Frequently, the values of the variable are desired on a regular and significantly finer grid than is practical to sample. This presents the problem of estimation , or of using sample data to predict values in areas which are unsampled. Here, vhat0 is an estimate of the value of the variable at x0, the unsample location. However, this goal is impossible to achieve in practice, since it would require prior knowledge of the true values at the unsampled locations. As a result, most estimation techniques make substantial simplifying assumptions regarding the behaviour of the variable in order to predict unsampled values.
Most methods give greater weight to samples which are closer to the point being estimated.
B. This intuitive notion is an implicit statement of continuity of the variable, in that values nearby are more likely to be similar than values far apart. This is indeed true for most variables occurring in physical and earth sciences. However, these methods do not take into account the observable spatial correlation between sample points. That is, the continuity between vi and vj. Kriging , which is based on Geostatistics is the technique which utilizes this additional information to produce more reliable estimates.