Simultaneous autoregressive models for spatial extremes

Fix, Miranda J.; Cooley, Daniel; Thibaud, Emeric

doi:10.1002/env.2656

Cited by 10 publications

(5 citation statements)

References 38 publications

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“…Spatial regression Spatial autoregressive models (Anselin 1988 ) (SAR) have remained relatively consistent, but have been expanded in some recent work (Yang and Lee 2017 ; Fix et al. 2021 ). Moving average (MA) models are often used in the context of time-series modelling (Durbin 1959 ), but can also be used for spatial regression problems using the “MA by AR” approach (Haining 1978 ).…”

Section: Related Workmentioning

confidence: 99%

VPint: value propagation-based spatial interpolation

Arp

Baratchi

Hoos

2022

Data Min Knowl Disc

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Given the common problem of missing data in real-world applications from various fields, such as remote sensing, ecology and meteorology, the interpolation of missing spatial and spatio-temporal data can be of tremendous value. Existing methods for spatial interpolation, most notably Gaussian processes and spatial autoregressive models, tend to suffer from (a) a trade-off between modelling local or global spatial interaction, (b) the assumption there is only one possible path between two points, and (c) the assumption of homogeneity of intermediate locations between points. Addressing these issues, we propose a value propagation-based spatial interpolation method called VPint, inspired by Markov reward processes (MRPs), and introduce two variants thereof: (i) a static discount (SD-MRP) and (ii) a data-driven weight prediction (WP-MRP) variant. Both these interpolation variants operate locally, while implicitly accounting for global spatial relationships in the entire system through recursion. We evaluated our proposed methods by comparing the mean absolute error, root mean squared error, peak signal-to-noise ratio and structural similarity of interpolated grid cells to those of 8 common baselines. Our analysis involved detailed experiments on a synthetic and two real-world datasets, as well as experiments on convergence and scalability. Empirical results demonstrate the competitive advantage of VPint on randomly missing data, where it performed better than baselines in terms of mean absolute error and structural similarity, as well as spatially clustered missing data, where it performed best on 2 out of 3 datasets.

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Section: Related Workmentioning

confidence: 99%

VPint: value propagation-based spatial interpolation

Arp

Baratchi

Hoos

2022

Data Min Knowl Disc

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“…Conditional Autoregressive (CAR) and Simultaneous Autoregressive (SAR) prior distributions are routinely used to model the spatially structured random effects [ 13 , 14 ]. In the majority of spatial studies, the spatially structured random effect is modelled using the CAR prior distribution.…”

Section: Introductionmentioning

confidence: 99%

A Systematic Review of Joint Spatial and Spatiotemporal Models in Health Research

Tesema

Tessema

Héritier

et al. 2023

IJERPH

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With the advancement of spatial analysis approaches, methodological research addressing the technical and statistical issues related to joint spatial and spatiotemporal models has increased. Despite the benefits of spatial modelling of several interrelated outcomes simultaneously, there has been no published systematic review on this topic, specifically when such models would be useful. This systematic review therefore aimed at reviewing health research published using joint spatial and spatiotemporal models. A systematic search of published studies that applied joint spatial and spatiotemporal models was performed using six electronic databases without geographic restriction. A search with the developed search terms yielded 4077 studies, from which 43 studies were included for the systematic review, including 15 studies focused on infectious diseases and 11 on cancer. Most of the studies (81.40%) were performed based on the Bayesian framework. Different joint spatial and spatiotemporal models were applied based on the nature of the data, population size, the incidence of outcomes, and assumptions. This review found that when the outcome is rare or the population is small, joint spatial and spatiotemporal models provide better performance by borrowing strength from related health outcomes which have a higher prevalence. A framework for the design, analysis, and reporting of such studies is also needed.

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“…Related to our analysis, recent examples of SAR models include neuroimaging (Messé et al. 2015 ) and extremes of areal data (Fix, Cooley, and Thibaud 2021 ). With respect to the GMRF approach, SAR models are well suited to maximum likelihood estimation, thus offering a natural setting for extending score-driven models to spatio-temporal data.…”

Section: Introductionmentioning

confidence: 99%

Score-Driven Modeling of Spatio-Temporal Data

Gasperoni

Luati

Paci

et al. 2021

Journal of the American Statistical Association

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A simultaneous autoregressive score-driven model with autoregressive disturbances is developed for spatio-temporal data that may exhibit heavy tails. The model specification rests on a signal plus noise decomposition of a spatially filtered process, where the signal can be approximated by a nonlinear function of the past variables and a set of explanatory variables, while the noise follows a multivariate Student- t distribution. The key feature of the model is that the dynamics of the space-time varying signal are driven by the score of the conditional likelihood function. When the distribution is heavy-tailed, the score provides a robust update of the space-time varying location. Consistency and asymptotic normality of maximum likelihood estimators are derived along with the stochastic properties of the model. The motivating application of the proposed model comes from brain scans recorded through functional magnetic resonance imaging when subjects are at rest and not expected to react to any controlled stimulus. We identify spontaneous activations in brain regions as extreme values of a possibly heavy-tailed distribution, by accounting for spatial and temporal dependence.

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Simultaneous autoregressive models for spatial extremes

Cited by 10 publications

References 38 publications

VPint: value propagation-based spatial interpolation

VPint: value propagation-based spatial interpolation

A Systematic Review of Joint Spatial and Spatiotemporal Models in Health Research

Score-Driven Modeling of Spatio-Temporal Data

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