arXiv subjects

Sudipto Banerjee

Publications and source records attributed to Sudipto Banerjee.

At least 37 records · Page 2Linked to original sources

arXiv2025

Detecting Spatial Health Disparities Using Disease Maps

Epidemiologists commonly use regional aggregates of health outcomes to map mortality or incidence rates and identify geographic disparities. However, to detect health disparities across regions, it is necessary to identify "difference boundaries" that separate neighboring regions with significantly different spatial effects. This can be particularly challenging when dealing with multiple outcomes for each unit and accounting for dependence among diseases and across areal units. In this study, we address the issue of multivariate difference boundary detection for correlated diseases by formulating the problem in terms of Bayesian pairwise multiple comparisons by extending it through the introduction of adjacency modeling and disease graph dependencies. Specifically, we seek the posterior probabilities of neighboring spatial effects being different. To accomplish this, we adopt a class of multivariate areally referenced Dirichlet process models that accommodate spatial and interdisease dependence by endowing the spatial random effects with a discrete probability law. Our method is evaluated through simulation studies and applied to detect difference boundaries for multiple cancers using data from the Surveillance, Epidemiology, and End Results Program of the National Cancer Institute.

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arXiv2025

Gridding and Parameter Expansion for Scalable Latent Gaussian Models of Spatial Multivariate Data

Scalable spatial GPs for massive datasets can be built via sparse Directed Acyclic Graphs (DAGs) where a small number of directed edges is sufficient to flexibly characterize spatial dependence. The DAG can be used to devise fast algorithms for posterior sampling of the latent process, but these may exhibit pathological behavior in estimating covariance parameters. In this article, we introduce gridding and parameter expansion methods to improve the practical performance of MCMC algorithms in terms of effective sample size per unit time (ESS/s). Gridding is a model-based strategy that reduces the number of expensive operations necessary during MCMC on irregularly spaced data. Parameter expansion reduces dependence in posterior samples in spatial regression for high resolution data. These two strategies lead to computational gains in the big data settings on which we focus. We consider popular constructions of univariate spatial processes based on Matérn covariance functions and multivariate coregionalization models for Gaussian outcomes in extensive analyses of synthetic datasets comparing with alternative methods. We demonstrate effectiveness of our proposed methods in a forestry application using remotely sensed data from NASA's Goddard LiDAR, Hyper-Spectral, and Thermal imager (G-LiHT).

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arXiv2025

Leveraging national forest inventory data to estimate forest carbon density status and trends for small areas

National forest inventory (NFI) data are often costly to collect, which inhibits efforts to estimate parameters of interest for small spatial, temporal, or biophysical domains. Traditionally, design-based estimators are used to estimate status of forest parameters of interest, but are unreliable for small areas where data are sparse. Additionally, design-based estimates constructed directly from the survey data are often unavailable when sample sizes are especially small. Traditional model-based small area estimation approaches, such as the Fay-Herriot (FH) model, rely on these direct estimates for inference; hence, missing direct estimates preclude the use of such approaches. Here, we detail a Bayesian spatio-temporal small area estimation model that efficiently leverages sparse NFI data to estimate status and trends for forest parameters. The proposed model bypasses the use of direct estimates and instead uses plot-level NFI measurements along with auxiliary data including remotely sensed tree canopy cover. We produce forest carbon estimates from the United States NFI over 14 years across the contiguous US (CONUS) and conduct a simulation study to assess our proposed model's accuracy, precision, and bias, compared to that of a design-based estimator. The proposed model provides improved precision and accuracy over traditional estimation methods, and provides useful insights into county-level forest carbon dynamics across the CONUS.

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arXiv2024

Graph-constrained Analysis for Multivariate Functional Data

Functional Gaussian graphical models (GGM) used for analyzing multivariate functional data customarily estimate an unknown graphical model representing the conditional relationships between the functional variables. However, in many applications of multivariate functional data, the graph is known and existing functional GGM methods cannot preserve a given graphical constraint. In this manuscript, we demonstrate how to conduct multivariate functional analysis that exactly conforms to a given inter-variable graph. We first show the equivalence between partially separable functional GGM and graphical Gaussian processes (GP), proposed originally for constructing optimal covariance functions for multivariate spatial data that retain the conditional independence relations in a given graphical model. The theoretical connection help design a new algorithm that leverages Dempster's covariance selection to calculate the maximum likelihood estimate of the covariance function for multivariate functional data under graphical constraints. We also show that the finite term truncation of functional GGM basis expansion used in practice is equivalent to a low-rank graphical GP, which is known to oversmooth marginal distributions. To remedy this, we extend our algorithm to better preserve marginal distributions while still respecting the graph and retaining computational scalability. The insights obtained from the new results presented in this manuscript will help practitioners better understand the relationship between these graphical models and in deciding on the appropriate method for their specific multivariate data analysis task. The benefits of the proposed algorithms are illustrated using empirical experiments and an application to functional modeling of neuroimaging data using the connectivity graph among regions of the brain.

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arXiv2024

Process-based Inference for Spatial Energetics Using Bayesian Predictive Stacking

Rapid developments in streaming data technologies have enabled real-time monitoring of human activity that can deliver high-resolution data on health variables over trajectories or paths carved out by subjects as they conduct their daily physical activities. Wearable devices, such as wrist-worn sensors that monitor gross motor activity, have become prevalent and have kindled the emerging field of "spatial energetics" in environmental health sciences. We devise a Bayesian inferential framework for analyzing such data while accounting for information available on specific spatial coordinates comprising a trajectory or path using a Global Positioning System (GPS) device embedded within the wearable device. We offer full probabilistic inference with uncertainty quantification using spatial-temporal process models adapted for data generated from "actigraph" units as the subject traverses a path or trajectory in their daily routine. Anticipating the need for fast inference for mobile health data, we pursue exact inference using conjugate Bayesian models and employ predictive stacking to assimilate inference across these individual models. This circumvents issues with iterative estimation algorithms such as Markov chain Monte Carlo. We devise Bayesian predictive stacking in this context for models that treat time as discrete epochs and that treat time as continuous. We illustrate our methods with simulation experiments and analysis of data from the Physical Activity through Sustainable Transport Approaches (PASTA-LA) study conducted by the Fielding School of Public Health at the University of California, Los Angeles.

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arXiv2024

Bayesian Modeling of Incompatible Spatial Data: A Case Study Involving Post-Adrian Storm Forest Damage Assessment

Modeling incompatible spatial data, i.e., data with different spatial resolutions, is a pervasive challenge in remote sensing data analysis. Typical approaches to addressing this challenge aggregate information to a common coarse resolution, i.e., compatible resolutions, prior to modeling. Such pre-processing aggregation simplifies analysis, but potentially causes information loss and hence compromised inference and predictive performance. To avoid losing potential information provided by finer spatial resolution data and improve predictive performance, we propose a new Bayesian method that constructs a latent spatial process model at the finest spatial resolution. This model is tailored to settings where the outcome variable is measured on a coarser spatial resolution than predictor variables -- a configuration seen increasingly when high spatial resolution remotely sensed predictors are used in analysis. A key contribution of this work is an efficient algorithm that enables full Bayesian inference using finer resolution data while optimizing computational and storage costs. The proposed method is applied to a forest damage assessment for the 2018 Adrian storm in Carinthia, Austria, that uses high-resolution laser imaging detection and ranging (LiDAR) measurements and relatively coarse resolution forest inventory measurements. Extensive simulation studies demonstrate the proposed approach substantially improves inference for small prediction units.

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arXiv2024

Spatio-temporal areal models to support small area estimation: An application to national-scale forest carbon monitoring

National Forest Inventory (NFI) programs can provide vital information on the status, trend, and change in forest parameters. These programs are being increasingly asked to provide forest parameter estimates for spatial and temporal extents smaller than their current design and accompanying design-based methods can deliver with desired levels of uncertainty. Many NFI designs and estimation methods focus on status and are not well equipped to provide acceptable estimates for trend and change parameters, especially over small spatial domains and/or short time periods. Fine-scale space-time indexed estimates are critical to a variety of environmental, ecological, and economic monitoring efforts. Estimates for forest carbon status, trend, and change are of particular importance to international initiatives to track carbon dynamics. Model-based small area estimation (SAE) methods for NFI and similar ecological monitoring data typically pursue inference on status within small spatial domains, with few demonstrated methods that account for spatio-temporal dependence needed for trend and change estimation. We propose a spatio-temporal Bayesian model framework that delivers statistically valid estimates with full uncertainty quantification for status, trend, and change. The framework accommodates a variety of space and time dependency structures, and we detail model configurations for different settings. Through analysis of simulated datasets, we compare the relative performance of candidate models and a traditional direct estimator. We then apply candidate models to a large-scale NFI dataset to demonstrate the utility of the proposed framework for providing unique quantification of forest carbon dynamics in the contiguous United States. We also provide computationally efficient algorithms, software, and data to reproduce our results and for benchmarking.

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arXiv2024

Bayesian Hierarchical Modeling and Inference for Mechanistic Systems in Industrial Hygiene

A series of experiments in stationary and moving passenger rail cars were conducted to measure removal rates of particles in the size ranges of SARS-CoV-2 viral aerosols, and the air changes per hour provided by existing and modified air handling systems. Such methods for exposure assessments are customarily based on mechanistic models derived from physical laws of particle movement that are deterministic and do not account for measurement errors inherent in data collection. The resulting analysis compromises on reliably learning about mechanistic factors such as ventilation rates, aerosol generation rates and filtration efficiencies from field measurements. This manuscript develops a Bayesian state space modeling framework that synthesizes information from the mechanistic system as well as the field data. We derive a stochastic model from finite difference approximations of differential equations explaining particle concentrations. Our inferential framework trains the mechanistic system using the field measurements from the chamber experiments and delivers reliable estimates of the underlying physical process with fully model-based uncertainty quantification. Our application falls within the realm of Bayesian "melding" of mechanistic and statistical models and is of significant relevance to industrial hygienists and public health researchers working on assessment of exposure to viral aerosols in rail car fleets.

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arXiv2024

Models to support forest inventory and small area estimation using sparsely sampled LiDAR: A case study involving G-LiHT LiDAR in Tanana, Alaska

A two-stage hierarchical Bayesian model is developed and implemented to estimate forest biomass density and total given sparsely sampled LiDAR and georeferenced forest inventory plot measurements. The model is motivated by the United States Department of Agriculture (USDA) Forest Service Forest Inventory and Analysis (FIA) objective to provide biomass estimates for the remote Tanana Inventory Unit (TIU) in interior Alaska. The proposed model yields stratum-level biomass estimates for arbitrarily sized areas. Model-based estimates are compared with the TIU FIA design-based post-stratified estimates. Model-based small area estimates (SAEs) for two experimental forests within the TIU are compared with each forest's design-based estimates generated using a dense network of independent inventory plots. Model parameter estimates and biomass predictions are informed using FIA plot measurements, LiDAR data that are spatially aligned with a subset of the FIA plots, and complete coverage remotely detected data used to define landuse/landcover stratum and percent forest canopy cover. Results support a model-based approach to estimating forest variables when inventory data are sparse or resources limit collection of enough data to achieve desired accuracy and precision using design-based methods.

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arXiv2023

Inference for Gaussian Processes with Matérn Covariogram on Compact Riemannian Manifolds

Gaussian processes are widely employed as versatile modelling and predictive tools in spatial statistics, functional data analysis, computer modelling and diverse applications of machine learning. They have been widely studied over Euclidean spaces, where they are specified using covariance functions or covariograms for modelling complex dependencies. There is a growing literature on Gaussian processes over Riemannian manifolds in order to develop richer and more flexible inferential frameworks for non-Euclidean data. While numerical approximations through graph representations have been well studied for the Matérn covariogram and heat kernel, the behaviour of asymptotic inference on the parameters of the covariogram has received relatively scant attention. We focus on the asymptotic inference for Gaussian processes constructed over compact Riemannian manifolds. Building upon the recently introduced Matérn covariogram on a compact Riemannian manifold, we employ formal notions and conditions for the equivalence of two Matérn Gaussian random measures on compact manifolds to derive the parameter that is identifiable, also known as the microergodic parameter, and formally establish the consistency of the maximum likelihood estimate and the asymptotic optimality of the best linear unbiased predictor. The circle is studied as a specific example of compact Riemannian manifolds with numerical experiments to illustrate and corroborate the theory.

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arXiv2023

Bayesian modeling with spatial curvature processes

Spatial process models are widely used for modeling point-referenced variables arising from diverse scientific domains. Analyzing the resulting random surface provides deeper insights into the nature of latent dependence within the studied response. We develop Bayesian modeling and inference for rapid changes on the response surface to assess directional curvature along a given trajectory. Such trajectories or curves of rapid change, often referred to as \emph{wombling} boundaries, occur in geographic space in the form of rivers in a flood plain, roads, mountains or plateaus or other topographic features leading to high gradients on the response surface. We demonstrate fully model based Bayesian inference on directional curvature processes to analyze differential behavior in responses along wombling boundaries. We illustrate our methodology with a number of simulated experiments followed by multiple applications featuring the Boston Housing data; Meuse river data; and temperature data from the Northeastern United States.

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arXiv2023

On identifiability and consistency of the nugget in Gaussian spatial process models

Spatial process models popular in geostatistics often represent the observed data as the sum of a smooth underlying process and white noise. The variation in the white noise is attributed to measurement error, or micro-scale variability, and is called the "nugget". We formally establish results on the identifiability and consistency of the nugget in spatial models based upon the Gaussian process within the framework of in-fill asymptotics, i.e. the sample size increases within a sampling domain that is bounded. Our work extends results in fixed domain asymptotics for spatial models without the nugget. More specifically, we establish the identifiability of parameters in the Matérn covariance function and the consistency of their maximum likelihood estimators in the presence of discontinuities due to the nugget. We also present simulation studies to demonstrate the role of the identifiable quantities in spatial interpolation.

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arXiv2023

Bayesian Hierarchical Modeling and Analysis for Actigraph Data from Wearable Devices

The majority of Americans fail to achieve recommended levels of physical activity, which leads to numerous preventable health problems such as diabetes, hypertension, and heart diseases. This has generated substantial interest in monitoring human activity to gear interventions toward environmental features that may relate to higher physical activity. Wearable devices, such as wrist-worn sensors that monitor gross motor activity (actigraph units) continuously record the activity levels of a subject, producing massive amounts of high-resolution measurements. Analyzing actigraph data needs to account for spatial and temporal information on trajectories or paths traversed by subjects wearing such devices. Inferential objectives include estimating a subject's physical activity levels along a given trajectory; identifying trajectories that are more likely to produce higher levels of physical activity for a given subject; and predicting expected levels of physical activity in any proposed new trajectory for a given set of health attributes. Here, we devise a Bayesian hierarchical modeling framework for spatial-temporal actigraphy data to deliver fully model-based inference on trajectories while accounting for subject-level health attributes and spatial-temporal dependencies. We undertake a comprehensive analysis of an original dataset from the Physical Activity through Sustainable Transport Approaches in Los Angeles (PASTA-LA) study to ascertain spatial zones and trajectories exhibiting significantly higher levels of physical activity while accounting for various sources of heterogeneity.

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arXiv2023

Fixed-Domain Asymptotics Under Vecchia's Approximation of Spatial Process Likelihoods

Statistical modeling for massive spatial data sets has generated a substantial literature on scalable spatial processes based upon Vecchia's approximation. Vecchia's approximation for Gaussian process models enables fast evaluation of the likelihood by restricting dependencies at a location to its neighbors. We establish inferential properties of microergodic spatial covariance parameters within the paradigm of fixed-domain asymptotics when they are estimated using Vecchia's approximation. The conditions required to formally establish these properties are explored, theoretically and empirically, and the effectiveness of Vecchia's approximation is further corroborated from the standpoint of fixed-domain asymptotics.

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arXiv2022

Joint species distribution models with imperfect detection for high-dimensional spatial data

Determining spatial distributions of species and communities are key objectives of ecology and conservation. Joint species distribution models use multi-species detection-nondetection data to estimate species and community distributions. The analysis of such data is complicated by residual correlations between species, imperfect detection, and spatial autocorrelation. While methods exist to accommodate each of these complexities, there are few examples in the literature that address and explore all three complexities simultaneously. Here we developed a spatial factor multi-species occupancy model to explicitly account for species correlations, imperfect detection, and spatial autocorrelation. The proposed model uses a spatial factor dimension reduction approach and Nearest Neighbor Gaussian Processes to ensure computational efficiency for data sets with both a large number of species (e.g., > 100) and spatial locations (e.g., 100,000). We compare the proposed model performance to five candidate models, each addressing a subset of the three complexities. We implemented the proposed and competing models in the spOccupancy software, designed to facilitate application via an accessible, well-documented, and open-source R package. Using simulations, we found ignoring the three complexities when present leads to inferior model predictive performance. Using a case study on 98 bird species across the continental US, the spatial factor multi-species occupancy model had the highest predictive performance among the candidate models. Our proposed framework, together with its implementation in spOccupancy, serves as a user-friendly tool to understand spatial variation in species distributions and biodiversity metrics while addressing common complexities in multi-species detection-nondetection data.

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arXiv2022

Bayesian Models for Multivariate Difference Boundary Detection in Areal Data

Regional aggregates of health outcomes over delineated administrative units (e.g., states, counties, zip codes), or areal units, are widely used by epidemiologists to map mortality or incidence rates and capture geographic variation. To capture health disparities over regions, we seek "difference boundaries" that separate neighboring regions with significantly different spatial effects. Matters are more challenging with multiple outcomes over each unit, where we capture dependence among diseases as well as across the areal units. Here, we address multivariate difference boundary detection for correlated diseases. We formulate the problem in terms of Bayesian pairwise multiple comparisons and seek the posterior probabilities of neighboring spatial effects being different. To achieve this, we endow the spatial random effects with a discrete probability law using a class of multivariate areally-referenced Dirichlet process (MARDP) models that accommodate spatial and inter-disease dependence. We evaluate our method through simulation studies and detect difference boundaries for multiple cancers using data from the Surveillance, Epidemiology, and End Results (SEER) Program of the National Cancer Institute.

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arXiv2022

bayesassurance: An R package for calculating sample size and Bayesian assurance

We present a bayesassurance R package that computes the Bayesian assurance under various settings characterized by different assumptions and objectives. The package offers a constructive set of simulation-based functions suitable for addressing a wide range of clinical trial study design problems. We provide a detailed description of the underlying framework embedded within each of the power and assurance functions and demonstrate their usage through a series of worked-out examples. Through these examples, we hope to corroborate the advantages that come with using a two-stage generalized structure. We also illustrate scenarios where the Bayesian assurance and frequentist power overlap, allowing the user to address both Bayesian and classical inference problems provided that the parameters are properly defined. All assurance-related functions included in this R package rely on a two-stage Bayesian method that assigns two distinct priors to evaluate the unconditional probability of observing a positive outcome, which in turn addresses subtle limitations that take place when using the standard single-prior approach.

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arXiv2021

A Unifying Bayesian Approach for Sample Size Determination Using Design and Analysis Priors

Power and sample size analysis comprises a critical component of clinical trial study design. There is an extensive collection of methods addressing this problem from diverse perspectives. The Bayesian paradigm, in particular, has attracted noticeable attention and includes different perspectives for sample size determination. Building upon a cost-effectiveness analysis undertaken by O'Hagan and Stevens (2001) with different priors in the design and analysis stage, we develop a general Bayesian framework for simulation-based sample size determination that can be easily implemented on modest computing architectures. We further qualify the need for different priors for the design and analysis stage. We work primarily in the context of conjugate Bayesian linear regression models, where we consider the situation with known and unknown variances. Throughout, we draw parallels with frequentist solutions, which arise as special cases, and alternate Bayesian approaches with an emphasis on how the numerical results from existing methods arise as special cases in our framework.

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