Graph spatial sampling

Abstract

We develop lagged Metropolis–Hastings walk for sampling from simple undirected graphs according to given stationary sampling probabilities. It is explained how the technique can be applied together with designed graphs for sampling of units‐in‐space. Compared with the existing spatial sampling methods, which chiefly focus on the sample spatial balance regardless of the associated outcomes of interest, the proposed graph spatial sampling method can considerably improve the efficiency because the graph can be designed to take into account the anticipated spatial distribution of the outcome of interest.