R. A. Fisher was clearly aware of spatial dependence in agricultural field experiments because he went to such great lengths to remove it! In the 1920s and 1930s, at Rothamsted Experimental Station in England, he established the principles of randomization, blocking, and replication. As well as controlling for unwanted bias, randomization also neutralizes (but does not remove) the effect of spatial correlation. However, it should be realized that randomization does not neutralize the spatial correlation at spatial scales larger or smaller than the plot dimensions.

In areas such as ecology, global climate, epidemiology, geology, and image processing, it is often not possible (nor always appropriate) to randomize, block, and replicate the data. There is a need for flexible statistical models that address questions arising from old and new technologies. Many of these questions, in areas such as resource assessment, environmental monitoring, and medical imaging, are spatial in nature. We suggest that (Bayesian) hierarchical statistical analysis is playing and will continue to play a prominent role in solving these problems.

• All data have a more-or-less precise spatial and temporal label associated with them. A purely spatial model usually has no causative component in it; such models are useful when a spatial-temporal process has reached temporal equilibrium (e.g., ore deposition) or when short-term causal effects are aggregated over a fixed time period (e.g., final presidential election returns from the states of the United States).
• Whether the spatial labels are thought to be an important part of the modeling and analysis of the data, is a concern that should be addressed problem-by-problem.
• Data that are close together in space (and time) are often more alike than those that are far apart. A spatial model incorporates this spatial variation into the model-generating mechanism, in contrast to a non-spatial model.
• It is almost always true that the classical, non-spatial model is a special case of a spatial model, and so the spatial model is more general (spatio-temporal models are even more general).
• Whether one chooses to model the spatial variation through the non-stochastic mean structure (sometimes called large-scale variation) or the stochastic-dependence structure (sometimes called small-scale variation) depends on the underlying scientific problem, and it can simply be a trade-off between model fit and parsimony of the model description. What is one person's (spatial) covariance structure may be another person's mean structure.
• Explanatory variables (suggested by the problem under investigation) should be included in the mean structure first, and great care should be taken to find all of them. A missed variable that is itself varying spatially will contribute to the spatial dependence, as can a misspecification of the functional relationship between the variable of interest and the explanatory variables. As a consequence, a model that includes a spatial-dependence component pays a low-cost premium that insures against misspecification of the mean structure.
• Having allowed for explanatory variables, models with spatial dependence typically have a more parsimonious description than classical trend-surface models. They also have more stable spatial-extrapolation properties and yield more efficient estimators of explanatory-variable effects.