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It seems to me that in literature these terms are used synonymously.

Does spatial autocorrelation strictly refer to linear dependence, or does spatial autocorrelation refer to the set of measures of spatial dependence (moran's i,...)?

Do you know of any precise definition of both terms?

Thank you very much

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  • $\begingroup$ It may be too much to expect universal agreement. In specific cases, authors will clearly distinguish particular mathematical forms of spatial correlation from statistical dependence, but there is a well-established tradition of doing just the opposite. E.g., Noel Cressie (in Statistics for Spatial Data, 1991) writes "...correlated ( i.e., cannot be modeled as statistically independent)" [p. 3]. Therefore you should anticipate that several different answers to this question are possible. Perhaps you have a specific subset of the "literature" in mind? $\endgroup$
    – whuber ♦
    Commented Mar 28, 2012 at 15:47
  • $\begingroup$ For me, spatial dependence is a characteristic of the data generating process (DGP), see @Emre, and spatial correlation is a characteristic of the pattern/configuration of your observations (empirical). So, it is expected that a spatially dependent DGP will result in spatially correlated values. $\endgroup$
    – b_dev
    Commented Dec 5, 2013 at 5:29
  • $\begingroup$ From my point of view it would be fair to say that spatial heterogeneity and spatial autocorrelation are special cases of spatial dependence. I found, however, no one in lterature who shares my opinion :) $\endgroup$
    – Funkwecker
    Commented Feb 8, 2021 at 7:14

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Correlation is a specific type of dependence--first order--thus dependence subsumes correlation. Furthermore, two random variables can be dependent without being correlated. Basic examples:

Auto-correlation: $R_X(\mathbf x_1, \mathbf x_2) = h_1(\| \mathbf x_1 - \mathbf x_2 \|)$

Cross-correlation: $R_{XY}(\mathbf x, \mathbf y) = h_2(\| \mathbf x - \mathbf y \|)$

Dependence: $f_{XY}(\mathbf x, \mathbf y) \neq f_X(\mathbf x) f_Y(\mathbf y)$

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  • $\begingroup$ What do $R$, $h_1$, $h_2$, and $f$ mean? $\endgroup$
    – whuber ♦
    Commented Mar 29, 2012 at 0:49
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    $\begingroup$ $h_1$ and $h_2$ are appropriate scalar functions, $f$ is a pdf, and $R$ is the correlation function, $X$ and $Y$ are random variables, $\mathbf{x}$ and $\mathbf{y}$ are vectors. $\endgroup$
    – Emre
    Commented Mar 29, 2012 at 1:00

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