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Spatial statistics is a field of applied statistics dealing with spatial data. It involves stochastic processes ( random fields , point processes ), sampling , smoothing and interpolation , regional ( areal unit ) and lattice ( gridded ) data, point patterns , as well as image analysis and stereology .
Spatial descriptive statistics is the intersection of spatial statistics and descriptive statistics; these methods are used for a variety of purposes in geography, particularly in quantitative data analyses involving Geographic Information Systems (GIS).
Local spatial autocorrelation statistics provide estimates disaggregated to the level of the spatial analysis units, allowing assessment of the dependency relationships across space. G {\displaystyle G} statistics compare neighborhoods to a global average and identify local regions of strong autocorrelation.
The concept of a spatial weight is used in spatial analysis to describe neighbor relations between regions on a map. [1] If location i {\displaystyle i} is a neighbor of location j {\displaystyle j} then w i j ≠ 0 {\displaystyle w_{ij}\neq 0} otherwise w i j = 0 {\displaystyle w_{ij}=0} .
Geographers use statistics in numerous ways: [citation needed] To describe and summarize spatial data. To make generalizations concerning complex spatial patterns. To estimate the probability of outcomes for an event at a given location. To use samples of geographic data to infer characteristics for a larger set of geographic data (population).
Getis–Ord statistics, also known as G i *, are used in spatial analysis to measure the local and global spatial autocorrelation.Developed by statisticians Arthur Getis and J. Keith Ord they are commonly used for Hot Spot Analysis [1] [2] to identify where features with high or low values are spatially clustered in a statistically significant way.
In spatial analysis, four major problems interfere with an accurate estimation of the statistical parameter: the boundary problem, scale problem, pattern problem (or spatial autocorrelation), and modifiable areal unit problem. [1] The boundary problem occurs because of the loss of neighbours in analyses that depend on the values of the neighbours.
Nevertheless, Mousavi recommends this book as an "introductory text on spatial information science" aimed at practitioners, and commends its use of QR codes and word clouds. [1] Stein praises the book's attempt to bridge mathematics and geography, and its potential use as a first step towards that bridge for practitioners. [ 2 ]