About

Brian J Reich is the Gertrude M. Cox Distinguished Professor in the Department of Statistics at NC State University. He earned his Ph.D. in Biostatistics from the University of Minnesota in 2005. His areas of expertise include Environmental Statistics, Bayesian Statistics, and Hierarchical Models. Dr. Reich has been recognized with awards such as the Dr. D. D. Mason Faculty Award for 2016-2017 and the Dr. Cavell Brownie Mentoring Faculty Award for 2021-2023. He is actively involved in research and teaching within the department, contributing to the fields of applied probability, data science, and statistical methodology.

Research topics

• Artificial Intelligence
• Computer Science
• Data Mining
• Geography
• Agronomy
• Mathematics
• Environmental science
• Ecology
• Remote sensing
• Geology
• Medicine
• Statistics
• Horticulture
• Meteorology
• Biology
• Paleontology
• Engineering
• Climatology
• Econometrics
• Environmental health

Selected publications

• Spatial Causal Tensor Completion for Multiple Exposures and Outcomes: An Application to the Health Effects of PFAS Pollution

  arXiv (Cornell University) · 2026-03-17

  preprintOpen access

  Per- and polyfluoroalkyl substances (PFAS) are typically encountered as mixtures of distinct chemicals with distinct effects on multiple health outcomes. Estimating joint causal effects using spatially-dependent observed data is challenging. We propose a spatial causal tensor completion framework that jointly models multiple exposures and outcomes within a low-rank tensor structure, while adjusting for observed confounders and latent spatial confounders. This method combines a low-rank tensor representation to pool information across exposures and outcomes with a spectral adjustment step that incorporates graph-Laplacian eigenvectors to approximate unmeasured spatial confounders, implemented via a projected-gradient descent algorithm. This framework enables causal inference in the presence of unmeasured spatial confounding and pervasive missingness of potential outcomes. We establish theoretical guarantees for the estimator and evaluate its finite-sample performance through extensive simulations. In an application to national PFAS monitoring data, our approach yields more conservative and credible causal relationships between PFOA and PFOS exposure and 13 chronic disease outcomes compared with existing alternatives.

  PublisherDOI

• Multivariate and Online Transfer Learning With Uncertainty Quantification

  Statistics in Medicine · 2026-02-01

  articleOpen access

  Untreated periodontitis causes inflammation within the supporting tissue of the teeth and can ultimately lead to tooth loss. Modeling periodontal outcomes is beneficial as they are difficult and time-consuming to measure, but disparities in representation between demographic groups must be considered. There may not be enough participants to build group-specific models, and it can be ineffective, and even dangerous, to apply a model to participants in an underrepresented group if demographic differences were not considered during training. We propose an extension to the RECaST Bayesian transfer learning framework. Our method jointly models multivariate outcomes, exhibiting significant improvement over the previous univariate RECaST method. Further, we introduce an online approach to model sequential data sets. Negative transfer is mitigated to ensure that the information shared from the other demographic groups does not negatively impact the modeling of the underrepresented participants. The Bayesian framework naturally provides uncertainty quantification on predictions. Especially important in medical applications, our method does not share data between domains. We demonstrate the effectiveness of our method in both predictive performance and uncertainty quantification on simulated data and on a database of dental records from the HealthPartners Institute.

  PublisherOA PDFDOI

• A Bayesian shrinkage estimator for transfer learning

  Journal of Multivariate Analysis · 2026-04-13

  preprintOpen accessSenior author

  Transfer learning (TL) has emerged as a powerful tool to supplement data collected for a target task with data collected for a related source task. The Bayesian framework is natural for TL because information from the source data can be incorporated in the prior distribution for the target data analysis. In this paper, we propose and study Bayesian TL methods for the normal-means problem and multiple linear regression. We propose two classes of prior distributions. The first class assumes the difference in the parameters for the source and target tasks is sparse, i.e., many parameters are shared across tasks. The second assumes that none of the parameters are shared across tasks, but the differences are bounded in $\ell_2$-norm. For the sparse case, we propose a Bayes shrinkage estimator with theoretical guarantees under mild assumptions. The proposed methodology is tested on synthetic data and outperforms state-of-the-art TL methods. We then use this method to fine-tune the last layer of a neural network model to predict the molecular gap property in a material science application. We report improved performance compared to classical fine tuning and methods using only the target data.

  PublisherDOI

• DANCE: Doubly Adaptive Neighborhood Conformal Estimation

  Open MIND · 2026-02-24

  preprint

  The recent developments of complex deep learning models have led to unprecedented ability to accurately predict across multiple data representation types. Conformal prediction for uncertainty quantification of these models has risen in popularity, providing adaptive, statistically-valid prediction sets. For classification tasks, conformal methods have typically focused on utilizing logit scores. For pre-trained models, however, this can result in inefficient, overly conservative set sizes when not calibrated towards the target task. We propose DANCE, a doubly locally adaptive nearest-neighbor based conformal algorithm combining two novel nonconformity scores directly using the data's embedded representation. DANCE first fits a task-adaptive kernel regression model from the embedding layer before using the learned kernel space to produce the final prediction sets for uncertainty quantification. We test against state-of-the-art local, task-adapted and zero-shot conformal baselines, demonstrating DANCE's superior blend of set size efficiency and robustness across various datasets.

  DOI

• Functional Principal Component Analysis for Sparse Censored Data

  Biometrika · 2026-04-15

  preprintOpen access

  Summary Functional principal component analysis is a key tool in the study of functional data, driving both exploratory analyses and feature construction for use in formal modelling and testing procedures. However, existing methods do not apply when functional observations are censored; for example, when the measurement instrument only supports recordings within a prespecified interval, thereby truncating values outside this range to the nearest boundary. A naïve application of existing methods, without correction for instrument-induced censoring, introduces bias into the estimators of the mean, covariance and functional principal component scores. We extend the functional principal component analysis framework to accommodate noisy and potentially sparse censored functional data. Local loglikelihood maximization is used to recover smooth estimates of the mean and covariance surface that are representative of the latent process’s mean and covariance functions. The covariance-smoothing procedure yields a positive semidefinite covariance surface, computed without the need to retroactively remove negative eigenvalues in the covariance-operator decomposition. Additionally, we construct a predictor of the scores, conditional on the censored functional data, and demonstrate its use in the generalized functional linear model. Convergence rates for the proposed estimators are established. In simulation experiments, the proposed method yields improved predictive performance and lower bias than existing alternatives. We illustrate its practical value in a study aimed at classifying eating disorder diagnoses in individuals with type 1 diabetes, using censored functional blood glucose data.

  PublisherOA PDFDOI

• Spatial Causal Tensor Completion for Multiple Exposures and Outcomes: An Application to the Health Effects of PFAS Pollution

  ArXiv.org · 2026-03-17

  articleOpen access

  Per- and polyfluoroalkyl substances (PFAS) are typically encountered as mixtures of distinct chemicals with distinct effects on multiple health outcomes. Estimating joint causal effects using spatially-dependent observed data is challenging. We propose a spatial causal tensor completion framework that jointly models multiple exposures and outcomes within a low-rank tensor structure, while adjusting for observed confounders and latent spatial confounders. This method combines a low-rank tensor representation to pool information across exposures and outcomes with a spectral adjustment step that incorporates graph-Laplacian eigenvectors to approximate unmeasured spatial confounders, implemented via a projected-gradient descent algorithm. This framework enables causal inference in the presence of unmeasured spatial confounding and pervasive missingness of potential outcomes. We establish theoretical guarantees for the estimator and evaluate its finite-sample performance through extensive simulations. In an application to national PFAS monitoring data, our approach yields more conservative and credible causal relationships between PFOA and PFOS exposure and 13 chronic disease outcomes compared with existing alternatives.

  PublisherOA PDF

• DANCE: Doubly Adaptive Neighborhood Conformal Estimation

  ArXiv.org · 2026-02-24

  articleOpen access

  The recent developments of complex deep learning models have led to unprecedented ability to accurately predict across multiple data representation types. Conformal prediction for uncertainty quantification of these models has risen in popularity, providing adaptive, statistically-valid prediction sets. For classification tasks, conformal methods have typically focused on utilizing logit scores. For pre-trained models, however, this can result in inefficient, overly conservative set sizes when not calibrated towards the target task. We propose DANCE, a doubly locally adaptive nearest-neighbor based conformal algorithm combining two novel nonconformity scores directly using the data's embedded representation. DANCE first fits a task-adaptive kernel regression model from the embedding layer before using the learned kernel space to produce the final prediction sets for uncertainty quantification. We test against state-of-the-art local, task-adapted and zero-shot conformal baselines, demonstrating DANCE's superior blend of set size efficiency and robustness across various datasets.

  PublisherOA PDF

• Machine learning

  2025-12-03

  book-chapter1st authorCorresponding
  PublisherDOI

• Case studies using hierarchical modeling

  2025-12-03

  book-chapter1st authorCorresponding
  PublisherDOI

• A Complete Density Correction using Normalizing Flows (CDC-NF) for CMIP6 GCMs

  Scientific Data · 2025-07-23 · 1 citations

  articleOpen access

  Global Climate Models (GCMs) are essential for climate projections but often exhibit biases, particularly in representing extremes and multivariate dependencies, which limit their utility in impact assessments. Traditional bias correction (BC) methods, such as quantile mapping, address marginal distributions but fail to correct joint extremes and cross-variable relationships. To address these challenges, we propose a Complete Density Correction using Normalizing Flows (CDC-NF), a novel method leveraging invertible transformations to adjust the full joint distribution of GCM outputs. Using observational data from NOAA nClimGrid-daily and CMIP6 GCM projections, The CDC-NF method was applied at a daily temporal resolution to precipitation and maximum temperature outputs from CMIP6 GCM projections. Compared to traditional BC methods, CDC-NF demonstrated substantial improvements in Wasserstein Distance, RMSE, and PBIAS, particularly for the 90th percentile extremes. Additionally, it preserved cross-correlation structure, enhancing reliability in modeling compound extremes. CDC-NF represents a significant advancement in BC, providing a robust framework for addressing GCM biases and improving climate impact studies in a changing climate.

  PublisherOA PDFDOI

Recent grants

• Projecting Flood Frequency Curves Under a Changing Climate Using Spatial Extreme Value Analysis

  NSF · $300k · 2022–2025

• Exploring tooth survival using Bayesian spatial models

  NIH · $322k · 2014–2018

• Spatial Causal Inference for Wildland Fire Smoke Effects on Air Pollution and Health

  NIH · $859k · 2020–2026

• Collaborative Research: NRT-DESE: Interdisciplinary Research Traineeships in Data-Enabled Science and Engineering of Atomic Structure

  NSF · $2.6M · 2016–2021

• NIH Grant R01ES014843

  NIH · $1.3M · 2017

Frequent coauthors

• Montserrat Fuentes

  55 shared

• Howard D. Bondell

  University of Melbourne

  32 shared

• Ana G. Rappold

  Environmental Protection Agency

  32 shared

• Benjamin A. Shaby

  Colorado State University

  27 shared

• Yawen Guan

  Lanzhou University

  24 shared

• Jane A. Hoppin

  North Carolina State University

  21 shared

• Krishna Pacifici

  North Carolina State University

  21 shared

• Ana‐Maria Staicu

  North Carolina State University

  21 shared

Labs

• Reich LabPI

Awards & honors

• 2016-2017, Dr. D. D. Mason Faculty Award
• 2021-2023, Dr. Cavell Brownie Mentoring Faculty Award