arXiv subjects

Sudipto Banerjee

Publications and source records attributed to Sudipto Banerjee.

At least 19 recordsLinked to original sources

arXiv2026

Spatial Disease Mapping and Disparity Detection Using Generative AI: An Amortized Bayesian Learning Framework

We introduce an amortized Bayesian framework for spatial boundary detection that generalizes posterior inference across areal graphs with varying numbers of regions and diverse adjacency structures. The underlying model couples a Poisson count likelihood with a covariate-driven rule to interrupt smoothing across dissimilar neighboring areas, utilizing a directed acyclic graph autoregressive (DAGAR) prior to capture residual spatial dependence. To approximate the target posterior distribution, a neural engine is trained on simulated maps: a permutation-invariant summary network encodes graph-aware representations of the observed counts, offsets, covariates, and adjacency matrices, while a conditional normalizing flow generates the approximate posterior draws. Simulation studies demonstrate accurate parameter recovery, near-nominal interval coverage, well-calibrated posterior predictive behavior, and informative posterior boundary probabilities. Benchmarking against Markov chain Monte Carlo (MCMC) confirms close agreement regarding primary boundary evidence, and an ablation study validates the inclusion of model-guided graph summaries. Finally, applications to Glasgow respiratory disease and California lung cancer data demonstrate that a single trained neural engine can be seamlessly deployed across real-world maps with distinct graph structures, yielding boundary conclusions consistent with established localized smoothing analyses.

stat.ME↗

arXiv2026

Amortized Bayesian inference for actigraph time sheet data from mobile devices

Mobile data technologies use ``actigraphs'' to furnish information on health variables as a function of a subject's movement. The advent of wearable devices and related technologies has propelled the creation of health databases consisting of human movement data to conduct research on mobility patterns and health outcomes. Statistical methods for analyzing high-resolution actigraph data depend on the specific inferential context, but the advent of Artificial Intelligence (AI) frameworks require that the methods be congruent to transfer learning and amortization. This article devises amortized Bayesian inference for actigraph time sheets. We pursue a Bayesian approach to ensure full propagation of uncertainty and its quantification using a hierarchical dynamic linear model. We build our analysis around actigraph data from the Physical Activity through Sustainable Transport Approaches in Los Angeles (PASTA-LA) study conducted by the Fielding School of Public Health in the University of California, Los Angeles. Apart from achieving probabilistic imputation of actigraph time sheets, we are also able to statistically learn about the time-varying impact of explanatory variables on the magnitude of acceleration (MAG) for a cohort of subjects.

stat.ML↗

arXiv2026

Dynamic Bayesian Predictive Stacking via Markovian Spatiotemporal Propagation

This manuscript develops computationally efficient online learning for multivariate spatiotemporal models. The proposed framework relies on matrix-variate Gaussian distributions, dynamic linear models, and Bayesian predictive stacking to efficiently share information across temporal data shards. The model facilitates effective information propagation over time while seamlessly integrating spatial components within a dynamic framework, building a Markovian dependence structure between datasets at successive time instants. This structure supports flexible, high-dimensional modeling of complex dependence patterns, as commonly found in spatiotemporal phenomena, where computational challenges arise rapidly with increasing dimensions. The proposed approach further manages exact inference through predictive stacking, enhancing robustness and interoperability. Combining sequential and parallel processing of temporal shards, each unit passes assimilated information forward and then back-smooths it to improve posterior estimation, incorporating all available information. This framework advances the scalability and adaptability of spatiotemporal modeling, making it suitable for dynamic, multivariate, and data-rich environments. Simulation experiments and an extracted data analysis from the Copernicus Data Space Ecosystem (CDSE) help evaluate and illustrate the framework.

stat.ME↗

arXiv2026

On Statistical Inference for Rates of Change in Spatial Processes over Riemannian Manifolds

Statistical inference for spatial processes from partially realized or scattered data has seen voluminous developments in diverse areas ranging from environmental sciences to business and economics. Inference on the associated rates of change has seen some recent developments. The literature has been restricted to Euclidean domains, where inference is sought on directional derivatives, rates along a chosen direction of interest, at arbitrary locations. Inference for higher order rates, particularly directional curvature has also proved useful in these settings. Modern spatial data often arise from non-Euclidean domains. This manuscript particularly considers spatial processes defined over compact Riemannian manifolds. We develop a comprehensive inferential framework for spatial rates of change for such processes over vector fields. In doing so, we formalize smoothness of process realizations and construct differential processes -- the derivative and curvature processes. We derive conditions for kernels that ensure the existence of these processes and establish validity of the joint multivariate process consisting of the ``parent'' Gaussian process (GP) over the manifold and the associated differential processes. Predictive inference on these rates is devised conditioned on the realized process over the manifold. Manifolds arise as polyhedral meshes in practice. The success of our simulation experiments for assessing derivatives for processes observed over such meshes validate our theoretical findings. By enhancing our understanding of GPs on manifolds, this manuscript unlocks a variety of potential applications in machine learning and statistics where GPs have seen wide usage. We propose a fully model-based approach to inference on the differential processes arising from a spatial process from partially observed or realized data across scattered location on a manifold.

math.ST↗

arXiv2025

The Nearest-Neighbor Derivative Process: Modeling Spatial Rates of Change in Massive Datasets

Gaussian processes (GPs) are instrumental in modeling spatial processes, offering precise interpolation and prediction capabilities across fields such as environmental science and biology. Recently, there has been growing interest in extending GPs to infer spatial derivatives, which are vital for analyzing spatial dynamics and detecting subtle changes in data patterns. Despite their utility, traditional GPs suffer from computational inefficiencies, due to the cubic scaling with the number of spatial locations. Fortunately, the computational challenge has spurred extensive research on scalable GP methods. However, these scalable approaches do not directly accommodate the inference of derivative processes. A straightforward approach is to use scalable GP models followed by finite-difference methods, known as the plug-in estimator. This approach, while intuitive, suffers from sensitivity to parameter choices, and the approximate gradient may not be a valid GP, leading to compromised inference. To bridge this gap, we introduce the Nearest-Neighbor Derivative Process (NNDP), an innovative framework that models the spatial processes and their derivatives within a single scalable GP model. NNDP significantly reduces the computational time complexity from $O(n^3)$ to $O(n)$, making it feasible for large datasets. We provide various theoretical supports for NNDP and demonstrate its effectiveness through extensive simulations and real data analysis.

stat.ME↗

arXiv2025

Bayesian Inference for Spatially-Temporally Misaligned Data Using Predictive Stacking

Air pollution remains a major environmental risk factor that is often associated with adverse health outcomes. However, quantifying and evaluating its effects on human health is challenging due to the complex nature of exposure data. Recent technological advances have led to the collection of various indicators of air pollution at increasingly high spatial-temporal resolutions (e.g., daily averages of pollutant levels at spatial locations referenced by latitude-longitude). However, health outcomes are typically aggregated over several spatial-temporal coordinates (e.g., annual prevalence for a county) to comply with survey regulations. This article develops a Bayesian hierarchical model to analyze such spatially-temporally misaligned exposure and health outcome data. We introduce Bayesian predictive stacking, which optimally combines multiple predictive spatial-temporal models and avoids iterative estimation algorithms such as Markov chain Monte Carlo that struggle due to convergence issues inflicted by the presence of weakly identified parameters. We apply our proposed method to study the effects of ozone on asthma in the state of California.

stat.ME↗

arXiv2025

Bayesian Data Sketching for Varying Coefficient Regression Models

Varying coefficient models are popular for estimating nonlinear regression functions in functional data models. Their Bayesian variants have received limited attention in large data applications, primarily due to prohibitively slow posterior computations using Markov chain Monte Carlo (MCMC) algorithms. We introduce Bayesian data sketching for varying coefficient models to obviate computational challenges presented by large sample sizes. To address the challenges of analyzing large data, we compress the functional response vector and predictor matrix by a random linear transformation to achieve dimension reduction and conduct inference on the compressed data. Our approach distinguishes itself from several existing methods for analyzing large functional data in that it requires neither the development of new models or algorithms, nor any specialized computational hardware while delivering fully model-based Bayesian inference. Well-established methods and algorithms for varying coefficient regression models can be applied to the compressed data.

stat.ML↗

arXiv2025

Spatial Confounding in Multivariate Areal Data Analysis

We investigate spatial confounding in the presence of multivariate disease dependence. In the "analysis model perspective" of spatial confounding, adding a spatially dependent random effect can lead to significant variance inflation of the posterior distribution of the fixed effects. The "data generation perspective" views covariates as stochastic and correlated with an unobserved spatial confounder, leading to inferior statistical inference over multiple realizations. Although multiple methods have been proposed for adjusting statistical models to mitigate spatial confounding in estimating regression coefficients, the results on interactions between spatial confounding and multivariate dependence are very limited. We contribute to this domain by investigating spatial confounding from the analysis and data generation perspectives in a Bayesian coregionalized areal regression model. We derive novel results that distinguish variance inflation due to spatial confounding from inflation based on multicollinearity between predictors and provide insights into the estimation efficiency of a spatial estimator under a spatially confounded data generation model. We demonstrate favorable performance of spatial analysis compared to a non-spatial model in our simulation experiments even in the presence of spatial confounding and a misspecified spatial structure. In this regard, we align with several other authors in the defense of traditional hierarchical spatial models (Gilbert et al., 2025; Khan and Berrett, 2023; Zimmerman and Ver Hoef, 2022) and extend this defense to multivariate areal models. We analyze county-level data from the US on obesity / diabetes prevalence and diabetes-related cancer mortality, comparing the results with and without spatial random effects.

stat.ME↗

arXiv2025

nimblewomble: An R package for Bayesian Wombling with nimble

This exposition presents nimblewomble, a software package to perform wombling, or boundary analysis, using the nimble Bayesian hierarchical modeling language in the R statistical computing environment. Wombling is used widely to track regions of rapid change within the spatial reference domain. Specific functions in the package implement Gaussian process models for point-referenced spatial data followed by predictive inference on rates of change over curves using line integrals. We demonstrate model based Bayesian inference using posterior distributions featuring simple analytic forms while offering uncertainty quantification over curves.

stat.CO↗

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.

stat.AP↗

arXiv2024

Bayesian Transfer Learning for Artificially Intelligent Geospatial Systems: A Predictive Stacking Approach

Building artificially intelligent geospatial systems requires rapid delivery of spatial data analysis on massive scales with minimal human intervention. Depending upon their intended use, data analysis can also involve model assessment and uncertainty quantification. This article devises transfer learning frameworks for deployment in artificially intelligent systems, where a massive data set is split into smaller data sets that stream into the analytical framework to propagate learning and assimilate inference for the entire data set. Specifically, we introduce Bayesian predictive stacking for multivariate spatial data and demonstrate rapid and automated analysis of massive data sets. Furthermore, inference is delivered without human intervention without excessively demanding hardware settings. We illustrate the effectiveness of our approach through extensive simulation experiments and in producing inference from massive dataset on vegetation index that are indistinguishable from traditional (and more expensive) statistical approaches.

stat.ME↗

arXiv2024

Assessing Spatial Disparities: A Bayesian Linear Regression Approach

Epidemiological investigations of regionally aggregated spatial data often involve detecting spatial health disparities among neighboring regions on a map of disease mortality or incidence rates. Analyzing such data introduces spatial dependence among health outcomes and seeks to report statistically significant spatial disparities by delineating boundaries that separate neighboring regions with disparate health outcomes. However, there are statistical challenges to appropriately define what constitutes a spatial disparity and to construct robust probabilistic inferences for spatial disparities. We enrich the familiar Bayesian linear regression framework to introduce spatial autoregression and offer model-based detection of spatial disparities. We derive exploitable analytical tractability that considerably accelerates computation. Simulation experiments conducted on a county map of the entire United States demonstrate the effectiveness of our method, and we apply our method to a data set from the Institute of Health Metrics and Evaluation (IHME) on age-standardized US county-level estimates of lung cancer mortality rates.

stat.ME↗

arXiv2024

Bayesian Spatiotemporal Wombling

Stochastic process models for spatiotemporal data underlying random fields find substantial utility in a range of scientific disciplines. Subsequent to predictive inference on the values of the random field (or spatial surface indexed continuously over time) at arbitrary space-time coordinates, scientific interest often turns to gleaning information regarding zones of rapid spatial-temporal change. We develop Bayesian modeling and inference for directional rates of change along a given surface. These surfaces, which demarcate regions of rapid change, are referred to as ``wombling'' surface boundaries. Existing methods for studying such changes have often been associated with curves and are not easily extendable to surfaces resulting from curves evolving over time. Our current contribution devises a fully model-based inferential framework for analyzing differential behavior in spatiotemporal responses by formalizing the notion of a ``wombling'' surface boundary using conventional multi-linear vector analytic frameworks and geometry followed by posterior predictive computations using triangulated surface approximations. We illustrate our methodology with comprehensive simulation experiments followed by multiple applications in environmental and climate science; pollutant analysis in environmental health; and brain imaging.

stat.ME↗

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.

stat.AP↗

arXiv2024

Bayesian Inference for Spatial-Temporal Non-Gaussian Data Using Predictive Stacking

Analysing non-Gaussian spatial-temporal data requires introducing spatial as well as temporal dependence in generalised linear models through the link function of an exponential family distribution. Unlike in Gaussian likelihoods, inference is considerably encumbered by the inability to analytically integrate out the random effects and reduce the dimension of the parameter space. Iterative estimation algorithms struggle to converge due to the presence of weakly identified parameters. We devise Bayesian inference using predictive stacking that assimilates inference from analytically tractable conditional posterior distributions. We achieve this by expanding upon the Diaconis-Ylvisaker family of conjugate priors and exploiting generalised conjugate multivariate (GCM) distribution theory for exponential families, which enables exact sampling from analytically available posterior distributions conditional upon some process parameters. Subsequently, we assimilate inference over a range of values of these parameters using Bayesian predictive stacking. We evaluate inferential performance on simulated data, compare with full Bayesian inference using Markov chain Monte Carlo (MCMC) and apply our method to analyse spatially-temporally referenced avian count data from the North American Breeding Bird Survey database.

stat.ME↗

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.

stat.ME↗

arXiv2023

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.

stat.ME↗

arXiv2023

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.

stat.ME↗