arXiv subjects

Samuel I. Berchuck

Publications and source records attributed to Samuel I. Berchuck.

8 recordsLinked to original sources

arXiv2026

Scalable and Calibrated Sampling for Bayesian Generalized Linear Mixed Model via Stochastic Gradient Markov Chain Monte Carlo

Generalized linear mixed models (GLMMs) are widely used for analyzing correlated data, particularly in large-scale biomedical and social science applications. Scalable Bayesian inference for GLMMs is challenging due to an intractable marginal likelihood and a high computational cost incurred by conventional Markov chain Monte Carlo (MCMC) methods. We develop a stochastic gradient MCMC (SGMCMC) algorithm tailored to GLMMs that enables accurate posterior inference in the large-sample regime. Our approach uses Fisher's identity to construct a (biased) Monte Carlo estimator of the gradient of the marginal log-likelihood, making SGMCMC feasible when direct gradient computation is impossible. We analyze the additional variability, introduced by both data subsampling and gradient approximation, to derive a post-hoc covariance correction that yields properly calibrated posterior uncertainty. We show through simulated studies that the proposed method provides accurate posterior means and variances in settings with a large number of groups, outperforming existing approaches, including control variate methods. We further demonstrate the method's practical utility in an analysis of electronic health records data, where accounting for variance inflation materially changes scientific conclusions.

stat.CO↗

arXiv2026

Safe, Scalable, and Accurate Bayes Posterior Sampling for Large-Data Generalized Linear Mixed Models

We consider the problem of scalable sampling algorithms to fit Bayesian generalized linear mixed models on large datasets. Stochastic gradient Langevin dynamics, coupled with smooth re-parameterizations of variance parameters, produces divergent Markov chains and cannot be reliably used for sampling covariance parameters of random effects. We advocate the use of a mirror Langevin dynamics algorithm, propose the novel stochastic mirror Langevin dynamics based on data subsampling, and provide concrete guidelines for its use in a Bayesian inference framework. Based on an explicit Wasserstein distance error bound between the posterior and its algorithmic approximation, we propose a post-processing step that yields an asymptotic, order-wise correct estimation of the posterior variance, eliminating the irreducible posterior variance estimation bias due to subsampling. Empirical performance of the method is evaluated through simulated experiments and a longitudinal study of pain trajectories in a study of breast cancer survivors.

stat.ME↗

arXiv2026

Multiple Imputation Diagnostics when using Electronic Health Record Data in Observational Studies: A Case Study

Missing values in electronic health record (EHR) data pose a significant challenge for epidemiologic research. Traditional methods for handling missing data, like mean imputation, may introduce bias. Multiple imputation (MI) offers a principled solution by generating multiple plausible values based on statistical models. However, MI requires careful model specification and validation of imputations, ideally using multivariate graphical tools. We demonstrate the application of such tools to validate MI in a study of chronic kidney disease, assessing cardiovascular outcomes linked to neighborhood socioeconomic status (nSES). This study used data from Duke University Health System (DUHS) and Lincoln Community Health Center (LCHC). Eligible patients had at least one encounter within DUHS or LCHC and had two estimated glomerular filtration rate (eGFR) values <60 mL/min per 1.73 m2 more than 90 days apart between January 1, 2007 and July 1, 2008. Socioeconomic status was assessed using the Agency for Healthcare Research and Quality (AHRQ) index based on census data. The main outcome was a cardiovascular disease-related hospitalization. Participants were mostly older (mean age 73 years), female (64%), and Black (43%). Participants living in lower nSES neighborhoods had higher mean systolic blood pressure (SBP: 140 mmHg) and hemoglobin A1c (HbA1c) levels (7.1%) as compared to participants living in higher nSES neighborhoods. A machine learning based approach, Classification and Regression Trees (CART), was the preferred approach to impute missing data. The distributions of imputed values of SBP and HbA1c were impacted by whether marginal or conditional values of SBP and HbA1c were imputed. The choice of MI had minimal impact on inference and prediction. Future research may want to extend our results and consider how results may differ when using EHR data from multiple health systems.

stat.ME↗

arXiv2023

Asymptotics of Bayesian Uncertainty Estimation in Random Features Regression

In this paper we compare and contrast the behavior of the posterior predictive distribution to the risk of the maximum a posteriori estimator for the random features regression model in the overparameterized regime. We will focus on the variance of the posterior predictive distribution (Bayesian model average) and compare its asymptotics to that of the risk of the MAP estimator. In the regime where the model dimensions grow faster than any constant multiple of the number of samples, asymptotic agreement between these two quantities is governed by the phase transition in the signal-to-noise ratio. They also asymptotically agree with each other when the number of samples grow faster than any constant multiple of model dimensions. Numerical simulations illustrate finer distributional properties of the two quantities for finite dimensions. We conjecture they have Gaussian fluctuations and exhibit similar properties as found by previous authors in a Gaussian sequence model, which is of independent theoretical interest.

stat.ML↗

arXiv2019

Bayesian Non-Parametric Factor Analysis for Longitudinal Spatial Surfaces

We introduce a Bayesian non-parametric spatial factor analysis model with spatial dependency induced through a prior on factor loadings. For each column of the loadings matrix, spatial dependency is encoded using a probit stick-breaking process (PSBP) and a multiplicative gamma process shrinkage prior is used across columns to adaptively determine the number of latent factors. By encoding spatial information into the loadings matrix, meaningful factors are learned that respect the observed neighborhood dependencies, making them useful for assessing rates over space. Furthermore, the spatial PSBP prior can be used for clustering temporal trends, allowing users to identify regions within the spatial domain with similar temporal trajectories, an important task in many applied settings. In the manuscript, we illustrate the model's performance in simulated data, but also in two real-world examples: longitudinal monitoring of glaucoma and malaria surveillance across the Peruvian Amazon. The R package spBFA, available on CRAN, implements the method.

stat.ME↗

arXiv2019

Scalable Modeling of Spatiotemporal Data using the Variational Autoencoder: an Application in Glaucoma

As big spatial data becomes increasingly prevalent, classical spatiotemporal (ST) methods often do not scale well. While methods have been developed to account for high-dimensional spatial objects, the setting where there are exceedingly large samples of spatial observations has had less attention. The variational autoencoder (VAE), an unsupervised generative model based on deep learning and approximate Bayesian inference, fills this void using a latent variable specification that is inferred jointly across the large number of samples. In this manuscript, we compare the performance of the VAE with a more classical ST method when analyzing longitudinal visual fields from a large cohort of patients in a prospective glaucoma study. Through simulation and a case study, we demonstrate that the VAE is a scalable method for analyzing ST data, when the goal is to obtain accurate predictions. R code to implement the VAE can be found on GitHub: https://github.com/berchuck/vaeST.

stat.AP↗

arXiv2018

A spatially varying change points model for monitoring glaucoma progression using visual field data

Glaucoma disease progression, as measured by visual field (VF) data, is often defined by periods of relative stability followed by an abrupt decrease in visual ability at some point in time. Determining the transition point of the disease trajectory to a more severe state is important clinically for disease management and for avoiding irreversible vision loss. Based on this, we present a unified statistical modeling framework that permits prediction of the timing and spatial location of future vision loss and informs clinical decisions regarding disease progression. The developed method incorporates anatomical information to create a biologically plausible data-generating model. We accomplish this by introducing a spatially varying coefficients model that includes spatially varying change points to detect structural shifts in both the mean and variance process of VF data across both space and time. The VF location-specific change point represents the underlying, and potentially censored, timing of true change in disease trajectory while a multivariate spatial boundary detection structure is introduced that accounts for the complex spatial connectivity of the VF and optic disc. We show that our method improves estimation and prediction of multiple aspects of disease management in comparison to existing methods through simulation and real data application. The R package spCP implements the new methodology.

stat.AP↗

arXiv2018

Diagnosing Glaucoma Progression with Visual Field Data Using a Spatiotemporal Boundary Detection Method

Diagnosing glaucoma progression is critical for limiting irreversible vision loss. A common method for assessing glaucoma progression uses a longitudinal series of visual fields (VF) acquired at regular intervals. VF data are characterized by a complex spatiotemporal structure due to the data generating process and ocular anatomy. Thus, advanced statistical methods are needed to make clinical determinations regarding progression status. We introduce a spatiotemporal boundary detection model that allows the underlying anatomy of the optic disc to dictate the spatial structure of the VF data across time. We show that our new method provides novel insight into vision loss that improves diagnosis of glaucoma progression using data from the Vein Pulsation Study Trial in Glaucoma and the Lions Eye Institute trial registry. Simulations are presented, showing the proposed methodology is preferred over existing spatial methods for VF data. Supplementary materials for this article are available online and the method is implemented in the R package womblR.

stat.AP↗