Statistical interpolation methods

Statistical methods of interpolation are all based on assuming that the process being reconstructed (for the purpose of this report, a temperature field in space or time or both) can be modeled as a random process. The best-known examples occur in spatial statistics, including the technique widely known as kriging, and in time series analysis. The process may depend on unknown parameters, which have to be estimated as part of the interpolation procedure. Once the process is specified, including any estimated parameters, optimal interpolators are calculated either by finding the best linear interpolator (the linear combination of known observations that minimizes the mean squared prediction error) or by computing a given function of the conditional probability distribution of the predicted quantity conditional observations. That function can be determined by appealing to statistical decision theory.