Graphical Gaussian process models for highly multivariate spatial data

Dey, Debangan; Datta, Abhirup; Banerjee, Sudipto

doi:10.1093/biomet/asab061

Cited by 18 publications

(15 citation statements)

References 38 publications

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“…Our work in this article will enable new research into nonstationary models of large scale non-Gaussian data. Furthermore, our methods can be applied for posterior sampling of Bayesian hierarchies based on more complex conditional independence models of multivariate dependence (Dey et al, 2021).…”

Section: Discussionmentioning

confidence: 99%

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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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Section: Discussionmentioning

confidence: 99%

“…These perspectives are reinforced when considering multivariate outcomes (see e.g. Zhang and Banerjee 2021;Dey et al 2021;.…”

Section: Introductionmentioning

confidence: 99%

Spatial meshing for general Bayesian multivariate models

Peruzzi¹,

Dunson²

2022

Preprint

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“…A very different approach will be to build scalable graphical models using two different graphs: one for areal units (CAR or DAGAR) and another undirected graph representing conditional independence among cancers. Multidimensional MRFs as well as developments analogous to recently introduced graphical Gaussian processes 52 can be pursued for high-dimensional disease mapping. Finally, spatial confounding in multivariate disease mapping [53][54][55] will be explored in the context of MDAGAR.…”

Section: Discussionmentioning

confidence: 99%

Hierarchical multivariate directed acyclic graph autoregressive models for spatial diseases mapping

Gao

Datta

Banerjee

2022

Statistics in Medicine

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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 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 program.

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“…The first is to extend spatial BPS to spatio-temporal or multivariate data. This can potentially be done by using the recently developed techniques of graphical Gaussian processes (Dey et al, 2021;Peruzzi and Dunson, 2022). Moreover, spatial BPS can be used, not only for synthesizing multiple models, but also for saving computational cost under a large number of covariates.…”

Section: Apartment Prices In Tokyomentioning

confidence: 99%

Spatially-Varying Bayesian Predictive Synthesis for Flexible and Interpretable Spatial Prediction

Cabel¹,

Kato²,

Takanashi³

et al. 2022

Preprint

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Spatial data are characterized by their spatial dependence, which is often complex, nonlinear, and difficult to capture with a single model. Significant levels of model uncertaintyarising from these characteristics-cannot be resolved by model selection or simple ensemble methods, as performances are not homogeneous. We address this issue by proposing a novel methodology that captures spatially-varying model uncertainty, which we call spatial Bayesian predictive synthesis. Our proposal is defined by specifying a latent factor spatially-varying coefficient model as the synthesis function, which enables model coefficients to vary over the region to achieve flexible spatial model ensembling. Two MCMC strategies are implemented for full uncertainty quantification, as well as a variational inference strategy for fast point inference. We also extend the estimation strategy for general responses. A finite sample theoretical guarantee is given for the predictive performance of our methodology, showing that the predictions are exact minimax. Through simulation examples and two real data applications, we demonstrate that our proposed spatial Bayesian predictive synthesis outperforms standard spatial models and advanced machine learning methods, in terms of predictive accuracy, while maintaining interpretability of the prediction mechanism.

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Graphical Gaussian process models for highly multivariate spatial data

Cited by 18 publications

References 38 publications

Spatial meshing for general Bayesian multivariate models

Spatial meshing for general Bayesian multivariate models

Hierarchical multivariate directed acyclic graph autoregressive models for spatial diseases mapping

Spatially-Varying Bayesian Predictive Synthesis for Flexible and Interpretable Spatial Prediction

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