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Estimating varying treatment effects in randomized trials with noncompliance is inherently challenging since variation comes from two separate sources: variation in the impact itself and variation in the compliance rate. In this setting, existing flexible machine learning methods are highly sensitive to the weak instruments problem, in which the compliance rate is (locally) close to zero. Our main methodological contribution is to present a Bayesian Causal Forest model for binary response variables in scenarios with noncompliance. By repeatedly imputing individuals' compliance types, we can flexibly estimate heterogeneous treatment effects among compliers. Simulation studies demonstrate the usefulness of our approach when compliance and treatment effects are heterogeneous. We apply the method to detect and analyze heterogeneity in the treatment effects in the Illinois Workplace Wellness Study, which not only features heterogeneous and one-sided compliance but also several binary outcomes of interest. We demonstrate the methodology on three outcomes one year after intervention. We confirm a null effect on the presence of a chronic condition, discover meaningful heterogeneity impact of the intervention on metabolic parameters though the average effect is null in classical partial effect estimates, and find substantial heterogeneity in individuals' perception of management prioritization of health and safety., Comment: 24 pages, 8 figures

We study the impact of teenage sports participation on early-adulthood health using longitudinal data from the National Study of Youth and Religion. We focus on two primary outcomes measured at ages 23--28 -- self-rated health and total score on the PHQ9 Patient Depression Questionnaire -- and control for several potential confounders related to demographics and family socioeconomic status. To probe the possibility that certain types of sports participation may have larger effects on health than others, we conduct a matched observational study at each level within a hierarchy of exposures. Our hierarchy ranges from broadly defined exposures (e.g., participation in any organized after-school activity) to narrow (e.g., participation in collision sports). We deployed an ordered testing approach that exploits the hierarchical relationships between our exposure definitions to perform our analyses while maintaining a fixed family-wise error rate. Compared to teenagers who did not participate in any after-school activities, those who participated in sports had statistically significantly better self-rated and mental health outcomes in early adulthood., Comment: The pre-analysis protocol for this study is available at arXiv:2211.02104

In the last quarter of a century, algebraic statistics has established itself as an expanding field which uses multilinear algebra, commutative algebra, computational algebra, geometry, and combinatorics to tackle problems in mathematical statistics. These developments have found applications in a growing number of areas, including biology, neuroscience, economics, and social sciences. Naturally, new connections continue to be made with other areas of mathematics and statistics. This paper outlines three such connections: to statistical models used in educational testing, to a classification problem for a family of nonparametric regression models, and to phase transition phenomena under uniform sampling of contingency tables. We illustrate the motivating problems, each of which is for algebraic statistics a new direction, and demonstrate an enhancement of related methodologies., Comment: This research was performed while the authors were visiting the Institute for Mathematical and Statistical Innovation (IMSI), which is supported by the National Science Foundation (Grant No. DMS-1929348). We participated in the long program "Algebraic Statistics and Our Changing World"

We introduce a three-step framework to determine at which pitches Major League batters should swing. Unlike traditional plate discipline metrics, which implicitly assume that all batters should always swing at (resp. take) pitches inside (resp. outside) the strike zone, our approach explicitly accounts not only for the players and umpires involved in the pitch but also in-game contextual information like the number of outs, the count, baserunners, and score. We first fit flexible Bayesian nonparametric models to estimate (i) the probability that the pitch is called a strike if the batter takes the pitch; (ii) the probability that the batter makes contact if he swings; and (iii) the number of runs the batting team is expected to score following each pitch outcome (e.g. swing and miss, take a called strike, etc.). We then combine these intermediate estimates to determine whether swinging increases the batting team's run expectancy. Our approach enables natural uncertainty propagation so that we can not only determine the optimal swing/take decision but also quantify our confidence in that decision. We illustrate our framework using a case study of pitches faced by Mike Trout in 2019.

Test log-likelihood is commonly used to compare different models of the same data or different approximate inference algorithms for fitting the same probabilistic model. We present simple examples demonstrating how comparisons based on test log-likelihood can contradict comparisons according to other objectives. Specifically, our examples show that (i) approximate Bayesian inference algorithms that attain higher test log-likelihoods need not also yield more accurate posterior approximations and (ii) conclusions about forecast accuracy based on test log-likelihood comparisons may not agree with conclusions based on root mean squared error., Comment: Presented at the ICBINB Workshop at NeurIPS 2022. This version accepted at TMLR, available at https://openreview.net/forum?id=n2YifD4Dxo

Most implementations of Bayesian additive regression trees (BART) one-hot encode categorical predictors, replacing each one with several binary indicators, one for every level or category. Regression trees built with these indicators partition the discrete set of categorical levels by repeatedly removing one level at a time. Unfortunately, the vast majority of partitions cannot be built with this strategy, severely limiting BART's ability to partially pool data across groups of levels. Motivated by analyses of baseball data and neighborhood-level crime dynamics, we overcame this limitation by re-implementing BART with regression trees that can assign multiple levels to both branches of a decision tree node. To model spatial data aggregated into small regions, we further proposed a new decision rule prior that creates spatially contiguous regions by deleting a random edge from a random spanning tree of a suitably defined network. Our re-implementation, which is available in the flexBART package, often yields improved out-of-sample predictive performance and scales better to larger datasets than existing implementations of BART., Comment: Software available at https://github.com/skdeshpande91/flexBART

We will study the impact of adolescent sports participation on early-adulthood health using longitudinal data from the National Study of Youth and Religion. We focus on two primary outcomes measured at ages 23--28 -- self-rated health and total score on the PHQ9 Patient Depression Questionnaire -- and control for several potential confounders related to demographics and family socioeconomic status. Comparing outcomes between sports participants and matched non-sports participants with similar confounders is straightforward. Unfortunately, an analysis based on such a broad exposure cannot probe the possibility that participation in certain types of sports (e.g. collision sports like football or soccer) may have larger effects on health than others. In this study, we introduce a hierarchy of exposure definitions, ranging from broad (participation in any after-school organized activity) to narrow (e.g. participation in limited-contact sports). We will perform separate matched observational studies, one for each definition, to estimate the health effects of several levels of sports participation. In order to conduct these studies while maintaining a fixed family-wise error rate, we developed an ordered testing approach that exploits the logical relationships between exposure definitions. Our study will also consider several secondary outcomes including body mass index, life satisfaction, and problematic drinking behavior.

We demonstrate how Hahn et al.'s Bayesian Causal Forests model (BCF) can be used to estimate conditional average treatment effects for the longitudinal dataset in the 2022 American Causal Inference Conference Data Challenge. Unfortunately, existing implementations of BCF do not scale to the size of the challenge data. Therefore, we developed flexBCF -- a more scalable and flexible implementation of BCF -- and used it in our challenge submission. We investigate the sensitivity of our results to the choice of propensity score estimation method and the use of sparsity-inducing regression tree priors. While we found that our overall point predictions were not especially sensitive to these modeling choices, we did observe that running BCF with flexibly estimated propensity scores often yielded better-calibrated uncertainty intervals.

As a baseball game progresses, batters appear to perform better the more times they face a particular pitcher. The apparent drop-off in pitcher performance from one time through the order to the next, known as the Time Through the Order Penalty (TTOP), is often attributed to within-game batter learning. Although the TTOP has largely been accepted within baseball and influences many managers' in-game decision making, we argue that existing approaches of estimating the size of the TTOP cannot disentangle continuous evolution in pitcher performance over the course of the game from discontinuities between successive times through the order. Using a Bayesian multinomial regression model, we find that, after adjusting for confounders like batter and pitcher quality, handedness, and home field advantage, there is little evidence of strong discontinuity in pitcher performance between times through the order. Our analysis suggests that the start of the third time through the order should not be viewed as a special cutoff point in deciding whether to pull a starting pitcher., Comment: Accepted to JQAS

We study the asymptotic properties of Deshpande et al.\ (2019)'s multivariate spike-and-slab LASSO (mSSL) procedure for simultaneous variable and covariance selection in the sparse multivariate linear regression problem. In that problem, $q$ correlated responses are regressed onto $p$ covariates and the mSSL works by placing separate spike-and-slab priors on the entries in the matrix of marginal covariate effects and off-diagonal elements in the upper triangle of the residual precision matrix. Under mild assumptions about these matrices, we establish the posterior contraction rate for the mSSL posterior in the asymptotic regime where both $p$ and $q$ diverge with $n.$ By ``de-biasing'' the corresponding MAP estimates, we obtain confidence intervals for each covariate effect and residual partial correlation. In extensive simulation studies, these intervals displayed close-to-nominal frequentist coverage in finite sample settings but tended to be substantially longer than those obtained using a version of the Bayesian bootstrap that randomly re-weights the prior. We further show that the de-biased intervals for individual covariate effects are asymptotically valid.

The multivariate regression interpretation of the Gaussian chain graph model simultaneously parametrizes (i) the direct effects of $p$ predictors on $q$ outcomes and (ii) the residual partial covariances between pairs of outcomes. We introduce a new method for fitting sparse Gaussian chain graph models with spike-and-slab LASSO (SSL) priors. We develop an Expectation Conditional Maximization algorithm to obtain sparse estimates of the $p \times q$ matrix of direct effects and the $q \times q$ residual precision matrix. Our algorithm iteratively solves a sequence of penalized maximum likelihood problems with self-adaptive penalties that gradually filter out negligible regression coefficients and partial covariances. Because it adaptively penalizes individual model parameters, our method is seen to outperform fixed-penalty competitors on simulated data. We establish the posterior contraction rate for our model, buttressing our method's excellent empirical performance with strong theoretical guarantees. Using our method, we estimated the direct effects of diet and residence type on the composition of the gut microbiome of elderly adults.