Vii. Computational Multi-point Bme and Bme Confidence Sets

Until now we have considered the estimation of the value of a S/TRF at one point at the time, independently of the estimated values at other estimation points, i.e. a single-point mapping approach. The Bayesian Maximum Entropy (BME; Christakos, 1990, 1992) method offers a framework where the prediction of a S/TRF at several estimation points may be considered jointly, which is referred to as a multi-point mapping approach. Whereas single-point mapping uses an univariate pdf to describe each estimated value separately, the multi-point mapping approach uses a more informative multivariate pdf describing all the estimated values jointly. Multi-point estimation leads in some cases to maps that are considerably different than that obtained with the single-point approach, thus providing a different representation that might be a considerable improvement. Additionally the hallmark of any stochastic estimation method is its ability to provide an assessment of the uncertainty associated to the estimated map, and BME provides an accurate and exhaustive assessment of uncertainty by means of BME confidence sets, which are a generalization of the idea of confidence intervals, for the case of multi-point mapping.