Modeling massive spatial datasets using a conjugate Bayesian linear modeling framework

Banerjee, Sudipto

doi:10.1016/j.spasta.2020.100417

Cited by 16 publications

(15 citation statements)

References 52 publications

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“…The argument given in (3) is free of distributional assumptions and is linked to the submodularity of entropy and the "information never hurts" principle; see Cover and Thomas (1991) and, more specifically, Eq. ( 18) in Banerjee (2020). Apart from providing a theoretical argument in favor of joint modeling, (3) also notes that models built upon hierarchical dependence structures depend upon the order in which the diseases enter the model.…”

Section: Motivating Multivariate Disease Mappingmentioning

confidence: 99%

Hierarchical Multivariate Directed Acyclic Graph Auto-Regressive (MDAGAR) models for spatial diseases mapping

Gao

Datta

Banerjee

2021

Preprint

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Disease mapping is an important statistical tool used by epidemiologists to assess geographic variation in disease rates and identify lurking environmental risk factors from spatial patterns. Such maps rely upon spatial models for regionally aggregated data, where neighboring regions tend to exhibit similar outcomes than those farther apart. We contribute to the literature on multivariate disease mapping, which deals with measurements on multiple (two or more) diseases in each region. We aim to disentangle associations among the multiple diseases from spatial autocorrelation in each disease. We develop Multivariate Directed Acyclic Graphical Autoregression (MDAGAR) models to accommodate spatial and inter-disease dependence. The hierarchical construction imparts flexibility and richness, interpretability of spatial autocorrelation and inter-disease relationships, and computational ease, but depends upon the order in which the cancers are modeled. To obviate this, we demonstrate how Bayesian model selection and averaging across orders are easily achieved using bridge sampling. We compare our method with a competitor using simulation studies and present an application to multiple cancer mapping using data from the Surveillance, Epidemiology, and End Results (SEER) Program.

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Section: Motivating Multivariate Disease Mappingmentioning

confidence: 99%

Hierarchical Multivariate Directed Acyclic Graph Auto-Regressive (MDAGAR) models for spatial diseases mapping

Gao

Datta

Banerjee

2021

Preprint

Self Cite

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“…By replacing the mean profiles as functions of the covariates, we can extend the proposed model to study the significance of a specific predictor in the context of fire modeling. The underlying dependence structures are assumed to be stationary for Stage 1 and Stage 3; however, some approaches available in the literature allow nonstationary spatial modeling for large datasets (Katzfuss, 2013;Banerjee, 2020), and we can extend the proposed model in that direction. Although the main focus in the data challenge is the accurate estimation of the upper tail of CNT and BA observations, we build our model using Gaussian processes that have been criticized for modeling spatial extremes (Davison et al, 2013).…”

Section: Possible Extensionsmentioning

confidence: 99%

A combined statistical and machine learning approach for spatial prediction of extreme wildfire frequencies and sizes

Daniela¹,

Gong²,

Yadav³

et al. 2021

Preprint

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Motivated by the Extreme Value Analysis 2021 (EVA 2021) data challenge we propose a method based on statistics and machine learning for the spatial prediction of extreme wildfire frequencies and sizes. This method is tailored to handle large datasets, including missing observations. Our approach relies on a four-stage high-dimensional bivariate sparse spatial model for zero-inflated data, which is developed using stochastic partial differential equations (SPDE). In Stage 1, the observations are categorized in zero/nonzero categories and are modeled using a two-layered hierarchical Bayesian sparse spatial model to estimate the probabilities of these two categories. In Stage 2, before modeling the positive observations using a spatiallyvarying coefficients, smoothed parameter surfaces are obtained from empirical estimates using fixed rank kriging. This approximate Bayesian method inference was employed to avoid the high computational burden of large spatial data modeling using spatially-varying coefficients. In Stage 3, the standardized log-transformed positive observations from the second stage are further modeled using a sparse bivariate spatial Gaussian process. The Gaussian distribution assumption for wildfire counts developed in the third stage, is computationally effective but erroneous. Thus in Stage 4, the predicted values are rectified using Random Forests. Posterior inference is drawn for Stages 1 and 3 using Markov chain Monte Carlo (MCMC) sampling. A cross-validation scheme is then created for the artificially generated gaps, and the EVA 2021 prediction scores of the proposed model are compared to those obtained using certain natural competitors.

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“…DAGs can be designed by taking a small number of "past" neighbors after choosing an arbitrary ordering of the data. In models of the response and in the conditionally-conjugate latent Gaussian case, posterior computations rely on sparse-matrix routines for scalability (Finley et al, 2019;Jurek and Katzfuss, 2020), enabling fast cross-validation (Shirota et al, 2019;Banerjee, 2020). Alternatives to sparse-matrix algorithms involve Gibbs samplers whose efficiency improves by prespecifying a DAG defined on domain partitions, resulting in spatially meshed GPs (MGPs; Peruzzi et al, 2020).…”

Section: Introductionmentioning

confidence: 99%

Spatial meshing for general Bayesian multivariate models

Peruzzi¹,

Dunson²

2022

Preprint

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Quantifying spatial and/or temporal associations in multivariate geolocated data of different types is achievable via spatial random effects in a Bayesian hierarchical model, but severe computational bottlenecks arise when spatial dependence is encoded as a latent Gaussian process (GP) in the increasingly common large scale data settings on which we focus. The scenario worsens in non-Gaussian models because the reduced analytical tractability leads to additional hurdles to computational efficiency. In this article, we introduce Bayesian models of spatially referenced data in which the likelihood or the latent process (or both) are not Gaussian. First, we exploit the advantages of spatial processes built via directed acyclic graphs, in which case the spatial nodes enter the Bayesian hierarchy and lead to posterior sampling via routine Markov chain Monte Carlo (MCMC) methods. Second, motivated by the possible inefficiencies of popular gradient-based sampling approaches in the multivariate contexts on which we focus, we introduce the simplified manifold preconditioner adaptation (SiMPA) algorithm which uses second order information about the target but avoids expensive matrix operations. We demostrate the performance and efficiency improvements of our methods relative to alternatives in extensive synthetic and real world remote sensing and community ecology applications with large scale data at up to hundreds of thousands of spatial locations and up to tens of outcomes. Software for the proposed methods is part of R package meshed, available on CRAN.

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Modeling massive spatial datasets using a conjugate Bayesian linear modeling framework

Cited by 16 publications

References 52 publications

Hierarchical Multivariate Directed Acyclic Graph Auto-Regressive (MDAGAR) models for spatial diseases mapping

Hierarchical Multivariate Directed Acyclic Graph Auto-Regressive (MDAGAR) models for spatial diseases mapping

A combined statistical and machine learning approach for spatial prediction of extreme wildfire frequencies and sizes

Spatial meshing for general Bayesian multivariate models

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