Efficient algorithms for Bayesian Nearest Neighbor Gaussian Processes

Improved fMRI-based pain prediction using Bayesian group-wise functional registration

In recent years, the field of neuroimaging has undergone a paradigm shift, moving away from the traditional brain mapping approach towards the development of integrated, multivariate brain models that can predict categories of mental events. However, large interindividual differences in both brain anatomy and functional localization after standard anatomical alignment remain a major limitation in performing this type of analysis, as it leads to feature misalignment across subjects in subsequent predictive models. This article addresses this problem by developing and validating a new computational technique for reducing misalignment across individuals in functional brain systems by spatially transforming each subject's functional data to a common latent template map. Our proposed Bayesian functional group-wise registration approach allows us to assess differences in brain function across subjects and individual differences in activation topology. We achieve the probabilistic registration with inverse-consistency by utilizing the generalized Bayes framework with a loss function for the symmetric group-wise registration. It models the latent template with a Gaussian process, which helps capture spatial features in the template, producing a more precise estimation. We evaluate the method in simulation studies and apply it to data from an fMRI study of thermal pain, with the goal of using functional brain activity to predict physical pain. We find that the proposed approach allows for improved prediction of reported pain scores over conventional approaches. Received on 2 January 2017. Editorial decision on 8 June 2021.

Integrating traffic pollution dispersion into spatiotemporal NO2 prediction

Accurately predicting ambient NO2 concentrations has great public health importance, as traffic-related air pollution is of major concern in urban areas. In this study, we present a novel approach incorporating traffic contribution to NO2 prediction in a fine-scale spatiotemporal model. We used nationally available traffic estimate dataset in a scalable dispersion model, Research LINE source dispersion model (RLINE). RLINE estimates then served as an additional input for a validated spatiotemporal pollution modeling approach. Our analysis uses measurement data collected by the Multi-Ethnic Study of Atherosclerosis and Air Pollution in the greater Los Angeles area between 2006 and 2009. We predicted road-type-specific annual average daily traffic (AADT) on road segments via national-level spatial regression models with nearest-neighbor Gaussian processes (spNNGP); the spNNGP models were trained based on over half a million point-level traffic volume measurements nationwide. AADT estimates on all highways were combined with meteorological data in RLINE models. We evaluated two strategies to integrate RLINE estimates into spatiotemporal NO2 models: 1) incorporating RLINE estimates as a space-only covariate and, 2) as a spatiotemporal covariate. The results showed that integrating the RLINE estimates as a space-only covariate improved overall cross-validation R2 from 0.83 to 0.84, and root mean squared error (RMSE) from 3.58 to 3.48 ppb. Incorporating the estimates as a spatiotemporal covariate resulted in similar model improvement. The improvement of our spatiotemporal model was more profound in roadside monitors alongside highways, with R2 increasing from 0.56 to 0.66 and RMSE decreasing from 3.52 to 3.11 ppb. The observed improvement indicates that the RLINE estimates enhanced the model's predictive capabilities for roadside NO2 concentration gradients even after considering a comprehensive list of geographic covariates including the distance to roads. Our proposed modeling framework can be generalized to improve high-resolution prediction of NO2 exposure - especially near major roads in the U.S.

Federal Nutrition Assistance for Young Children: Underutilized and Unequally Accessed

INTRODUCTION

The federal Child and Adult Care Food Program (CACFP) improves nutrition and reduces food insecurity among young children by helping cover the food costs for child care providers and families. This nationwide study evaluated the extent and predictors of the CACFP's utilization among licensed child care centers to identify opportunities for expanding CACFP nutrition support.

METHODS

Administrative data from the CACFP and child care licensing agencies in 47 states and District of Columbia were compiled and geocoded for 93,227 licensed child care centers. CACFP participation was predicted using a multivariable Bayesian spatial logistic regression model in the sample of low-income areas to target CACFP eligible child care centers. Data were collected in 2020-2021 and analyzed in 2022.

RESULTS

Of all licensed child care centers, 36.5% participated in the CACFP, ranging from 15.2% to 65.3% across states; when restricted to low-income areas, 57.5% participated (range, 15.7%-85.7%). Income differences did not explain the large variation in CACFP participation rates across states. Having at least three CACFP sponsoring agencies per state predicted a 38% higher probability of CACFP participation (OR=1.38; 95% Credible Interval=1.08-1.78).

CONCLUSIONS

Currently CACFP participation rates among licensed child care centers point to program underutilization and unequal access, particularly in some states and regions. Work at the federal and state levels is warranted to expand participation in the program, above all in low-income areas, so that more young children could eat healthfully with the CACFP.

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.

A DYNAMIC SPATIAL FILTERING APPROACH TO MITIGATE UNDERESTIMATION BIAS IN FIELD CALIBRATED LOW-COST SENSOR AIR POLLUTION DATA

Low-cost air pollution sensors, offering hyper-local characterization of pollutant concentrations, are becoming increasingly prevalent in environmental and public health research. However, low-cost air pollution data can be noisy, biased by environmental conditions, and usually need to be field-calibrated by collocating low-cost sensors with reference-grade instruments. We show, theoretically and empirically, that the common procedure of regression-based calibration using collocated data systematically underestimates high air pollution concentrations, which are critical to diagnose from a health perspective. Current calibration practices also often fail to utilize the spatial correlation in pollutant concentrations. We propose a novel spatial filtering approach to collocation-based calibration of low-cost networks that mitigates the underestimation issue by using an inverse regression. The inverse-regression also allows for incorporating spatial correlations by a second-stage model for the true pollutant concentrations using a conditional Gaussian Process. Our approach works with one or more collocated sites in the network and is dynamic, leveraging spatial correlation with the latest available reference data. Through extensive simulations, we demonstrate how the spatial filtering substantially improves estimation of pollutant concentrations, and measures peak concentrations with greater accuracy. We apply the methodology for calibration of a low-cost PM2.5 network in Baltimore, Maryland, and diagnose air pollution peaks that are missed by the regression-calibration.

Prior elicitation for Gaussian spatial process: An application to TMS brain mapping

The power and commensurate prior distributions are informative prior distributions that incorporate historical data as prior knowledge in Bayesian analysis to improve inference about a phenomenon under study. Although these distributions have been developed for analyzing non-spatial data, little or no attention has been given to spatial geostatistical data. In this study, we extend these informative prior distributions to a Gaussian spatial process, which enables the elicitation of prior knowledge from historical geostatistical data for Bayesian analysis. Three informative prior distributions were developed for spatial modeling, and an efficient Markov Chain Monte Carlo algorithm was developed for performing Bayesian analysis. Simulation studies were used to assess the adequacy of the informative prior distributions. Hierarchical models combined with the developed informative prior distributions were applied to analyze transcranial magnetic stimulation (TMS) brain mapping data to gain insights into the spatial pattern of a patient's response to motor cortex stimulation. The study quantified the uncertainty in motor response and found that the primary motor cortex of the hand is responsible for most of the movement of the right first dorsal interosseous muscle. The findings provide a deeper understanding of the neural mechanisms underlying motor function and ultimately aid the improvement of treatment options for individuals with health issues.

Modeling Multivariate Spatial Dependencies Using Graphical Models

Graphical models have witnessed significant growth and usage in spatial data science for modeling data referenced over a massive number of spatial-temporal coordinates. Much of this literature has focused on a single or relatively few spatially dependent outcomes. Recent attention has focused upon addressing modeling and inference for substantially large number of outcomes. While spatial factor models and multivariate basis expansions occupy a prominent place in this domain, this article elucidates a recent approach, graphical Gaussian Processes, that exploits the notion of conditional independence among a very large number of spatial processes to build scalable graphical models for fully model-based Bayesian analysis of multivariate spatial data.

Fast Bayesian inference for large occupancy datasets

In recent years, the study of species' occurrence has benefited from the increased availability of large-scale citizen-science data. While abundance data from standardized monitoring schemes are biased toward well-studied taxa and locations, opportunistic data are available for many taxonomic groups, from a large number of locations and across long timescales. Hence, these data provide opportunities to measure species' changes in occurrence, particularly through the use of occupancy models, which account for imperfect detection. These opportunistic datasets can be substantially large, numbering hundreds of thousands of sites, and hence present a challenge from a computational perspective, especially within a Bayesian framework. In this paper, we develop a unifying framework for Bayesian inference in occupancy models that account for both spatial and temporal autocorrelation. We make use of the Pólya-Gamma scheme, which allows for fast inference, and incorporate spatio-temporal random effects using Gaussian processes (GPs), for which we consider two efficient approximations: subset of regressors and nearest neighbor GPs. We apply our model to data on two UK butterfly species, one common and widespread and one rare, using records from the Butterflies for the New Millennium database, producing occupancy indices spanning 45 years. Our framework can be applied to a wide range of taxa, providing measures of variation in species' occurrence, which are used to assess biodiversity change.

nnSVG for the scalable identification of spatially variable genes using nearest-neighbor Gaussian processes

Feature selection to identify spatially variable genes or other biologically informative genes is a key step during analyses of spatially-resolved transcriptomics data. Here, we propose nnSVG, a scalable approach to identify spatially variable genes based on nearest-neighbor Gaussian processes. Our method (i) identifies genes that vary in expression continuously across the entire tissue or within a priori defined spatial domains, (ii) uses gene-specific estimates of length scale parameters within the Gaussian process models, and (iii) scales linearly with the number of spatial locations. We demonstrate the performance of our method using experimental data from several technological platforms and simulations. A software implementation is available at https://bioconductor.org/packages/nnSVG .

Big problems in spatio-temporal disease mapping: Methods and software

BACKGROUND AND OBJECTIVE

Fitting spatio-temporal models for areal data is crucial in many fields such as cancer epidemiology. However, when data sets are very large, many issues arise. The main objective of this paper is to propose a general procedure to analyze high-dimensional spatio-temporal areal data, with special emphasis on mortality/incidence relative risk estimation.

METHODS

We present a pragmatic and simple idea that permits hierarchical spatio-temporal models to be fitted when the number of small areas is very large. Model fitting is carried out using integrated nested Laplace approximations over a partition of the spatial domain. We also use parallel and distributed strategies to speed up computations in a setting where Bayesian model fitting is generally prohibitively time-consuming or even unfeasible.

RESULTS

Using simulated and real data, we show that our method outperforms classical global models. We implement the methods and algorithms that we develop in the open-source R package bigDM where specific vignettes have been included to facilitate the use of the methodology for non-expert users.

CONCLUSIONS

Our scalable methodology proposal provides reliable risk estimates when fitting Bayesian hierarchical spatio-temporal models for high-dimensional data.

Nonnegative spatial factorization applied to spatial genomics

Nonnegative matrix factorization (NMF) is widely used to analyze high-dimensional count data because, in contrast to real-valued alternatives such as factor analysis, it produces an interpretable parts-based representation. However, in applications such as spatial transcriptomics, NMF fails to incorporate known structure between observations. Here, we present nonnegative spatial factorization (NSF), a spatially-aware probabilistic dimension reduction model based on transformed Gaussian processes that naturally encourages sparsity and scales to tens of thousands of observations. NSF recovers ground truth factors more accurately than real-valued alternatives such as MEFISTO in simulations, and has lower out-of-sample prediction error than probabilistic NMF on three spatial transcriptomics datasets from mouse brain and liver. Since not all patterns of gene expression have spatial correlations, we also propose a hybrid extension of NSF that combines spatial and nonspatial components, enabling quantification of spatial importance for both observations and features. A TensorFlow implementation of NSF is available from https://github.com/willtownes/nsf-paper .

Spatially-enhanced clusterwise inference for testing and localizing intermodal correspondence

With the increasing availability of neuroimaging data from multiple modalities-each providing a different lens through which to study brain structure or function-new techniques for comparing, integrating, and interpreting information within and across modalities have emerged. Recent developments include hypothesis tests of associations between neuroimaging modalities, which can be used to determine the statistical significance of intermodal associations either throughout the entire brain or within anatomical subregions or functional networks. While these methods provide a crucial foundation for inference on intermodal relationships, they cannot be used to answer questions about where in the brain these associations are most pronounced. In this paper, we introduce a new method, called CLEAN-R, that can be used both to test intermodal correspondence throughout the brain and also to localize this correspondence. Our method involves first adjusting for the underlying spatial autocorrelation structure within each modality before aggregating information within small clusters to construct a map of enhanced test statistics. Using structural and functional magnetic resonance imaging data from a subsample of children and adolescents from the Philadelphia Neurodevelopmental Cohort, we conduct simulations and data analyses where we illustrate the high statistical power and nominal type I error levels of our method. By constructing an interpretable map of group-level correspondence using spatially-enhanced test statistics, our method offers insights beyond those provided by earlier methods.

Scalable Predictions for Spatial Probit Linear Mixed Models Using Nearest Neighbor Gaussian Processes

Spatial probit generalized linear mixed models (spGLMM) with a linear fixed effect and a spatial random effect, endowed with a Gaussian Process prior, are widely used for analysis of binary spatial data. However, the canonical Bayesian implementation of this hierarchical mixed model can involve protracted Markov Chain Monte Carlo sampling. Alternate approaches have been proposed that circumvent this by directly representing the marginal likelihood from spGLMM in terms of multivariate normal cummulative distribution functions (cdf). We present a direct and fast rendition of this latter approach for predictions from a spatial probit linear mixed model. We show that the covariance matrix of the cdf characterizing the marginal cdf of binary spatial data from spGLMM is amenable to approximation using Nearest Neighbor Gaussian Processes (NNGP). This facilitates a scalable prediction algorithm for spGLMM using NNGP that only involves sparse or small matrix computations and can be deployed in an embarrassingly parallel manner. We demonstrate the accuracy and scalability of the algorithm via numerous simulation experiments and an analysis of species presence-absence data.

BAYESIAN FUNCTIONAL REGISTRATION OF FMRI ACTIVATION MAPS

Functional magnetic resonance imaging (fMRI) has provided invaluable insight into our understanding of human behavior. However, large inter-individual differences in both brain anatomy and functional localization after anatomical alignment remain a major limitation in conducting group analyses and performing population level inference. This paper addresses this problem by developing and validating a new computational technique for reducing misalignment across individuals in functional brain systems by spatially transforming each subjects functional data to a common reference map. Our proposed Bayesian functional registration approach allows us to assess differences in brain function across subjects and individual differences in activation topology. It combines intensity-based and feature-based information into an integrated framework, and allows inference to be performed on the transformation via the posterior samples. We evaluate the method in a simulation study and apply it to data from a study of thermal pain. We find that the proposed approach provides increased sensitivity for group-level inference.

CLEAN: Leveraging spatial autocorrelation in neuroimaging data in clusterwise inference

While clusterwise inference is a popular approach in neuroimaging that improves sensitivity, current methods do not account for explicit spatial autocorrelations because most use univariate test statistics to construct cluster-extent statistics. Failure to account for such dependencies could result in decreased reproducibility. To address methodological and computational challenges, we propose a new powerful and fast statistical method called CLEAN (Clusterwise inference Leveraging spatial Autocorrelations in Neuroimaging). CLEAN computes multivariate test statistics by modelling brain-wise spatial autocorrelations, constructs cluster-extent test statistics, and applies a refitting-free resampling approach to control false positives. We validate CLEAN using simulations and applications to the Human Connectome Project. This novel method provides a new direction in neuroimaging that paces with advances in high-resolution MRI data which contains a substantial amount of spatial autocorrelation.

Spatial Multivariate Trees for Big Data Bayesian Regression

High resolution geospatial data are challenging because standard geostatistical models based on Gaussian processes are known to not scale to large data sizes. While progress has been made towards methods that can be computed more efficiently, considerably less attention has been devoted to methods for large scale data that allow the description of complex relationships between several outcomes recorded at high resolutions by different sensors. Our Bayesian multivariate regression models based on spatial multivariate trees (SpamTrees) achieve scalability via conditional independence assumptions on latent random effects following a treed directed acyclic graph. Information-theoretic arguments and considerations on computational efficiency guide the construction of the tree and the related efficient sampling algorithms in imbalanced multivariate settings. In addition to simulated data examples, we illustrate SpamTrees using a large climate data set which combines satellite data with land-based station data. Software and source code are available on CRAN at https://CRAN.R-project.org/package=spamtree.

Evaluating Methodology for the Service Extent of Refugee Parks in Changchun, China

Refugee parks are general parks that can serve as emergency shelters in cities. The core issue of refugee parks lies in their service extent they provided. Globally, the service extent of refugee parks is determined by the Euclidean or actual road network distance methods. The former lacks measurement accuracy, whereas the latter lacks the consideration of human dimension and proximity. Hence, we propose the nearest neighbor method, which considers not only the locations of refugee parks and sub-districts, but also road networks and census data. Using this method, we evaluated the service extent of refugee parks in Changchun, northern China. We compared our results with the Euclidean distance method. Results showed that the nearest neighbor method effectively accounted for the effect of road network resistance and results aligned with the refuge needs of residents. Differences in both methods were mainly affected by the size of the parks and local road network and population densities. The Euclidean approach determines the service extent based on a unified service radius, thus producing greater errors. The nearest neighbor method can reveal the spatial imbalance of refugee parks, as well as the mismatch between the park size and population distribution. Furthermore, the nearest neighbor method implements policies of spatial optimization of urban refugee parks. As a general method, it should be suited to different types of disasters.

Modeling Massive Spatial Datasets Using a Conjugate Bayesian Linear Modeling Framework

Geographic Information Systems (GIS) and related technologies have generated substantial interest among statisticians with regard to scalable methodologies for analyzing large spatial datasets. A variety of scalable spatial process models have been proposed that can be easily embedded within a hierarchical modeling framework to carry out Bayesian inference. While the focus of statistical research has mostly been directed toward innovative and more complex model development, relatively limited attention has been accorded to approaches for easily implementable scalable hierarchical models for the practicing scientist or spatial analyst. This article discusses how point-referenced spatial process models can be cast as a conjugate Bayesian linear regression that can rapidly deliver inference on spatial processes. The approach allows exact sampling directly (avoids iterative algorithms such as Markov chain Monte Carlo) from the joint posterior distribution of regression parameters, the latent process and the predictive random variables, and can be easily implemented on statistical programming environments such as R.

Computationally efficient joint species distribution modeling of big spatial data

The ongoing global change and the increased interest in macroecological processes call for the analysis of spatially extensive data on species communities to understand and forecast distributional changes of biodiversity. Recently developed joint species distribution models can deal with numerous species efficiently, while explicitly accounting for spatial structure in the data. However, their applicability is generally limited to relatively small spatial data sets because of their severe computational scaling as the number of spatial locations increases. In this work, we propose a practical alleviation of this scalability constraint for joint species modeling by exploiting two spatial-statistics techniques that facilitate the analysis of large spatial data sets: Gaussian predictive process and nearest-neighbor Gaussian process. We devised an efficient Gibbs posterior sampling algorithm for Bayesian model fitting that allows us to analyze community data sets consisting of hundreds of species sampled from up to hundreds of thousands of spatial units. The performance of these methods is demonstrated using an extensive plant data set of 30,955 spatial units as a case study. We provide an implementation of the presented methods as an extension to the hierarchical modeling of species communities framework.

Spatial Factor Models for High-Dimensional and Large Spatial Data: An Application in Forest Variable Mapping

Gathering information about forest variables is an expensive and arduous activity. As such, directly collecting the data required to produce high-resolution maps over large spatial domains is infeasible. Next generation collection initiatives of remotely sensed Light Detection and Ranging (LiDAR) data are specifically aimed at producing complete-coverage maps over large spatial domains. Given that LiDAR data and forest characteristics are often strongly correlated, it is possible to make use of the former to model, predict, and map forest variables over regions of interest. This entails dealing with the high-dimensional (~102) spatially dependent LiDAR outcomes over a large number of locations (~105-106). With this in mind, we develop the Spatial Factor Nearest Neighbor Gaussian Process (SF-NNGP) model, and embed it in a two-stage approach that connects the spatial structure found in LiDAR signals with forest variables. We provide a simulation experiment that demonstrates inferential and predictive performance of the SF-NNGP, and use the two-stage modeling strategy to generate complete-coverage maps of forest variables with associated uncertainty over a large region of boreal forests in interior Alaska.

A Case Study Competition Among Methods for Analyzing Large Spatial Data

The Gaussian process is an indispensable tool for spatial data analysts. The onset of the "big data" era, however, has lead to the traditional Gaussian process being computationally infeasible for modern spatial data. As such, various alternatives to the full Gaussian process that are more amenable to handling big spatial data have been proposed. These modern methods often exploit low-rank structures and/or multi-core and multi-threaded computing environments to facilitate computation. This study provides, first, an introductory overview of several methods for analyzing large spatial data. Second, this study describes the results of a predictive competition among the described methods as implemented by different groups with strong expertise in the methodology. Specifically, each research group was provided with two training datasets (one simulated and one observed) along with a set of prediction locations. Each group then wrote their own implementation of their method to produce predictions at the given location and each was subsequently run on a common computing environment. The methods were then compared in terms of various predictive diagnostics. Supplementary materials regarding implementation details of the methods and code are available for this article online.

ELECTRONIC SUPPLEMENTARY MATERIAL

Supplementary materials for this article are available at 10.1007/s13253-018-00348-w.