A statistical test on the local effects of spatially structured variance

Westerholt, René; Resch, Bernd; Mocnik, Franz-Benjamin; Hoffmeister, Dirk

doi:10.1080/13658816.2017.1402914

Cited by 13 publications

(10 citation statements)

References 93 publications

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“…Since conditional permutation assumes that the local and (conditional, without x i ) global distributions of x are equivalent, perhaps the divergence between analytical and conditional permutations is driven by local spatial heterogeneity. Ord and Getis (2012) propose a measure of local spatial heterogeneity (LOSH), and very recently an implementation has been added to spdep thanks to Rene Westerholt in connection with Westerholt et al (2015) and Westerholt et al (2018). The implementation also includes inferential mechanisms proposed by Xu et al (2014).…”

Section: Discussionmentioning

confidence: 99%

Comparing implementations of global and local indicators of spatial association

Bivand

Wong

2018

TEST

725

476

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Functions to calculate measures of spatial association, especially measures of spatial autocorrelation, have been made available in many software applications. Measures may be global, applying to the whole data set under consideration, or local, applying to each observation in the data set. Methods of statistical inference may also be provided, but these will, like the measures themselves, depend on the support of the observations, chosen assumptions, and the way in which spatial association is represented; spatial weights are often used as a representational technique. In addition, assumptions may be made about the underlying mean model, and about error distributions. Different software implementations may choose to expose these choices to the analyst, but the sets of choices available may vary between these implementations, as may default settings. This comparison will consider the implementations of global Moran's I, Getis-Ord G and Geary's C, local Ii and Gi, available in a range of software including Crimestat, GeoDa, ArcGIS, PySAL and R contributed packages.

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Section: Discussionmentioning

confidence: 99%

Comparing implementations of global and local indicators of spatial association

Bivand

Wong

2018

TEST

725

476

View full text Add to dashboard Cite

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“…Applications of the metric range from identifying rare earth contamination (Yuan, Cave, and Zhang 2018) to analysing land cover change patterns (Das and Ghosh 2017). Throughout the years, Moran's I has also motivated several methodological expansions, analysing for example spatial heteroskedasticity (Ord and Getis 2012) and local spatial dispersion (Westerholt et al 2018). Moran's I has also seen some expansions into the spatio-temporal domain.…”

Section: Related Work Autocorrelation Metrics For Spatio-temporal Phe...mentioning

confidence: 99%

SPATE-GAN: Improved Generative Modeling of Dynamic Spatio-Temporal Patterns with an Autoregressive Embedding Loss

Klemmer

Acciaio

et al. 2022

AAAI

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From ecology to atmospheric sciences, many academic disciplines deal with data characterized by intricate spatio-temporal complexities, the modeling of which often requires specialized approaches. Generative models of these data are of particular interest, as they enable a range of impactful downstream applications like simulation or creating synthetic training data. Recently, COT-GAN, a new GAN algorithm inspired by the theory of causal optimal transport (COT), was proposed in an attempt to improve generation of sequential data. However, the task of learning complex patterns over time and space requires additional knowledge of the specific data structures. In this study, we propose a novel loss objective combined with COT-GAN based on an autoregressive embedding to reinforce the learning of spatio-temporal dynamics. We devise SPATE (spatio-temporal association), a new metric measuring spatio-temporal autocorrelation. We compute SPATE for real and synthetic data samples and use it to compute an embedding loss that considers space-time interactions, nudging the GAN to learn outputs that are faithful to the observed dynamics. We test our new SPATE-GAN on a diverse set of spatio-temporal patterns: turbulent flows, log-Gaussian Cox processes and global weather data. We show that our novel embedding loss improves performance without any changes to the architecture of the GAN backbone, highlighting our model's increased capacity for capturing autoregressive structures.

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“…Xu et al (2014) have investigated the distributional properties of LOSH and recommend a Monte Carlo strategy for inference instead of the parametric chi-square test originally proposed. Based on LOSH, Westerholt et al (2018) develop a test for strictly local spatial heteroscedasticity to characterise spatial variance in subregions regardless of other locations. Background is the detection of pronounced variances that may only stand out within small subregions but not in a global comparison.…”

Section: Spatial Heterogeneitymentioning

confidence: 99%

Exploratory Statistical Analysis of Spatial Structures in Urban Datasets

Westerholt¹

2022

Metropolitan Research

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A statistical test on the local effects of spatially structured variance

Cited by 13 publications

References 93 publications

Comparing implementations of global and local indicators of spatial association

Comparing implementations of global and local indicators of spatial association

SPATE-GAN: Improved Generative Modeling of Dynamic Spatio-Temporal Patterns with an Autoregressive Embedding Loss

Exploratory Statistical Analysis of Spatial Structures in Urban Datasets

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