Bayesian Spatial Modelling for High Dimensional Seismic Inverse Problems

Zhang, Ran; Czado, Claudia; Sigloch, Karin

doi:10.1111/rssc.12118

Cited by 8 publications

(3 citation statements)

References 41 publications

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“…It is also possible to generalize the operators and the SPDE approach to higher dimensions, as gradients and divergence have natural extension to three or more dimensions. In Figure 6, we show an example simulation of the model in Section 6.5 on the sphere, and refer to Zhang, Czado, and Sigloch (2016) for an application to threedimensional seismic inversion.…”

Section: Spdes On Manifoldsmentioning

confidence: 99%

Spatial modeling with R‐INLA: A review

Bakka

Rue

Fuglstad

et al. 2018

WIREs Computational Stats

304

246

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Coming up with Bayesian models for spatial data is easy, but performing inference with them can be challenging. Writing fast inference code for a complex spatial model with realistically‐sized datasets from scratch is time‐consuming, and if changes are made to the model, there is little guarantee that the code performs well. The key advantages of R‐INLA are the ease with which complex models can be created and modified, without the need to write complex code, and the speed at which inference can be done even for spatial problems with hundreds of thousands of observations. R‐INLA handles latent Gaussian models, where fixed effects, structured and unstructured Gaussian random effects are combined linearly in a linear predictor, and the elements of the linear predictor are observed through one or more likelihoods. The structured random effects can be both standard areal model such as the Besag and the BYM models, and geostatistical models from a subset of the Matérn Gaussian random fields. In this review, we discuss the large success of spatial modeling with R‐INLA and the types of spatial models that can be fitted, we give an overview of recent developments for areal models, and we give an overview of the stochastic partial differential equation (SPDE) approach and some of the ways it can be extended beyond the assumptions of isotropy and separability. In particular, we describe how slight changes to the SPDE approach leads to straight‐forward approaches for nonstationary spatial models and nonseparable space–time models. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory Statistical Models > Bayesian Models Data: Types and Structure > Massive Data

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Section: Spdes On Manifoldsmentioning

confidence: 99%

Spatial modeling with R‐INLA: A review

Bakka

Rue

Fuglstad

et al. 2018

WIREs Computational Stats

304

246

View full text Add to dashboard Cite

show abstract

“…While our examples focused on applications to ecological data, the SPDE approach and the functionality of sdmTMB has applications in many other fields. Examples include spatial models of disease spread (Moraga, Dean, Inoue, Morawiecki, Noureen, and Wang 2021), spatial econometric models of quantities such as housing prices (Bivand, Gómez-Rubio, and Rue 2014), analyzing medical imaging data such as MRI scans (Parisa Naseri and Tabatabaei 2022), and geophysical models of seismic waves following earthquakes (Zhang, Czado, and Sigloch 2015). The sdmTMB model is further relevant to what is commonly referred to as spatial (Elhorst 2010; Lee and Yu 2010) and dynamic spatial panel data models (Elhorst 2012) in econometrics.…”

Section: Discussionmentioning

confidence: 99%

sdmTMB: An R Package for Fast, Flexible, and User-Friendly Generalized Linear Mixed Effects Models with Spatial and Spatiotemporal Random Fields

Anderson

Ward

English

et al. 2022

Preprint

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Geostatistical data---spatially referenced observations related to some continuous spatial phenomenon---are ubiquitous in ecology and can reveal ecological processes and inform management decisions. However, appropriate models to analyze these data, such as generalized linear mixed effects models (GLMMs) with Gaussian random fields, are often computationally intensive and challenging to implement, interpret, and evaluate. Here, we introduce the R package sdmTMB, which implements predictive-process SPDE- (stochastic partial differential equation) based spatial and spatiotemporal models. Estimation is conducted via maximum marginal likelihood with Template Model Builder (TMB) but can be extended to penalized likelihood or Bayesian inference. We describe the statistical model, illustrate the package's use through two case studies, and compare the functionality, speed, and interface to related software. We highlight advantages of using sdmTMB for this class of models: (1) sdmTMB provides a flexible interface familiar to users of glm(), lme4, glmmTMB, or mgcv; (2) estimation is often faster than alternatives; (3) sdmTMB provides simple out-of-sample cross validation; (4) non-stationary processes (time-varying and spatially varying coefficients) are easily constructed with a formula interface; and (5) sdmTMB includes features not available as a combination in related packages (e.g., penalized smoothers and break-point effects, anisotropy, abundance index standardization). We hope that sdmTMB's user-friendly interface will open this useful class of models to a wider audience within species distribution modelling and beyond.

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“…The finite element methods used in the Hilbert space construction works in the same way for tetrahedralisations as it does for triangulations. This was exploited by Zhang et al (2016), to estimate seismic velocity under the western USA down to 700 km depth. In this complex inverse problem, thy applied the SPDE models to both the sub-surface velocity field, and to the seismic source and receiver fields on the surface.…”

Section: Seismology and Materials Sciencementioning

confidence: 99%

The SPDE approach for Gaussian and non-Gaussian fields: 10 years and still running

Lindgren¹,

Bolin²,

Rue³

2021

Preprint

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Gaussian processes and random fields have a long history, covering multiple approaches to representing spatial and spatio-temporal dependence structures, such as covariance functions, spectral representations, reproducing kernel Hilbert spaces, and graph based models. This article describes how the stochastic partial differential equation approach to generalising Matérn covariance models via Hilbert space projections connects with several of these approaches, with each connection being useful in different situations. In addition to an overview of the main ideas, some important extensions, theory, applications, and other recent developments are discussed. The methods include both Markovian and non-Markovian models, non-Gaussian random fields, non-stationary fields and space-time fields on arbitrary manifolds, and practical computational considerations.

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Bayesian Spatial Modelling for High Dimensional Seismic Inverse Problems

Cited by 8 publications

References 41 publications

Spatial modeling with R‐INLA: A review

Spatial modeling with R‐INLA: A review

sdmTMB: An R Package for Fast, Flexible, and User-Friendly Generalized Linear Mixed Effects Models with Spatial and Spatiotemporal Random Fields

The SPDE approach for Gaussian and non-Gaussian fields: 10 years and still running

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