiments also show that the proposed method generally outperforms the current state-of-the-art methods in terms of signal recovery. [ABSTRACT FROM AUTHOR]

Statistical models can involve implicitly defined quantities, such as solutions to nonlinear ordinary differential equations (ODEs), that unavoidably need to be numerically approximated in order to evaluate the model. The approximation error inherently biases statistical inference results, but the amount of this bias is generally unknown and often ignored in Bayesian parameter inference. We propose a computationally efficient method for verifying the reliability of posterior inference for such models, when the inference is performed using Markov chain Monte Carlo methods. We validate the efficiency and reliability of our workflow in experiments using simulated and real data and different ODE solvers. We highlight problems that arise with commonly used adaptive ODE solvers and propose robust and effective alternatives, which, accompanied by our workflow, can now be taken into use without losing reliability of the inferences. [ABSTRACT FROM AUTHOR]

We propose a novel hybrid quantum computing strategy for parallel MCMC algorithms that generate multiple proposals at each step. This strategy makes the rate-limiting step within parallel MCMC amenable to quantum parallelization by using the Gumbel-max trick to turn the generalized accept-reject step into a discrete optimization problem. When combined with new insights from the parallel MCMC literature, such an approach allows us to embed target density evaluations within a well-known extension of Grover's quantum search algorithm. Letting P denote the number of proposals in a single MCMC iteration, the combined strategy reduces the number of target evaluations required from O (P) to O (P) . In the following, we review the rudiments of quantum computing, quantum search and the Gumbel-max trick in order to elucidate their combination for as wide a readership as possible. [ABSTRACT FROM AUTHOR]

Quantile regression is a popular method with a wide range of scientific applications, but the computation for quantile regression is challenging. Hunter and Lange proposed an MM algorithm for solving optimization problems in parametric quantile regression models. For nonparametric and semiparametric quantile regression, their algorithm can be applied to estimate unknown quantile functions in a pointwise manner. However, the resulting estimates may suffer from drawbacks like nonsmooth with discontinuous points and unstable at extreme quantile levels. To remedy the above issues, we propose a new MM algorithm and show that it yields continuous, smoother, and faster estimated quantile functions. We systematically study the new MM algorithm using the local linear quantile regression model. We prove that the proposed algorithm preserves the monotone descent property in an asymptotic sense. We then extend it to some popular nonparametric and semiparametric quantile regression models. For semiparametric models, we propose new efficient backfitting algorithms based on the new MM algorithm. Compared to traditional backfitting algorithms, the new procedures can significantly reduce computational costs for fully iterative backfitting. The performance of the proposed algorithms is demonstrated via extensive simulation studies and a real data example. for this article are available online. [ABSTRACT FROM AUTHOR]

A modern statistics or data science course aims to equip students with both conceptual and computing skills. This is a challenging task as instructors do not want to increase students’ cognitive load with new tools and technical details and have to balance limited teaching time to help students in achieving the learning outcomes of both content and tool use. Interactive tutorials, built with the R package learnr, can support student learning with progressive reveal of content, interactive code exercises, and quizzes with automatic feedback, and an interface with the potential to reduce technical burdens via deployment as a web application. We describe different use-cases for learnr tutorials including introductory and upper-level statistics and data science courses based on our own teaching experiences. We also discuss the common benefits and lessons learned from implementing and teaching with learnr tutorials.

Computing makes up a large and growing component of data science and statistics courses. Many of those courses, especially when taught by faculty who are statisticians by training, teach R as the programming language. A number of instructors have opted to build much of their teaching around use of the tidyverse. The tidyverse, in the words of its developers, "is a collection of R packages that share a high-level design philosophy and low-level grammar and data structures, so that learning one package makes it easier to learn the next" (Wickham et al. 2019). The shared principles have led to the widespread adoption of the tidyverse ecosystem. No small part of this usage is because the tidyverse tools have been intentionally designed to ease the learning process and cognitive load for users as they engage with each new piece of the larger ecosystem. Moreover, the functionality offered by the packages within the tidyverse spans the entire data science cycle, which includes data import, visualisation, wrangling, modeling, and communication. We believe the tidyverse provides an effective and efficient pathway to data science mastery for students at a variety of different levels of experience. In this paper, we introduce the tidyverse from an educator's perspective, touching on the what (a brief introduction to the tidyverse), the why (pedagogical benefits, opportunities, and challenges), the how (scoping and implementation options), and the where (details on courses, curricula, and student populations).

The road passenger transportation enterprise is a complex system, requiring a clear understanding of their active safety situation (ASS), trends, and influencing factors. This facilitates transportation authorities to promptly receive signals and take effective measures. Through exploratory factor analysis and confirmatory factor analysis, we delved into potential factors for evaluating ASS and extracted an ASS index. To predict obtaining a higher ASS information rate, we compared multiple time series models, including GRU (gated recurrent unit), LSTM (long short-term memory), ARIMA, Prophet, Conv_LSTM, and TCN (temporal convolutional network). This paper proposed the WDA-DBN (water drop algorithm-Deep Belief Network) model and employed DEEPSHAP to identify factors with higher ASS information content. TCN and GRU performed well in the prediction. Compared to the other models, WDA-DBN exhibited the best performance in terms of MSE and MAE. Overall, deep learning models outperform econometric models in terms of information processing. The total time spent processing alarms positively influences ASS, while variables such as fatigue driving occurrences, abnormal driving occurrences, and nighttime driving alarm occurrences have a negative impact on ASS.

Nonstationary Gaussian process models can capture complex spatially varying dependence structures in spatial data. However, the large number of observations in modern datasets makes fitting such models computationally intractable with conventional dense linear algebra. In addition, derivative-free or even first-order optimization methods can be slow to converge when estimating many spatially varying parameters. We present here a computational framework that couples an algebraic block-diagonal plus low-rank covariance matrix approximation with stochastic trace estimation to facilitate the efficient use of second-order solvers for maximum likelihood estimation of Gaussian process models with many parameters. We demonstrate the effectiveness of these methods by simultaneously fitting 192 parameters in the popular nonstationary model of Paciorek and Schervish using 107,600 sea surface temperature anomaly measurements. [ABSTRACT FROM AUTHOR]

This article describes new user controls for examining high-dimensional data using low-dimensional linear projections and slices. A user can interactively change the contribution of a given variable to a low-dimensional projection, which is useful for exploring the sensitivity of structure to particular variables. The user can also interactively shift the center of a slice, for example, to explore how structure changes in local subspaces. The Mathematica package as well as example notebooks are provided, which contain functions enabling the user to experiment with these new manual controls, with one specifically for exploring regions and boundaries produced by classification models. The advantage of Mathematica is its linear algebra capabilities and interactive cursor location controls. Some limited implementation has also been made available in the R package tourr. for this article are available online. [ABSTRACT FROM AUTHOR]

While many statistical approaches have tackled the problem of large spatial datasets, the issues arising from costly data movement and data storage have long been set aside. Having easy access to the data has been taken for granted and is now becoming an important bottleneck in the performance of statistical inference. As the availability of high resolution spatial data continues to grow, the need to develop efficient modeling techniques that leverage multi-processor and multi-storage capabilities is becoming a priority. To that end, the development of a distributed method to implement Nearest-Neighbor Gaussian Process (NNGP) models for spatial interpolation and inference for large datasets is of interest. The proposed framework retains the exact implementation of the NNGP while allowing for distributed or sequential computation of the posterior inference. The method allows for any choice of grouping of the data whether it is at random or by region. As a result of this new method, the NNGP model can be implemented with an even split of the computation burden with minimum overload at the master node level. [ABSTRACT FROM AUTHOR]

Despite the large body of research on missing value distributions and imputation, there is comparatively little literature with a focus on how to make it easy to handle, explore, and impute missing values in data. This paper addresses this gap. The new methodology builds upon tidy data principles, with the goal of integrating missing value handling as a key part of data analysis workflows. We define a new data structure, and a suite of new operations. Together, these provide a connected framework for handling, exploring, and imputing missing values. These methods are available in the R package naniar.

Summary: Maternal colonization by Group B Streptococcus (GBS) can lead to severe infection in neonates and has also been associated with prematurity and stillbirth. Better quantitative understanding of the trajectories of GBS carriage during pregnancy is essential for the design of informative epidemiological studies. Here, we describe analyses of published longitudinal data using Bayesian hidden Markov models, which involve the estimation of parameters related to the succession of latent states (infection status) and observations (culture positivity). In addition to quantifying infection acquisition and clearance probabilities, the statistical approach also suggests that for some longitudinal patterns of culture results, pregnant women were likely to have been GBS-colonized despite a negative diagnostic result. We believe this method, if used in future longitudinal studies of maternal GBS colonization, would improve our understanding of the pathologies linked to this bacterium and could also inform maternal GBS vaccine trial design.

The field of statistical computing is rapidly developing and evolving. Shifting away from the formerly siloed landscape of mathematics, statistics, and computer science, recent advancements in statistical computing are largely characterized by a fusing of these worlds; namely, programming, software development, and applied statistics are merging in new and exciting ways. There are numerous drivers behind this advancement, including open movement (encompassing development, science, and access), the advent of data science as a field, and collaborative problem-solving, as well as practice-altering advances in subfields such as artificial intelligence, machine learning, and Bayesian estimation. In this paper, we trace this shift in how modern statistical computing is performed, and that which has recently emerged from it. This discussion points to a future of boundless potential for the field. [ABSTRACT FROM AUTHOR]

It has become increasingly important for future business professionals to understand statistical computing methods as data science has gained widespread use in contemporary organizational decision processes in recent years. Used by scores of academics and practitioners in a variety of fields, Monte Carlo simulation is one of the most broadly applicable statistical computing methods. This article describes efforts to teach Monte Carlo simulation using Python. A series of simulation assignments are completed first in Google Sheets, as described in a previous article. Then, the same simulation assignments are completed in Python, as detailed in this article. This pedagogical strategy appears to support student learning for those who are unfamiliar with statistical computing but familiar with the use of spreadsheets. Supplementary materials for this article are available online.

Summary: Environmental data science is a multi‐disciplinary and mature field of research at the interface of statistics, machine learning, information technology, climate and environmental science. The two‐part special issue 'Environmental Data Science' comprises a set of research articles and opinion pieces led by statisticians who are at the forefront of the field. This editorial identifies and discusses common strands of research that appear in the contributions to Part 1, which largely focus on statistical methodology. These include temporal, spatial and spatio‐temporal modeling; statistical computing; machine learning and artificial intelligence; and the critical question of decision‐making in the presence of uncertainty. This editorial complements that of Part 2, which largely focuses on applications; see Burr, Newlands, and Zammit‐Mangion (2023). [ABSTRACT FROM AUTHOR]

This paper introduces the Group Linear Algorithm with Sparse Principal decomposition, an algorithm for supervised variable selection and clustering. Our approach extends the Sparse Group Lasso regularization to calculate clusters as part of the model fit. Therefore, unlike Sparse Group Lasso, our idea does not require prior specification of clusters between variables. To determine the clusters, we solve a particular case of sparse Singular Value Decomposition, with a regularization term that follows naturally from the Group Lasso penalty. Moreover, this paper proposes a unified implementation to deal with, but not limited to, linear regression, logistic regression, and proportional hazards models with right-censoring. Our methodology is evaluated using both biological and simulated data, and details of the implementation in R and hyperparameter search are discussed. [ABSTRACT FROM AUTHOR]

Customization of cardiac action potential models has become increasingly important with the recognition of patient-specific models and virtual patient cohorts as valuable predictive tools. Nevertheless, developing customized models by fitting parameters to data poses technical and methodological challenges: despite noise and variability associated with real-world datasets, traditional optimization methods produce a single "best-fit" set of parameter values. Bayesian estimation methods seek distributions of parameter values given the data by obtaining samples from the target distribution, but in practice widely known Bayesian algorithms like Markov chain Monte Carlo tend to be computationally inefficient and scale poorly with the dimensionality of parameter space. In this paper, we consider two computationally efficient Bayesian approaches: the Hamiltonian Monte Carlo (HMC) algorithm and the approximate Bayesian computation sequential Monte Carlo (ABC-SMC) algorithm. We find that both methods successfully identify distributions of model parameters for two cardiac action potential models using model-derived synthetic data and an experimental dataset from a zebrafish heart. Although both methods appear to converge to the same distribution family and are computationally efficient, HMC generally finds narrower marginal distributions, while ABC-SMC is less sensitive to the algorithmic settings including the prior distribution. [ABSTRACT FROM AUTHOR]

It has become increasingly important for future business professionals to understand statistical computing methods as data science has gained widespread use in contemporary organizational decision processes in recent years. Used by scores of academics and practitioners in a variety of fields, Monte Carlo simulation is one of the most broadly applicable statistical computing methods. This article describes efforts to teach Monte Carlo simulation using Python. A series of simulation assignments are completed first in Google Sheets, as described in a previous article. Then, the same simulation assignments are completed in Python, as detailed in this article. This pedagogical strategy appears to support student learning for those who are unfamiliar with statistical computing but familiar with the use of spreadsheets. for this article are available online. [ABSTRACT FROM AUTHOR]

Core‐periphery structure is an important network feature where the network is broken into two components: a densely connected core and a loosely connected periphery. In this work, we propose a divide‐and‐conquer algorithm to identify the core‐periphery structure in large networks. By finding this structure on much smaller sub‐samples of the network and then combining the results across sub‐samples, this method yields fast and accurate core‐periphery labels. Additionally, the method provides a measure of the statistical significance of the structure. We apply our approach to synthetic data to find the algorithm's detection limit and on a real‐world network with more than 35,000 nodes. [ABSTRACT FROM AUTHOR]

Undergraduate Bayesian education is an area that has started getting attention lately. As many educational innovations and articles are published and increasingly more teaching and learning materials are shared, statistics educators might be interested in incorporating Bayesian statistics in their undergraduate statistics and data science curriculum. In this paper, we share a succinct overview of two undergraduate Bayesian courses we have been teaching, with a comparison analysis to present the similarities and differences in our approaches. We dive deeper into various choices of Markov chain Monte Carlo estimation methods of Bayesian models with a working example and discuss their pros and cons for different learning objectives of computing that aspiring Bayesian educators might have in mind. Furthermore, we share challenges and opportunities for course development and curriculum design. The paper is suitable for aspiring Bayesian educators who are interested in learning ways to introduce Bayesian statistics to undergraduate students. [ABSTRACT FROM AUTHOR]

With the rapid development of Internet and the widespread application of distributed computing, people enjoy various conveniences while at the same time their privacy has also been threatened. Secure multiparty computation (MPC) can solve the problem of how data owners who do not trust each other jointly compute in distributed scenarios. Using MPC technique, people can not only realize data joint computing, but also ensure data privacy. In most data application scenarios, private data held by different parties can often be represented by sets. To complete the relevant statistical computations of the intersection of two private sets, we propose a suite of protocols based on MPC. These protocols can compute the statistical functions of the associated data of the intersection, including cardinality, sum, average, variance, range, and so forth, without revealing any additional information other than the result. To achieve these functions, we design a private membership test protocol with the result as the arithmetic sharing value, called the arithmetic shared private membership test (ASPMT) protocol. On the basis of the ASPMT protocol, the size and other statistics of the intersection can be computed securely and efficiently. All fundamental computations are constructed based on secret sharing and oblivious transfer techniques. Thanks to the use of precomputation technique, all protocols are highly efficient. [ABSTRACT FROM AUTHOR]

This paper proposes a new mixed-integer programming (MIP) formulation to optimize split rule selection in the decision tree induction process and develops an efficient search algorithm that is able to solve practical instances of the MIP model faster than commercial solvers. The formulation is novel for it directly maximizes the Gini reduction, an effective split selection criterion that has never been modeled in a mathematical program for its nonconvexity. The proposed approach differs from other optimal classification tree models in that it does not attempt to optimize the whole tree; therefore, the flexibility of the recursive partitioning scheme is retained, and the optimization model is more amenable. The approach is implemented in an open-source R package named bsnsing. Benchmarking experiments on 75 open data sets suggest that bsnsing trees are the most capable of discriminating new cases compared with trees trained by other decision tree codes including the rpart, C50, party, and tree packages in R. Compared with other optimal decision tree packages, including DL8.5, OSDT, GOSDT, and indirectly more, bsnsing stands out in its training speed, ease of use, and broader applicability without losing in prediction accuracy. History: Accepted by RamRamesh, Area Editor for Data Science & Machine Learning. Funding: This work was supported by the National Science Foundation Division of Civil, MechanicalandManufacturing Innovation [Grant 1944068]. Supplemental Material: Data are available at https://doi.org/10.1287/ijoc.2022.1225. [ABSTRACT FROM AUTHOR]

This study aims to identify some perceived gaps in a selection of statistical skills and software abilities of professors of education in United States colleges and universities. In addition to a general U. S. sample, a sample of education professors in Historically Black Colleges and Universities (HBCUs) was examined in order to understand their unique needs. Results showed that many professors from both samples felt they were weak in their abilities with more advanced statistical methods such as structural equation modeling and propensity score matching. Professors of education at HBCUs, however, had significant perceived skill-need methodology gaps in most of the methodologies evaluated. The general U.S. sample indicated a skill-need gap with statistical software packages such as R, and the HBCU sample indicated a skill-need gap with all five software packages evaluated (Excel, SPSS, SAS, Stata, and R). Affordable training workshops addressing the greatest areas of perceived need should be helpful in reducing this skill-need gap.

The field of statistical computing is rapidly developing and evolving. Shifting away from the formerly siloed landscape of mathematics, statistics, and computer science, recent advancements in statistical computing are largely characterized by a fusing of these worlds; namely, programming, software development, and applied statistics are merging in new and exciting ways. There are numerous drivers behind this advancement, including open movement (encompassing development, science, and access), the advent of data science as a field, and collaborative problem-solving, as well as practice-altering advances in subfields such as artificial intelligence, machine learning, and Bayesian estimation. In this paper, we trace this shift in how modern statistical computing is performed, and that which has recently emerged from it. This discussion points to a future of boundless potential for the field.

The recent advent of high-throughput sequencing technology has enabled us to study the associations between human microbiome and diseases. The DNA sequences of microbiome samples are clustered as operational taxonomic units (OTUs) according to their similarity. The OTU table containing counts of OTUs present in each sample is used to measure correlations between OTUs and disease status and find key microbes for prediction of the disease status. Various statistical methods have been proposed for such microbiome data analysis. However, none of these methods reflects the hierarchy of taxonomy information. In this paper, we propose a hierarchical structural component model for microbiome data (HisCoM-microb) using taxonomy information as well as OTU table data. The proposed HisCoM-microb consists of two layers: one for OTUs and the other for taxa at the higher taxonomy level. Then we calculate simultaneously coefficient estimates of OTUs and taxa of the two layers inserted in the hierarchical model. Through this analysis, we can infer the association between taxa or OTUs and disease status, considering the impact of taxonomic structure on disease status. Both simulation study and real microbiome data analysis show that HisCoM-microb can successfully reveal the relations between each taxon and disease status and identify the key OTUs of the disease at the same time. [ABSTRACT FROM AUTHOR]

In a world awash with data, the ability to think and compute with data has become an important skill for students in many fields. For that reason, inclusion of some level of statistical computing in many introductory-level courses has grown more common in recent years. Existing literature has documented multiple success stories of teaching statistics with R, bolstered by the capabilities of R Markdown. In this article, we present an in-class data visualization activity intended to expose students to R and R Markdown during the first week of an introductory statistics class. The activity begins with a brief lecture on exploratory data analysis in R. Students are then placed in small groups tasked with exploring a new dataset to produce three visualizations that describe particular insights that are not immediately obvious from the data. Upon completion, students will have produced a series of univariate and multivariate visualizations on a real dataset and practiced describing them.

Efforts to explain animal population cycles often invoke consumer-resource theory, which has shown that consumer-resource interactions alone can drive population cycles. Eco-evo theory instead argues that population cycles are partly driven by fluctuating selection for resistance in the resource, but support for eco-evo theory has come almost entirely from laboratory microcosms. Here we ask, Can eco-evo theory explain population cycles in the field? We compared the ability of eco-evo models and classical "eco-only" models to explain data on cycles in the insect Lymantria dispar , in which outbreaks of the insect are terminated by a fatal baculovirus. We carried out a statistical comparison of the ability of eco-only and eco-evo models to explain combined data from L. dispar outbreak cycles and baculovirus epizootics (epidemics in animals). Both models require high host variation in resistance to explain the epizootic data, but high host variation in the eco-evo model leads to consistently accurate predictions of outbreak cycles, whereas in the presence of high host variation the eco-only model can explain outbreak cycles only by invoking high levels of stochasticity, which leads to highly variable and often inaccurate predictions of outbreak cycles. Our work provides statistically robust evidence that eco-evo models can explain population cycles in the field. [ABSTRACT FROM AUTHOR]

In high-dimensional data analysis, the curse of dimensionality reasons that points tend to be far away from the center of the distribution and on the edge of high-dimensional space. Contrary to this, is that projected data tends to clump at the center. This gives a sense that any structure near the center of the projection is obscured, whether this is true or not. A geometric transformation to reverse the curse, is defined in this article, which uses radial transformations on the projected data. It is integrated seamlessly into the grand tour algorithm, and we have called it a burning sage tour, to indicate that it reverses the curse. The work is implemented into the tourr package in R. Several case studies are included that show how the sage visualizations enhance exploratory clustering and classification problems. Supplementary files for this article are available online. [ABSTRACT FROM AUTHOR]

This study aims to identify some perceived gaps in a selection of statistical skills and software abilities of professors of education in United States colleges and universities. In addition to a general U. S. sample, a sample of education professors in Historically Black Colleges and Universities (HBCUs) was examined in order to understand their unique needs. Results showed that many professors from both samples felt they were weak in their abilities with more advanced statistical methods such as structural equation modeling and propensity score matching. Professors of education at HBCUs, however, had significant perceived skillneed methodology gaps inmost of the methodologies evaluated. The general U.S. sample indicated a skillneed gap with statistical software packages such as R, and the HBCU sample indicated a skill-need gap with all five software packages evaluated (Excel, SPSS, SAS, Stata, and R). Affordable training workshops addressing the greatest areas of perceived need should be helpful in reducing this skill-need gap. [ABSTRACT FROM AUTHOR]

Gaussian processes (GPs) are a popular model for spatially referenced data and allow descriptive statements, predictions at new locations, and simulation of new fields. Often, a few parameters are sufficient to parameterize the covariance function, and maximum likelihood (ML) methods can be used to estimate these parameters from data. ML methods, however, are computationally demanding. For example, in the case of local likelihood estimation, even fitting covariance models on modest size windows can overwhelm typical computational resources for data analysis. This limitation motivates the idea of using neural network (NN) methods to approximate ML estimates. We train NNs to take moderate size spatial fields or variograms as input and return the range and noise‐to‐signal covariance parameters. Once trained, the NNs provide estimates with a similar accuracy compared to ML estimation and at a speedup by a factor of 100 or more. Although we focus on a specific covariance estimation problem motivated by a climate science application, this work can be easily extended to other, more complex, spatial problems and provides a proof‐of‐concept for this use of machine learning in computational statistics. [ABSTRACT FROM AUTHOR]

Smoothing splines provide a powerful and flexible means for nonparametric estimation and inference. With a cubic time complexity, fitting smoothing spline models to large data is computationally prohibitive. In this paper, we use the theoretical optimal eigenspace to derive a low‐rank approximation of the smoothing spline estimates. We develop a method to approximate the eigensystem when it is unknown and derive error bounds for the approximate estimates. The proposed methods are easy to implement with existing software. Extensive simulations show that the new methods are accurate, fast and compare favourably against existing methods. [ABSTRACT FROM AUTHOR]

The Hilbert–Schmidt independence criterion (HSIC) and its d‐variable extension dHSIC are measures of (joint) dependence between random variables. While combining these statistics with a permutation test has become a popular method of testing the null hypothesis of (joint) independence, it had thus far not been proved that this results in a consistent test. In this work, we provide a simple proof that the permutation test with the test statistic HSIC or dHSIC is indeed consistent when using characteristic kernels. That is, we prove that under each alternative hypothesis, the power of these permutation tests indeed converges to 1 as the sample size converges to infinity. Since the test is consistent for each number of permutations, we further give a brief discussion of how the number of permutations relates to the power of the test and how the number of permutations may be selected in practice. [ABSTRACT FROM AUTHOR]

The advancement of scientific knowledge increasingly depends on ensuring that data‐driven research is reproducible: that two people with the same data obtain the same results. However, while the necessity of reproducibility is clear, there are significant behavioral and technical challenges that impede its widespread implementation and no clear consensus on standards of what constitutes reproducibility in published research. We present fertile, an R package that focuses on a series of common mistakes programmers make while conducting data science projects in R, primarily through the RStudio integrated development environment. fertile operates in two modes: proactively, to prevent reproducibility mistakes from happening in the first place, and retroactively, analyzing code that is already written for potential problems. Furthermore, fertile is designed to educate users on why their mistakes are problematic and how to fix them. [ABSTRACT FROM AUTHOR]

We review the most important statistical ideas of the past half century, which we categorize as: counterfactual causal inference, bootstrapping and simulation-based inference, overparameterized models and regularization, Bayesian multilevel models, generic computation algorithms, adaptive decision analysis, robust inference, and exploratory data analysis. We discuss key contributions in these subfields, how they relate to modern computing and big data, and how they might be developed and extended in future decades. The goal of this article is to provoke thought and discussion regarding the larger themes of research in statistics and data science. [ABSTRACT FROM AUTHOR]

This article presents a new ensemble learning method for classification problems called projection pursuit random forest (PPF). PPF uses the PPtree algorithm where trees are constructed by splitting on linear combinations of randomly chosen variables. Projection pursuit is used to choose a projection of the variables that best separates the classes. Using linear combinations of variables to separate classes takes the correlation between variables into account which allows PPF to outperform a traditional random forest when separations between groups occurs in combinations of variables. The method presented here can be used in multi-class problems and is implemented into an R package, PPforest, which is available on CRAN. Supplementary files for this article are available online. [ABSTRACT FROM AUTHOR]

We propose a semester-long Bayesian statistics course for undergraduate students with calculus and probability background. We cultivate students’ Bayesian thinking with Bayesian methods applied to real data problems. We leverage modern Bayesian computing techniques not only for implementing Bayesian methods, but also to deepen students’ understanding of the methods. Collaborative case studies further enrich students’ learning and provide experience to solve open-ended applied problems. The course has an emphasis on undergraduate research, where accessible academic journal articles are read, discussed, and critiqued in class. With increased confidence and familiarity, students take the challenge of reading, implementing, and sometimes extending methods in journal articles for their course projects. Supplementary materials for this article are available online.

Sample survey design is a topic usually taught to students undertaking a minor or major in statistics in the latter part of their bachelor’s degree. This article describes an assessment project that fosters active learning and helps to develop a set of essential skills for statistical practice. The project is completed in pairs and submitted in two parts. This allows feedback from the first part to be acted upon for the second part. Ideally, students would gain experience sampling from an actual population. However, the time involved in obtaining approval from the university’s ethics committee may not be feasible for a short course. An alternative is to use an online virtual population such as the Islands, which provides students with an experience in setting up a sampling frame, requesting consent from potential participants, and collecting data. Proficiency in written communication and teamwork are highly valued by employers of statistics graduates. This project encourages collaborative learning in the design of the sample survey, statistical analysis of data collected, and the development of a final written report. It can easily be adapted for first year students and also be extended to suit Honors or Masters level students.

Summary: Bayes' rule is a fundamental principle that has been applied across multiple disciplines. However, few studies have addressed its origin as a cognitive strategy or the underlying basis for generalization from a small sample. Using a simple binary choice model subject to natural selection, we derive Bayesian inference as an adaptive behavior under certain stochastic environments. Such behavior emerges purely through the forces of evolution, despite the fact that our population consists of mindless individuals without any ability to reason, act strategically, or accurately encode or infer environmental states probabilistically. In addition, three specific environments favor the emergence of finite memory—those that are Markov, nonstationary, and environments where sampling contains too little or too much information about local conditions. These results provide an explanation for several known phenomena in human cognition, including deviations from the optimal Bayesian strategy and finite memory beyond resource constraints.