arXiv subjects

Daniel R. Kowal

Publications and source records attributed to Daniel R. Kowal.

At least 19 recordsLinked to original sources

arXiv2026

Graph-dependent shrinkage priors for Bayesian trend filtering

Many common data dependencies can be characterized by graphs: time series data are sequential (chain graph), images appear as pixels (lattice graph), areal data are defined by neighboring units (spatial adjacency graph), etc. Graph trend filtering seeks to smooth and predict such data. However, classical trend filtering only incorporates the graph for estimation of the trend, which limits its adaptivity, and is brittle in the presence of missing data. Further, it lacks uncertainty quantification and faces certain computing challenges. We address these limitations with a comprehensive Bayesian framework for (graph-) dependent data. Our approach leverages the graph at three critical junctures: 1) the trend, to enable smoothing, imputation, and prediction; 2) the local shrinkage, to enhance adaptivity and precision; and 3) the MCMC sampling algorithm, to deliver scalable posterior (predictive) inference via sparse and banded operations. For the proposed graph-dependent shrinkage priors, we study the local concentration and adaptivity properties and establish conditions for posterior propriety. Simulation studies demonstrate that, relative to state-of-the-art frequentist and Bayesian alternatives, this framework provides more accurate point estimates, more precise interval estimates, and highly competitive computing. We apply our methods for spatio-temporal modeling and forecasting of local area unemployment data for every county in the continental U.S. during the 2020 COVID-19 unemployment shock.

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arXiv2025

Efficient Bayesian inference for two-stage models in environmental epidemiology

Statistical models often require inputs that are not completely known. This can occur when inputs are measured with error, indirectly, or when they are predicted using another model. In environmental epidemiology, air pollution exposure is a key determinant of health, yet typically must be estimated for each observational unit by a complex model. Bayesian two-stage models combine this stage-one model with a stage-two model for the health outcome given the exposure. However, analysts usually only have access to the stage-one model output without all of its specifications or input data, making joint Bayesian inference apparently intractable. We show that two prominent workarounds-using a point estimate or using the posterior from the stage-one model without feedback from the stage-two model-lead to miscalibrated inference. Instead, we propose efficient algorithms to facilitate joint Bayesian inference and provide more accurate estimates and well-calibrated uncertainties. Comparing different approaches, we investigate the association between PM2.5 exposure and county-level mortality rates in the South-Central USA.

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arXiv2025

A dynamic copula model for probabilistic forecasting of non-Gaussian multivariate time series

Multivariate time series (MTS) data often include a heterogeneous mix of non-Gaussian distributional features (asymmetry, multimodality, heavy tails) and data types (continuous and discrete variables). Traditional MTS methods based on convenient parametric distributions are typically ill-equipped to model this heterogeneity. Copula models provide an appealing alternative, but present significant obstacles for fully Bayesian inference and probabilistic forecasting. To overcome these challenges, we propose a novel and general strategy for posterior approximation in MTS copula models and apply it to a Gaussian copula built from a dynamic factor model. This framework provides scalable, fully Bayesian inference for cross-sectional and serial dependencies and nonparametrically learns heterogeneous marginal distributions. We validate this approach by establishing posterior consistency and confirm excellent finite-sample performance even under model misspecification using simulated data. We apply our method to crime count and macroeconomic MTS data and find superior probabilistic forecasting performance compared to popular MTS models. These results demonstrate that the proposed method is a versatile, general-purpose utility for probabilistic forecasting of MTS that works well across of range of applications with minimal user input.

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arXiv2024

Bayesian Functional Graphical Models with Change-Point Detection

Functional data analysis, which models data as realizations of random functions over a continuum, has emerged as a useful tool for time series data. Often, the goal is to infer the dynamic connections (or time-varying conditional dependencies) among multiple functions or time series. For this task, a dynamic and Bayesian functional graphical model is introduced. The proposed modeling approach prioritizes the careful definition of an appropriate graph to identify both time-invariant and time-varying connectivity patterns. A novel block-structured sparsity prior is paired with a finite basis expansion, which together yield effective shrinkage and graph selection with efficient computations via a Gibbs sampling algorithm. Crucially, the model includes (one or more) graph changepoints, which are learned jointly with all model parameters and incorporate graph dynamics. Simulation studies demonstrate excellent graph selection capabilities, with significant improvements over competing methods. The proposed approach is applied to study of dynamic connectivity patterns of sea surface temperatures in the Pacific Ocean and reveals meaningful edges.

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arXiv2024

Uncovering dynamics between SARS-CoV-2 wastewater concentrations and community infections via Bayesian spatial functional concurrent regression

Monitoring wastewater concentrations of SARS-CoV-2 yields a low-cost, noninvasive method for tracking disease prevalence and provides early warning signs of upcoming outbreaks in the serviced communities. There is tremendous clinical and public health interest in understanding the exact dynamics between wastewater viral loads and infection rates in the population. As both data sources may contain substantial noise and missingness, in addition to spatial and temporal dependencies, properly modeling this relationship must address these numerous complexities simultaneously while providing interpretable and clear insights. We propose a novel Bayesian functional concurrent regression model that accounts for both spatial and temporal correlations while estimating the dynamic effects between wastewater concentrations and positivity rates over time. We explicitly model the time lag between the two series and provide full posterior inference on the possible delay between spikes in wastewater concentrations and subsequent outbreaks. We estimate a time lag likely between 5 to 11 days between spikes in wastewater levels and reported clinical positivity rates. Additionally, we find a dynamic relationship between wastewater concentration levels and the strength of its association with positivity rates that fluctuates between outbreaks and non-outbreaks.

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arXiv2024

Gaussian Copula Models for Nonignorable Missing Data Using Auxiliary Marginal Quantiles

We present an approach for modeling and imputation of nonignorable missing data. Our approach uses Bayesian data integration to combine (1) a Gaussian copula model for all study variables and missingness indicators, which allows arbitrary marginal distributions, nonignorable missingess, and other dependencies, and (2) auxiliary information in the form of marginal quantiles for some study variables. We prove that, remarkably, one only needs a small set of accurately-specified quantiles to estimate the copula correlation consistently. The remaining marginal distribution functions are inferred nonparametrically and jointly with the copula parameters using an efficient MCMC algorithm. We also characterize the (additive) nonignorable missingness mechanism implied by the copula model. Simulations confirm the effectiveness of this approach for multivariate imputation with nonignorable missing data. We apply the model to analyze associations between lead exposure and end-of-grade test scores for 170,000 North Carolina students. Lead exposure has nonignorable missingness: children with higher exposure are more likely to be measured. We elicit marginal quantiles for lead exposure using statistics provided by the Centers for Disease Control and Prevention. Multiple imputation inferences under our model support stronger, more adverse associations between lead exposure and educational outcomes relative to complete case and missing-at-random analyses.

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arXiv2024

Facilitating heterogeneous effect estimation via statistically efficient categorical modifiers

Categorical covariates such as race, sex, or group are ubiquitous in regression analysis. While main-only (or ANCOVA) linear models are predominant, cat-modified linear models that include categorical-continuous or categorical-categorical interactions are increasingly important and allow heterogeneous, group-specific effects. However, with standard approaches, the addition of cat-modifiers fundamentally alters the estimates and interpretations of the main effects, often inflates their standard errors, and introduces significant concerns about group (e.g., racial) biases. We advocate an alternative parametrization and estimation scheme using abundance-based constraints (ABCs). ABCs induce a model parametrization that is both interpretable and equitable. Crucially, we show that with ABCs, the addition of cat-modifiers 1) leaves main effect estimates unchanged and 2) enhances their statistical power, under reasonable conditions. Thus, analysts can, and arguably should include cat-modifiers in linear regression models to discover potential heterogeneous effects--without compromising estimation, inference, and interpretability for the main effects. Using simulated data, we verify these invariance properties for estimation and inference and showcase the capabilities of ABCs to increase statistical power. We apply these tools to study demographic heterogeneities among the effects of social and environmental factors on STEM educational outcomes for children in North Carolina. An R package lmabc is available.

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arXiv2024

Monte Carlo inference for semiparametric Bayesian regression

Data transformations are essential for broad applicability of parametric regression models. However, for Bayesian analysis, joint inference of the transformation and model parameters typically involves restrictive parametric transformations or nonparametric representations that are computationally inefficient and cumbersome for implementation and theoretical analysis, which limits their usability in practice. This paper introduces a simple, general, and efficient strategy for joint posterior inference of an unknown transformation and all regression model parameters. The proposed approach directly targets the posterior distribution of the transformation by linking it with the marginal distributions of the independent and dependent variables, and then deploys a Bayesian nonparametric model via the Bayesian bootstrap. Crucially, this approach delivers (1) joint posterior consistency under general conditions, including multiple model misspecifications, and (2) efficient Monte Carlo (not Markov chain Monte Carlo) inference for the transformation and all parameters for important special cases. These tools apply across a variety of data domains, including real-valued, positive, and compactly-supported data. Simulation studies and an empirical application demonstrate the effectiveness and efficiency of this strategy for semiparametric Bayesian analysis with linear models, quantile regression, and Gaussian processes. The R package SeBR is available on CRAN.

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arXiv2023

Ultra-efficient MCMC for Bayesian longitudinal functional data analysis

Functional mixed models are widely useful for regression analysis with dependent functional data, including longitudinal functional data with scalar predictors. However, existing algorithms for Bayesian inference with these models only provide either scalable computing or accurate approximations to the posterior distribution, but not both. We introduce a new MCMC sampling strategy for highly efficient and fully Bayesian regression with longitudinal functional data. Using a novel blocking structure paired with an orthogonalized basis reparametrization, our algorithm jointly samples the fixed effects regression functions together with all subject- and replicate-specific random effects functions. Crucially, the joint sampler optimizes sampling efficiency for these key parameters while preserving computational scalability. Perhaps surprisingly, our new MCMC sampling algorithm even surpasses state-of-the-art algorithms for frequentist estimation and variational Bayes approximations for functional mixed models -- while also providing accurate posterior uncertainty quantification -- and is orders of magnitude faster than existing Gibbs samplers. Simulation studies show improved point estimation and interval coverage in nearly all simulation settings over competing approaches. We apply our method to a large physical activity dataset to study how various demographic and health factors associate with intraday activity.

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arXiv2023

Warped Dynamic Linear Models for Time Series of Counts

Dynamic Linear Models (DLMs) are commonly employed for time series analysis due to their versatile structure, simple recursive updating, ability to handle missing data, and probabilistic forecasting. However, the options for count time series are limited: Gaussian DLMs require continuous data, while Poisson-based alternatives often lack sufficient modeling flexibility. We introduce a novel semiparametric methodology for count time series by warping a Gaussian DLM. The warping function has two components: a (nonparametric) transformation operator that provides distributional flexibility and a rounding operator that ensures the correct support for the discrete data-generating process. We develop conjugate inference for the warped DLM, which enables analytic and recursive updates for the state space filtering and smoothing distributions. We leverage these results to produce customized and efficient algorithms for inference and forecasting, including Monte Carlo simulation for offline analysis and an optimal particle filter for online inference. This framework unifies and extends a variety of discrete time series models and is valid for natural counts, rounded values, and multivariate observations. Simulation studies illustrate the excellent forecasting capabilities of the warped DLM. The proposed approach is applied to a multivariate time series of daily overdose counts and demonstrates both modeling and computational successes.

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arXiv2023

Nonparametric Copula Models for Multivariate, Mixed, and Missing Data

Modern datasets commonly feature both substantial missingness and many variables of mixed data types, which present significant challenges for estimation and inference. Complete case analysis, which proceeds using only the observations with fully-observed variables, is often severely biased, while model-based imputation of missing values is limited by the ability of the model to capture complex dependencies among (possibly many) variables of mixed data types. To address these challenges, we develop a novel Bayesian mixture copula for joint and nonparametric modeling of multivariate count, continuous, ordinal, and unordered categorical variables, and deploy this model for inference, prediction, and imputation of missing data. Most uniquely, we introduce a new and computationally efficient strategy for marginal distribution estimation that eliminates the need to specify any marginal models yet delivers posterior consistency for each marginal distribution and the copula parameters under missingness-at-random. Extensive simulation studies demonstrate exceptional modeling and imputation capabilities relative to competing methods, especially with mixed data types, complex missingness mechanisms, and nonlinear dependencies. We conclude with a data analysis that highlights how improper treatment of missing data can distort a statistical analysis, and how the proposed approach offers a resolution.

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arXiv2023

Semiparametric discrete data regression with Monte Carlo inference and prediction

Discrete data are abundant and often arise as counts or rounded data. These data commonly exhibit complex distributional features such as zero-inflation, over-/under-dispersion, boundedness, and heaping, which render many parametric models inadequate. Yet even for parametric regression models, approximations such as MCMC typically are needed for posterior inference. This paper introduces a Bayesian modeling and algorithmic framework that enables semiparametric regression analysis for discrete data with Monte Carlo (not MCMC) sampling. The proposed approach pairs a nonparametric marginal model with a latent linear regression model to encourage both flexibility and interpretability, and delivers posterior consistency even under model misspecification. For a parametric or large-sample approximation of this model, we identify a class of conjugate priors with (pseudo) closed-form posteriors. All posterior and predictive distributions are available analytically or via direct Monte Carlo sampling. These tools are broadly useful for linear regression, nonlinear models via basis expansions, and variable selection with discrete data. Simulation studies demonstrate significant advantages in computing, prediction, estimation, and selection relative to existing alternatives. This novel approach is applied successfully to self-reported mental health data that exhibit zero-inflation, overdispersion, boundedness, and heaping.

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arXiv2022

Bayesian adaptive and interpretable functional regression for exposure profiles

Pollutant exposure during gestation is a known and adverse factor for birth and health outcomes. However, the links between prenatal air pollution exposures and educational outcomes are less clear, in particular the critical windows of susceptibility during pregnancy. Using a large cohort of students in North Carolina, we study the link between prenatal daily $\mbox{PM}_{2.5}$ exposure and 4th end-of-grade reading scores. We develop and apply a locally adaptive and highly scalable Bayesian regression model for scalar responses with functional and scalar predictors. The proposed model pairs a B-spline basis expansion with dynamic shrinkage priors to capture both smooth and rapidly-changing features in the regression surface. The model is accompanied by a new decision analysis approach for functional regression that extracts the critical windows of susceptibility and guides the model interpretations. These tools help to identify and address broad limitations with the interpretability of functional regression models. Simulation studies demonstrate more accurate point estimation, more precise uncertainty quantification, and far superior window selection than existing approaches. Leveraging the proposed modeling, computational, and decision analysis framework, we conclude that prenatal $\mbox{PM}_{2.5}$ exposure during early and late pregnancy is most adverse for 4th end-of-grade reading scores.

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arXiv2022

Semiparametric Functional Factor Models with Bayesian Rank Selection

Functional data are frequently accompanied by a parametric template that describes the typical shapes of the functions. However, these parametric templates can incur significant bias, which undermines both utility and interpretability. To correct for model misspecification, we augment the parametric template with an infinite-dimensional nonparametric functional basis. The nonparametric basis functions are learned from the data and constrained to be orthogonal to the parametric template, which preserves distinctness between the parametric and nonparametric terms. This distinctness is essential to prevent functional confounding, which otherwise induces severe bias for the parametric terms. The nonparametric factors are regularized with an ordered spike-and-slab prior that provides consistent rank selection and satisfies several appealing theoretical properties. The versatility of the proposed approach is illustrated through applications to synthetic data, human motor control data, and dynamic yield curve data. Relative to parametric and semiparametric alternatives, the proposed semiparametric functional factor model eliminates bias, reduces excessive posterior and predictive uncertainty, and provides reliable inference on the effective number of nonparametric terms--all with minimal additional computational costs.

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arXiv2022

Subset selection for linear mixed models

Linear mixed models (LMMs) are instrumental for regression analysis with structured dependence, such as grouped, clustered, or multilevel data. However, selection among the covariates--while accounting for this structured dependence--remains a challenge. We introduce a Bayesian decision analysis for subset selection with LMMs. Using a Mahalanobis loss function that incorporates the structured dependence, we derive optimal linear coefficients for (i) any given subset of variables and (ii) all subsets of variables that satisfy a cardinality constraint. Crucially, these estimates inherit shrinkage or regularization and uncertainty quantification from the underlying Bayesian model, and apply for any well-specified Bayesian LMM. More broadly, our decision analysis strategy deemphasizes the role of a single "best" subset, which is often unstable and limited in its information content, and instead favors a collection of near-optimal subsets. This collection is summarized by key member subsets and variable-specific importance metrics. Customized subset search and out-of-sample approximation algorithms are provided for more scalable computing. These tools are applied to simulated data and a longitudinal physical activity dataset, and demonstrate excellent prediction, estimation, and selection ability.

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arXiv2022

Bayesian subset selection and variable importance for interpretable prediction and classification

Subset selection is a valuable tool for interpretable learning, scientific discovery, and data compression. However, classical subset selection is often avoided due to selection instability, lack of regularization, and difficulties with post-selection inference. We address these challenges from a Bayesian perspective. Given any Bayesian predictive model $\mathcal{M}$, we extract a family of near-optimal subsets of variables for linear prediction or classification. This strategy deemphasizes the role of a single "best" subset and instead advances the broader perspective that often many subsets are highly competitive. The acceptable family of subsets offers a new pathway for model interpretation and is neatly summarized by key members such as the smallest acceptable subset, along with new (co-) variable importance metrics based on whether variables (co-) appear in all, some, or no acceptable subsets. More broadly, we apply Bayesian decision analysis to derive the optimal linear coefficients for any subset of variables. These coefficients inherit both regularization and predictive uncertainty quantification via $\mathcal{M}$. For both simulated and real data, the proposed approach exhibits better prediction, interval estimation, and variable selection than competing Bayesian and frequentist selection methods. These tools are applied to a large education dataset with highly correlated covariates. Our analysis provides unique insights into the combination of environmental, socioeconomic, and demographic factors that predict educational outcomes, and identifies over 200 distinct subsets of variables that offer near-optimal out-of-sample predictive accuracy.

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arXiv2021

Semiparametric count data regression for self-reported mental health

"For how many days during the past 30 days was your mental health not good?" The responses to this question measure self-reported mental health and can be linked to important covariates in the National Health and Nutrition Examination Survey (NHANES). However, these count variables present major distributional challenges: the data are overdispersed, zero-inflated, bounded by 30, and heaped in five- and seven-day increments. To meet these challenges, we design a semiparametric estimation and inference framework for count data regression. The data-generating process is defined by simultaneously transforming and rounding (STAR) a latent Gaussian regression model. The transformation is estimated nonparametrically and the rounding operator ensures the correct support for the discrete and bounded data. Maximum likelihood estimators are computed using an EM algorithm that is compatible with any continuous data model estimable by least squares. STAR regression includes asymptotic hypothesis testing and confidence intervals, variable selection via information criteria, and customized diagnostics. Simulation studies validate the utility of this framework. STAR is deployed to study the factors associated with self-reported mental health and demonstrates substantial improvements in goodness-of-fit compared to existing count data regression models.

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arXiv2020

Fast, Optimal, and Targeted Predictions using Parametrized Decision Analysis

Prediction is critical for decision-making under uncertainty and lends validity to statistical inference. With targeted prediction, the goal is to optimize predictions for specific decision tasks of interest, which we represent via functionals. Although classical decision analysis extracts predictions from a Bayesian model, these predictions are often difficult to interpret and slow to compute. Instead, we design a class of parametrized actions for Bayesian decision analysis that produce optimal, scalable, and simple targeted predictions. For a wide variety of action parametrizations and loss functions--including linear actions with sparsity constraints for targeted variable selection--we derive a convenient representation of the optimal targeted prediction that yields efficient and interpretable solutions. Customized out-of-sample predictive metrics are developed to evaluate and compare among targeted predictors. Through careful use of the posterior predictive distribution, we introduce a procedure that identifies a set of near-optimal, or acceptable targeted predictors, which provide unique insights into the features and level of complexity needed for accurate targeted prediction. Simulations demonstrate excellent prediction, estimation, and variable selection capabilities. Targeted predictions are constructed for physical activity data from the National Health and Nutrition Examination Survey (NHANES) to better predict and understand the characteristics of intraday physical activity.

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