Optimization of second-phase spatial sampling using auxiliary information
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In spatial sampling, once initial samples of the primary variable have been collected, it is possible to take additional measurements at other locations, an approach known as second-phase sampling. In this dissertation, the use of covariates to optimize the configuration of a second-phase sampling scheme is suggested, reducing the sampling cost and effort. Usually, the set of additional samples is collected where the kriging variance is maximum. However, the prediction error is independent of data values and assumes a stationary spatial process, an assumption violated in practice. A more intelligent approach consists of combining the prediction error with other criteria, giving greater importance to locations where the primary variable shows greater spatial variation, and where the spatial information provided by auxiliary variables is limited. There is indeed little incentive to take additional samples where secondary variables can predict the value of the primary variable with great confidence. Once the problem has been formulated, known heuristic methods can be used to solve the problem in a timely manner, avoiding total enumeration.