Data worth analysis in geostatistics and spatial prediction

A main challenge in decision making on soil remediation is risk management through acquisition of knowledge using more informative models and data. To demonstrate the approach to this problem, value of information should be considered and computed. To improve the quality of prediction of contamination we need to have more data or samples. When we add new samples to our model, we get new probability distribution function for the quantity of interest. Then we need to compare the old (prior) and new (posterior) predictions and quantify the difference and improvement from one prediction to another one and measure information content of predictions. Also, to find the best design for location of new samples, we should find the samples that provide maximum information compared to other samples. Samples with maximum information will be the optimal design for location of new data. The optimal design minimizes the cost of sampling because it provides the most possible information with minimum number of samples. In this research we try to identify the best locations for new samples. To address this problem, Kullback-Leibler divergence which is a measure in probability theory is used. The Kullback-Leibler divergence represents the difference between two probability distribution functions. Under the assumption of Multi-variate normal distribution for log-transformed concentration data, the Kullback-Leibler divergence can be considered as a tool to measure the information content of new samples. Computation of information content of new samples helps us to optimize the location of new samples.