| Many decision-making processes in the Earth sciences require the combination of multiple data originating from diverse sources. These data are often indirect and uncertain, and their combination would call for a probabilistic approach. These data are also partially redundant, anyone with each other or with all others taken jointly. This overlap in information arises due to a variety of reasons---because the data rise from the same physical process (geology), because they originate from the same location or the same measurement device, etc. When combining such redundant data, one must account for their information overlap, less we run the risk of over compounding apparently consistent, but actually redundant, data with the risk of a wrong decision. Unfortunately most numerical algorithms for data integration assume data to be independent or conditionally independent one from each other. The better algorithms (kriging, principal components) would correct for correlation between the data, but only taken two by two, and the only correlation considered is linear.; The tau model is proposed for combining partially redundant data, each taking the form of a prior probability for the event being assessed to occur given that datum taken alone. The parameters of that tau model measures the additional contribution brought by any single datum over that of all previously considered data; they are data sequence-dependent and also data values-dependent. As one should expect, data redundancy depends on the order in which the data are considered and also on the data values themselves. However, averaging the tau model parameters over all possible data values leads to exact analytical expressions and corresponding approximations and inference avenues.; Two such inference avenues are proposed and tested on a reference multivariate data set linked to prediction of permeable path connectivity from well logs, well tests and seismic information. The two resulting redundancy models and their impact on prediction after data combination are compared to the reference values. The theoretical properties of the tau model are verified. The two approximations lead to mixed results, yet both much superior to those obtained from the traditional data conditional independence assumption. It is demonstrated that optimal utilization of data calls for understanding and modeling their information overlap, ignoring data redundancy is almost never a safe hypothesis and can lead to severe errors in decision-making. |
