Online decision making aims to learn the optimal decision rule by making personalized decisions and updating the decision rule recursively. It has become easier than before with the help of big data, but new challenges also come along. Since the decision rule should be updated once per step, an offline update which uses all the historical data is inefficient in computation and storage. To this end

Prior distributions for high-dimensional linear regression require specifying a joint distribution for the unobserved regression coefficients, which is inherently difficult. We instead propose a new class of shrinkage priors for linear regression via specifying a prior first on the model fit, in particular, the coefficient of determination, and then distributing through to the coefficients in a novel

Determining the number of common factors is an important and practical topic in high-dimensional factor models. The existing literature is mainly based on the eigenvalues of the covariance matrix. Owing to the incomparability of the eigenvalues of the covariance matrix caused by the heterogeneous scales of the observed variables, it is not easy to find an accurate relationship between these eigenvalues

Balancing important covariates is often critical in clinical trials and causal inference. Stratified permuted block (STR-PB) and covariate-adaptive randomization (CAR) procedures are widely used to balance observed covariates in practice. The balance properties of these procedures with respect to the observed covariates have been well studied. However, it has been questioned whether these methods will

Bridge sampling is an effective Monte Carlo method for estimating the ratio of normalizing constants of two probability densities, a routine computational problem in statistics, physics, chemistry, and other fields. The Monte Carlo error of the bridge sampling estimator is determined by the amount of overlap between the two densities. In the case of uni-modal densities, Warp-I, II, and III transformations

We consider in this paper detection of signal regions associated with disease outcomes in whole genome association studies. Gene- or region-based methods have become increasingly popular in whole genome association analysis as a complementary approach to traditional individual variant analysis. However, these methods test for the association between an outcome and the genetic variants in a pre-specified

Multidimensional function data arise from many fields nowadays. The covariance function plays an important role in the analysis of such increasingly common data. In this paper, we propose a novel nonparametric covariance function estimation approach under the framework of reproducing kernel Hilbert spaces (RKHS) that can handle both sparse and dense functional data. We extend multilinear rank structures

Understanding how adult humans learn nonnative speech categories such as tone information has shed novel insights into the mechanisms underlying experience-dependent brain plasticity. Scientists have traditionally examined these questions using longitudinal learning experiments under a multi-category decision making paradigm. Drift-diffusion processes are popular in such contexts for their ability

Individualized treatment rules (ITRs) recommend treatment according to patient characteristics. There is a growing interest in developing novel and efficient statistical methods in constructing ITRs. We propose an improved doubly robust estimator of the optimal ITRs. The proposed estimator is based on a direct optimization of an augmented inverse-probability weighted estimator of the expected clinical

The stochastic block model is widely used for detecting community structures in network data. How to test the goodness of fit of the model is one of the fundamental problems and has gained growing interests in recent years. In this article, we propose a novel goodness-of-fit test based on the maximum entry of the centered and rescaled adjacency matrix for the stochastic block model. One noticeable

Monitoring large-scale datastreams with limited resources has become increasingly important for real-time detection of abnormal activities in many applications. Despite the availability of large datasets, the challenges associated with designing an efficient change-detection when clustering or spatial pattern exists are not yet well addressed. In this paper, a design-adaptive testing procedure is developed

A dynamic treatment regime (DTR) is a sequence of decision rules that adapt to the time-varying states of an individual. Black-box learning methods have shown great potential in predicting the optimal treatments; however, the resulting DTRs lack interpretability, which is of paramount importance for medical experts to understand and implement. We present a stochastic tree-based reinforcement learning

We introduce a statistical graphical model for multivariate functional data, which are common in medical applications such as EEG and fMRI. Recently published functional graphical models rely on the multivariate Gaussian process assumption, but we relax it by introducing the Functional Copula Gaussian Graphical Model (FCGGM). This model removes the marginal Gaussian assumption but retains the simplicity

For many mental disorders, latent mental status from multiple-domain psychological or clinical symptoms may perform as a better characterization of the underlying disorder status than a simple summary score of the symptoms, and they may also serve as more reliable and representative features to differentiate treatment responses. Therefore, in order to address the complexity and heterogeneity of treatment

What is the premium on house price for a particular school district? To estimate this in New York City we use a novel implementation of a Geographic Regression Discontinuity Design (GeoRDD) built from Gaussian processes regression (kriging) to model spatial structure. With a GeoRDD, we specifically examine price differences along borders between “treatment” and “control” school districts. GeoRDDs extend

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(2020). Statistical Computing With R. Journal of the American Statistical Association: Vol. 115, No. 531, pp. 1557-1558.

(2020). Time Series Clustering and Classification. Journal of the American Statistical Association: Vol. 115, No. 531, pp. 1558-1558.

Due to the recent advancements in wearables and sensing technology, health scientists are increasingly developing mobile health (mHealth) interventions. In mHealth interventions, mobile devices are used to deliver treatment to individuals as they go about their daily lives. These treatments are generally designed to impact a near time, proximal outcome such as stress or physical activity. The mHealth

We introduce Bayesian additive regression trees (BART) for log-linear models including multinomial logistic regression and count regression with zero-inflation and overdispersion. BART has been applied to nonparametric mean regression and binary classification problems in a range of settings. However, existing applications of BART have been mostly limited to models for Gaussian “data”, either observed

We derive new variance formulas for inference on a general class of estimands of causal average treatment effects in a randomized control trial. We generalize the seminal work of Robins and show that when the researcher’s objective is inference on sample average treatment effect of the treated (SATT), a consistent variance estimator exists. Although this estimand is equal to the sample average treatment

By mixing the target posterior distribution with a surrogate distribution, of which the normalizing constant is tractable, we propose a method for estimating the marginal likelihood using the Wang-Landau algorithm. We show that a faster convergence of the proposed method can be achieved via the momentum acceleration. Two implementation strategies are detailed: (i) facilitating global jumps between

One fundamental statistical question for research areas such as precision medicine and health disparity is about discovering effect modification of treatment or exposure by observed covariates. We propose a semiparametric framework for identifying such effect modification. Instead of using the traditional outcome models, we directly posit semiparametric models on contrasts, or expected differences

Methods for inferring average causal effects have traditionally relied on two key assumptions: (i) the intervention received by one unit cannot causally influence the outcome of another; and (ii) units can be organized into non-overlapping groups such that outcomes of units in separate groups are independent. In this paper, we develop new statistical methods for causal inference based on a single realization

K-fold cross-validation (CV) with squared error loss is widely used for evaluating predictive models, especially when strong distributional assumptions cannot be taken. However, CV with squared error loss is not free from distributional assumptions, in particular in cases involving non-i.i.d. data. This paper analyzes CV for correlated data. We present a criterion for suitability of standard CV in

Although increasingly used as a data resource for assembling cohorts, electronic health records (EHRs) pose many analytic challenges. In particular, a patient’s health status influences when and what data are recorded, generating sampling bias in the collected data. In this paper, we consider recurrent event analysis using EHR data. Conventional regression methods for event risk analysis usually require

Hierarchical classification problems are commonly seen in practice. However, most existing methods do not fully utilize the hierarchical information among class labels. In this paper, a novel label embedding approach is proposed, which keeps the hierarchy of labels exactly, and reduces the complexity of the hypothesis space significantly. Based on the newly proposed label embedding approach, a new

The venerable method of maximum likelihood has found numerous recent applications in nonparametric estimation of regression and shape constrained densities. For mixture models the nonparametric maximum likelihood estimator (NPMLE) of Kiefer and Wolfowitz (1956) plays a central role in recent developments of empirical Bayes methods. The NPMLE has also been proposed by Cosslett (1983) as an estimation

Comparative biologists are often interested in inferring covariation between multiple biological traits sampled across numerous related taxa. To properly study these relationships, we must control for the shared evolutionary history of the taxa to avoid spurious inference. An additional challenge arises as obtaining a full suite of measurements becomes increasingly difficult with increasing taxa. This

We develop a causal inference approach to estimate the number of adverse health events that were prevented due to changes in exposure to multiple pollutants attributable to a large-scale air quality intervention/regulation, with a focus on the 1990 Clean Air Act Amendments (CAAA). We introduce a causal estimand called the Total Events Avoided (TEA) by the regulation, defined as the difference in the

Health care payments are an important component of health care utilization and are thus a major focus in health services and health policy applications. However, payment outcomes are semi-continuous in that over a given period of time some patients incur no payments and some patients incur large costs. Individualized treatment rules (ITRs) are a major part of the push for tailoring treatments and interventions

Climate field reconstructions (CFR) attempt to estimate spatiotemporal fields of climate variables in the past using climate proxies such as tree rings, ice cores, and corals. Data Assimilation (DA) methods are a recent and promising new means of deriving CFRs that optimally fuse climate proxies with climate model output. Despite the growing application of DA-based CFRs, little is understood about

In this paper, we study low rank high dimensional multivariate linear models (LRMLM) for high dimensional multi-response data. We propose an intuitively appealing estimation approach, and develop an algorithm for implementation purposes. Asymptotic properties are established in order to justify the estimation procedure theoretically. Intensive simulation studies are also conducted to demonstrate performance

Modern statistical analyses often involve testing large numbers of hypotheses. In many situations, these hypotheses may have an underlying tree structure that both helps determine the order that tests should be conducted but also imposes a dependency between tests that must be accounted for. Our motivating example comes from testing the association between a trait of interest and groups of microbes

It is common in modern prediction problems for many predictor variables to be counts of rarely occurring events. This leads to design matrices in which many columns are highly sparse. The challenge posed by such “rare features” has received little attention despite its prevalence in diverse areas, ranging from natural language processing (e.g., rare words) to biology (e.g., rare species). We show,

Astrophysicists are interested in recovering the 3D gas emissivity of a galaxy cluster from a 2D telescope image. Blurring and point sources make this inverse problem harder to solve. The conventional approach requires in a first step to identify and mask the point sources. Instead we model all astrophysical components in a single Poisson generalized linear model. To enforce sparsity on the parameters

Genetics plays a role in age-related macular degeneration (AMD), a common cause of blindness in the elderly. There is a need for powerful methods for carrying out region-based association tests between a dichotomous trait like AMD and genetic variants on family data. Here we apply our new generalized functional linear mixed models (GFLMM) developed to test for gene-based association in a set of AMD

Partial association refers to the relationship between variables Y1,Y2,…,YK while adjusting for a set of covariates X={X1,…,Xp}. To assess such an association when Yk’s are recorded on ordinal scales, a classical approach is to use partial correlation between the latent continuous variables. This so-called polychoric correlation is inadequate, as it requires multivariate normality and it only reflects

Recent development in the data-driven decision science has seen great advances in individualized decision making. Given data with individual covariates, treatment assignments and outcomes, policy makers best individualized treatment rule (ITR) that maximizes the expected outcome, known as the value function. Many existing methods assume that the training and testing distributions are the same. However

Peer effects, in which an individual’s behavior is affected by peers’ behavior, are posited by multiple theories in the social sciences. Randomized field experiments that identify peer effects, however, are often expensive or infeasible, so many studies of peer effects use observational data, which is expected to suffer from confounding. Here we show, in the context of information and media diffusion

Item nonresponse is frequently encountered in practice. Ignoring missing data can lose efficiency and lead to misleading inference. Fractional imputation is a frequentist approach of imputation for handling missing data. However, the parametric fractional imputation of Kim (2011) may be subject to bias under model misspecification. In this paper, we propose a novel semiparametric fractional imputation

Investigating the similarity and changes in brain networks under different mental conditions has become increasingly important in neuroscience research. A standard separate estimation strategy fails to pool information across networks and hence has reduced estimation accuracy and power to detect between-network differences. Motivated by a fMRI Stroop task experiment that involves multiple related tasks

There is a fast-growing literature on estimating optimal treatment regimes based on randomized trials or observational studies under a key identifying condition of no unmeasured confounding. Because confounding by unmeasured factors cannot generally be ruled out with certainty in observational studies or randomized trials subject to noncompliance, we propose a general instrumental variable approach

In this paper, the defining properties of any valid measure of the dependence between two continuous random variables are revisited and complemented with two original ones, shown to imply other usual postulates. While other popular choices are proved to violate some of these requirements, a class of dependence measures satisfying all of them is identified. One particular measure, that we call the Hellinger

We propose a generative model and an inference scheme for epidemic processes on dynamic, adaptive contact networks. Network evolution is formulated as a link-Markovian process, which is then coupled to an individual-level stochastic SIR model, in order to describe the interplay between the dynamics of the disease spread and the contact network underlying the epidemic. A Markov chain Monte Carlo framework

Model average techniques are very useful for model-based prediction. However most earlier works in this field focused on parametric models and continuous responses. In this paper, we study varying coefficient multinomial logistic models and propose a semiparametric model averaging prediction (SMAP) approach for multi-category outcomes. The proposed procedure does not need any artificial specification

The issue of spatial confounding between the spatial random effect and the fixed effects in regression analyses has been identified as a concern in the statistical literature. Multiple authors have offered perspectives and potential solutions. In this paper, for the areal spatial data setting, we show that many of the methods designed to alleviate spatial confounding can be viewed as special cases

We consider the common setting where one observes probability estimates for a large number of events, such as default risks for numerous bonds. Unfortunately, even with unbiased estimates, selecting events corresponding to the most extreme probabilities can result in systematically underestimating the true level of uncertainty. We develop an empirical Bayes approach “Excess Certainty Adjusted Probabilities”

In this paper we propose a nonparametric graphical test based on optimal matching, for assessing the equality of multiple unknown multivariate probability distributions. Our procedure pools the data from the different classes to create a graph based on the minimum non-bipartite matching, and then utilizes the number of edges connecting data points from different classes to examine the closeness between

Policy learning can be used to extract individualized treatment regimes from observational data in healthcare, civics, e-commerce, and beyond. One big hurdle to policy learning is a commonplace lack of overlap in the data for different actions, which can lead to unwieldy policy evaluation and poorly performing learned policies. We study a solution to this problem based on retargeting, that is, changing

Conventional multiple testing procedures often assume hypotheses for different features are exchangeable. However, in many scientific applications, additional covariate information regarding the patterns of signals and nulls are available. In this paper, we introduce an FDR control procedure in large-scale inference problem that can incorporate covariate information. We develop a fast algorithm to

Dietary data collected from 24-hour dietary recalls are observed with significant measurement errors. In the nonparametric curve estimation literature, much of the effort has been devoted to designing methods that are consistent under contamination by noise, and which have been traditionally applied for analysing those data. However, some foods such as alcohol or fruits are consumed only episodically

This paper considers the problem of estimating a change point in the covariance matrix in a sequence of high-dimensional vectors, where the dimension is substantially larger than the sample size. A two-stage approach is proposed to efficiently estimate the location of the change point. The first step consists of a reduction of the dimension to identify elements of the covariance matrices corresponding

Personalized policy represents a paradigm shift from one-decision-rule-for-all users to an individualized decision rule for each user. Developing personalized policy in mobile health applications imposes challenges. First, for lack of adherence, data from each user are limited. Second, unmeasured contextual factors can potentially impact on decision making. Aiming to optimize immediate rewards, we

This paper investigates the problem of testing independence of two random vectors of general dimensions. For this, we give for the first time a distribution-free consistent test. Our approach combines distance covariance with the center-outward ranks and signs developed in Hallin (2017). In technical terms, the proposed test is consistent and distribution-free in the family of multivariate distributions

This paper proposes a model-free and data-adaptive feature screening method for ultra-high dimensional data. The proposed method is based on the projection correlation which measures the dependence between two random vectors. This projection correlation based method does not require specifying a regression model, and applies to data in the presence of heavy tails and multivariate responses. It enjoys

In many social science experiments, subjects often interact with each other and as a result one unit’s treatment influences the outcome of another unit. Over the last decade, a significant progress has been made towards causal inference in the presence of such interference between units. Researchers have shown that the two-stage randomization of treatment assignment enables the identification of average

Causal inference on a population of units connected through a network often presents technical challenges, including how to account for interference. In the presence of interference, for instance, potential outcomes of a unit depend on its treatment as well as on the treatments of other units, such as its neighbors in the network. In observational studies, a further complication is that the typical

Traditional MCMC algorithms are computationally intensive and do not scale well to large data. In particular, the Metropolis-Hastings (MH) algorithm requires passing over the entire dataset to evaluate the likelihood ratio in each iteration. We propose a general framework for performing MH-MCMC using mini-batches of the whole dataset and show that this gives rise to approximately a tempered stationary

Space-filling designs are widely used in both computer and physical experiments. Column-orthogonality, maximin distance and projection uniformity are three basic and popular space-filling criteria proposed from different perspectives, but their relationships have been rarely investigated. We show that the average squared correlation metric is a function of the pairwise L2-distances between the rows