NDLI: Positive spatial autocorrelation, mixture distributions, and geospatial data histograms

Content Provider	IEEE Xplore Digital Library
Author	Griffith, D.A.
Copyright Year	2011
Description	Author affiliation: School of Economic, Political, and Policy Sciences University of Texas at Dallas (Griffith, D.A.)
Abstract	Researchers commonly construct histograms as a first step in representing and visualizing their geospatial data. Because of the presence of spatial autocorrelation in these data, these graphs usually fail to closely align with any of the several hundred existing ideal frequency distributions. The purpose of this paper is to address how positive spatial autocorrelation — the most frequently encountered in practice — can distort histograms constructed with geospatial data. Following the auto-normal parameter specification employed in WinBUGS for Bayesian analysis, this paper summarizes results for normal, Poisson, and binomial random variables (RVs) — three of the most commonly employed ones by geospatial scientists — in terms of mixture distributions. A spatial filter description of positive spatial autocorrelation is shown to approximate a normal distribution in its initial form, a gamma distribution when exponentiated, and a beta distribution when embedded in a logistic equation. In turn, these conceptualizations allow: the mean for a normal distribution to be distributed as a normal random variable (RV) with a zero mean and a specific variance; the mean for a Poisson distribution to be distributed as a gamma RV with specific parameters (i.e., a negative binomial distribution); and, the probability for a binomial distribution to be distributed as a beta RV with specific parameters (i.e., a beta-binomial distribution). Results allow impacts of positive spatial autocorrelation on histograms to be better understood. A methodology is outlined for recovering the underlying unautocorrelated frequency distributions.
Starting Page	1
Ending Page	6
File Size	234099
Page Count	6
File Format	PDF
ISBN	9781424483525
e-ISBN	9781424483518
DOI	10.1109/ICSDM.2011.5968119
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-06-29
Publisher Place	China
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Correlation Histogram Poisson random variable Binomial random variable Gaussian distribution Normal random variable Histograms Gamma random variable Spatial filters Eigenvalues and eigenfunctions Random variables Mathematical model Spatial autocorrelation Beta random variable
Content Type	Text
Resource Type	Article

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