The New England Journal of Statistics in Data Science

When testing a statistical hypothesis, is it legitimate to deliberate on the basis of initial data about whether and how to collect further data? Game-theoretic probability’s fundamental principle for testing by betting says yes, provided that you are testing the hypothesis’s predictions by betting and do not risk more capital than initially committed. Standard statistical theory uses Cournot’s principle, which does not allow such optional continuation. Cournot’s principle can be extended to allow optional continuation when testing is carried out by multiplying likelihood ratios, but the extension lacks the simplicity and generality of testing by betting.

Sequential change detection is a classical problem with a variety of applications. However, the majority of prior work has been parametric, for example, focusing on exponential families. We develop a fundamentally new and general framework for sequential change detection when the pre- and post-change distributions are nonparametrically specified (and thus composite). Our procedures come with clean, nonasymptotic bounds on the average run length (frequency of false alarms). In certain nonparametric cases (like sub-Gaussian or sub-exponential), we also provide near-optimal bounds on the detection delay following a changepoint. The primary technical tool that we introduce is called an e-detector, which is composed of sums of e-processes—a fundamental generalization of nonnegative supermartingales—that are started at consecutive times. We first introduce simple Shiryaev-Roberts and CUSUM-style e-detectors, and then show how to design their mixtures in order to achieve both statistical and computational efficiency. Our e-detector framework can be instantiated to recover classical likelihood-based procedures for parametric problems, as well as yielding the first change detection method for many nonparametric problems. As a running example, we tackle the problem of detecting changes in the mean of a bounded random variable without i.i.d. assumptions, with an application to tracking the performance of a basketball team over multiple seasons.

In this paper, we present the U.S. Mental Health Dashboard, an R Shiny web application that facilitates exploratory data analysis of U.S. mental health data collected through national surveys. Mental health affects almost every aspect of people’s lives including their social relationships, substance use, academic success, professional productivity, and physical wellness. Even so, mental illnesses are often perceived as less legitimate or serious than physical diseases, and as a result of this stigmatization, many people suffer in silence without access to proper treatment. To address the lack of accessible healthcare information related to mental illness, the U.S. Mental Health Dashboard presents dynamic visualizations, tables, and choropleth maps of the prevalence and geographic distribution of key mental health metrics based on data from the National Survey on Drug Use and Health (NSDUH) and Behavioral Risk Factor Surveillance System (BRFSS). National and state-level estimates are provided for the civilian, non-institutionalized adult population of the United States as well as within relevant demographic subpopulations. By demonstrating the pervasiveness of mental illness and stark health inequities between demographic groups, this application aims to raise mental health awareness and reduce self-blame and stigmatization, especially for individuals that may inherently be at high risk. The U.S. Mental Health Dashboard has a wide variety of potential use cases: to illustrate to individuals suffering from mental illness and those in close proximity to them that they are not alone, identify subpopulations with the biggest need for mental health care, and help epidemiologists planning studies identify the target population for specific mental illness symptoms.

We address the estimation of the Integrated Squared Error (ISE) of a predictor $\eta (x)$ of an unknown function f learned using data acquired on a given design ${\mathbf{X}_{n}}$. We consider ISE estimators that are weighted averages of the residuals of the predictor $\eta (x)$ on a set of selected points ${\mathbf{Z}_{m}}$. We show that, under a stochastic model for f, minimisation of the mean squared error of these ISE estimators is equivalent to minimisation of a Maximum Mean Discrepancy (MMD) for a non-stationary kernel that is adapted to the geometry of ${\mathbf{X}_{n}}$. Sequential Bayesian quadrature then yields sequences of nested validation designs that minimise, at each step of the construction, the relevant MMD. The optimal ISE estimate can be written in terms of the integral of a linear reconstruction, for the assumed model, of the square of the interpolator residuals over the domain of f. We present an extensive set of numerical experiments which demonstrate the good performance and robustness of the proposed solution. Moreover, we show that the validation designs obtained are space-filling continuations of ${\mathbf{X}_{n}}$, and that correct weighting of the observed interpolator residuals is more important than the precise configuration ${\mathbf{Z}_{m}}$ of the points at which they are observed.

Variable selection in large-dimensional data has been extensively studied in different settings over the past decades. In a recent article, Shokoohi et. al. [29, DOI:10.1214/18-AOAS1198] proposed a method for variable selection in finite mixture of accelerated failure time regression models for studies on time-to-event data to capture heterogeneity within the population and account for censoring. In this paper, we introduce the fmrs package, which implements the variable selection methodology for such models. Furthermore, as a byproduct, the fmrs package facilitates variable selection in finite mixture regression models. The package also incorporates a tuning parameter selection mechanism based on component-wise bic. Commonly used penalties, such as Least Absolute Shrinkage and Selection Operator, and Smoothly Clipped Absolute Deviation, are integrated into fmrs. Additionally, the package offers an option for non-mixture regression models. The C language is chosen to boost the optimization speed. We provide an overview of the fmrs principles and the strategies employed for optimization. Hands-on illustrations are presented to help users get acquainted with fmrs. Finally, we apply fmrs to a lung cancer dataset and observe that a two-component mixture model reveals a subgroup with a more aggressive form of the disease, displaying a lower survival time.

Graphical models have witnessed significant growth and usage in spatial data science for modeling data referenced over a massive number of spatial-temporal coordinates. Much of this literature has focused on a single or relatively few spatially dependent outcomes. Recent attention has focused upon addressing modeling and inference for substantially large number of outcomes. While spatial factor models and multivariate basis expansions occupy a prominent place in this domain, this article elucidates a recent approach, graphical Gaussian Processes, that exploits the notion of conditional independence among a very large number of spatial processes to build scalable graphical models for fully model-based Bayesian analysis of multivariate spatial data.

Basket trials have captured much attention in oncology research in recent years, as advances in health technology have opened up the possibility of classification of patients at the genomic level. Bayesian methods are particularly prevalent in basket trials as the hierarchical structure is adapted to basket trials to allow for information borrowing. In this article, we extend the Bayesian methods to basket trials with treatment and control arms for continuous endpoints, which are often the cases in clinical trials for rare diseases. To account for the imbalance in the covariates which are potentially strong predictors but not stratified in a randomized trial, our models make adjustments for these covariates, and allow different coefficients across baskets. In addition, comparisons are drawn between two-stage design and one-stage design for the four Bayesian methods. Extensive simulation studies are conducted to examine the empirical performance of all models under consideration. A real data analysis is carried out to further demonstrate the usefulness of the Bayesian methods.