First and second order effect of spatial processes

[DjurdjicaIvkovic]

Hello,

I am not sure if I understand properly what is the meaning of the existence of large scale spatial variation in the mean value when first order effect is present. The spatial pattern that is the result of the process is only concerned with locational information, not attribute information, so what do non-constant variance and mean in space actually pertain to? It will be helpful if someone can also provide simple illustrative example of this locational dependence of mean and variation in space.

Thank you.

[JeffreyEvans]

You are somewhat convolving a few different concepts in spatial statistics. Your question "The spatial pattern that is the result of the process is only concerned with locational information, not attribute information, so what do non-constant variance and mean in space actually pertain to?". is confusing the idea of point process following a Complete Spatial Randomness (CSR) under a Poisson process and nonstationarity in a random state variable. Non-constant variance, mean or variance/mean are different models if nonstationarity and are measured on your dependent variable. You can have also nonstationarity in a point pattern (unmarked point locations) that is represented by an inhomogenious intensity function but, this is functionally different than nonstaionarity models defined by mean or variance.