Sampling and geostatistics for spatial data

The goals of classical statistical sampling, (e.g estimation of population means using simple random sampling, stratified random sampling. etc.) and geostatistics (eg. estimation Of population means using block kriging) can be identical. For example, both can be used to estimate the average value, or total amount, of a variable of interest in some area. The most fundamental difference between classical sampling and geostatistics is that classical sampling relies on design-based inference while (geostatistics relies on model-based inference. These differences arc illustrated with examples. Classical sampling usually considers sampling for finite populations, but in the spatial context, it is easily adapted to infinite Populations. Geostatistics has only considered infinite populations but methods for finite populations have been developed recently. To compare classical sampling to geostatistics for both infinite and finite populations. I consider the following data sets. 1) a fabricated fixed spatial pattern from all infinite Population of a spatially-continuous variable 2) a single, fixed, real data set from a finite population on a grid of spatial locations: and 3) simulated random patterns from all autocorrelated model from a finite population on a grid of spatial locations. For each data set. I select samples randomly. Then I use classical sampling estimators and geostatistical estimators of the mean values. Results show that both methods provide unbiased estimates and have variances and confidence intervals that are valid. but in general the geostatistical methods are more efficient, having estimates closer to the true values.