# What is the difference between spatial dependence and spatial (auto)correlation?

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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 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? – whuber♦ Mar 28 '12 at 15:47

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: $f_{XY}(\mathbf x, \mathbf y) \neq f_X(\mathbf x) f_Y(\mathbf y)$
What do $R$, $h_1$, $h_2$, and $f$ mean? – whuber Mar 29 '12 at 0:49
$h_1$ 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. – Emre Mar 29 '12 at 1:00