spatial statistics

FC-37 - Spatial Autocorrelation

The scientific term spatial autocorrelation describes Tobler’s first law of geography: everything is related to everything else, but nearby things are more related than distant things. Spatial autocorrelation has a:

  • past characterized by scientists’ non-verbal awareness of it, followed by its formalization;
  • present typified by its dissemination across numerous disciplines, its explication, its visualization, and its extension to non-normal data; and
  • an anticipated future in which it becomes a standard in data analytic computer software packages, as well as a routinely considered feature of space-time data and in spatial optimization practice.

Positive spatial autocorrelation constitutes the focal point of its past and present; one expectation is that negative spatial autocorrelation will become a focal point of its future.

AM-25 - Bayesian methods
  • Define “prior and posterior distributions” and “Markov-Chain Monte Carlo”
  • Explain how the Bayesian perspective is a unified framework from which to view uncertainty
  • Compare and contrast Bayesian methods and classical “frequentist” statistical methods
AM-23 - Local measures of spatial association
  • Describe the effect of non-stationarity on local indices of spatial association
  • Decompose Moran’s I and Geary’s c into local measures of spatial association
  • Compute the Gi and Gi* statistics
  • Explain how geographically weighted regression provides a local measure of spatial association
  • Explain how a weights matrix can be used to convert any classical statistic into a local measure of spatial association
  • Compare and contrast global and local statistics and their uses
AM-22 - Global Measures of Spatial Association

Spatial association broadly describes how the locations and values of samples or observations vary across space. Similarity in both the attribute values and locations of observations can be assessed using measures of spatial association based upon the first law of geography. In this entry, we focus on the measures of spatial autocorrelation that assess the degree of similarity between attribute values of nearby observations across the entire study region. These global measures assess spatial relationships with the combination of spatial proximity as captured in the spatial weights matrix and the attribute similarity as captured by variable covariance (i.e. Moran’s I) or squared difference (i.e. Geary’s C). For categorical data, the join count statistic provides a global measure of spatial association. Two visualization approaches for spatial autocorrelation measures include Moran scatterplots and variograms (also known as semi-variograms).

AM-19 - Exploratory data analysis (EDA)
  • Describe the statistical characteristics of a set of spatial data using a variety of graphs and plots (including scatterplots, histograms, boxplots, q–q plots)
  • Select the appropriate statistical methods for the analysis of given spatial datasets by first exploring them using graphic methods
FC-37 - Spatial Autocorrelation

The scientific term spatial autocorrelation describes Tobler’s first law of geography: everything is related to everything else, but nearby things are more related than distant things. Spatial autocorrelation has a:

  • past characterized by scientists’ non-verbal awareness of it, followed by its formalization;
  • present typified by its dissemination across numerous disciplines, its explication, its visualization, and its extension to non-normal data; and
  • an anticipated future in which it becomes a standard in data analytic computer software packages, as well as a routinely considered feature of space-time data and in spatial optimization practice.

Positive spatial autocorrelation constitutes the focal point of its past and present; one expectation is that negative spatial autocorrelation will become a focal point of its future.

AM-22 - Global Measures of Spatial Association

Spatial association broadly describes how the locations and values of samples or observations vary across space. Similarity in both the attribute values and locations of observations can be assessed using measures of spatial association based upon the first law of geography. In this entry, we focus on the measures of spatial autocorrelation that assess the degree of similarity between attribute values of nearby observations across the entire study region. These global measures assess spatial relationships with the combination of spatial proximity as captured in the spatial weights matrix and the attribute similarity as captured by variable covariance (i.e. Moran’s I) or squared difference (i.e. Geary’s C). For categorical data, the join count statistic provides a global measure of spatial association. Two visualization approaches for spatial autocorrelation measures include Moran scatterplots and variograms (also known as semi-variograms).

AM-25 - Bayesian methods
  • Define “prior and posterior distributions” and “Markov-Chain Monte Carlo”
  • Explain how the Bayesian perspective is a unified framework from which to view uncertainty
  • Compare and contrast Bayesian methods and classical “frequentist” statistical methods
AM-19 - Exploratory data analysis (EDA)
  • Describe the statistical characteristics of a set of spatial data using a variety of graphs and plots (including scatterplots, histograms, boxplots, q–q plots)
  • Select the appropriate statistical methods for the analysis of given spatial datasets by first exploring them using graphic methods
AM-23 - Local measures of spatial association
  • Describe the effect of non-stationarity on local indices of spatial association
  • Decompose Moran’s I and Geary’s c into local measures of spatial association
  • Compute the Gi and Gi* statistics
  • Explain how geographically weighted regression provides a local measure of spatial association
  • Explain how a weights matrix can be used to convert any classical statistic into a local measure of spatial association
  • Compare and contrast global and local statistics and their uses

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