Evaluating Information Redundancy Through the Tau Model

Abstract

The general problem of data integration is expressed into that of combining individual probabilistic information into a joint posterior probability. Any such combination of information necessarily requires taking into account redundancy within the information utilized. It is shown that the tau model (Journel 2002) can provide an exact analytical representation of such combination. The tau weights express data redundancy for each specific sequence of data conditioning. Instead of using this exact definition of the tau weights, a more practical calibration-based method is proposed. The method requires a prior ranking of the data based on their information content, then the tau weights are approximated by a function of the correlation of each datum with the single most informative one. Such calibration would require training information in the form of joint vectorial data. The tau model can also be expressed as a log-linear estimator of the distance to the unknown event. This definition requires considering the distances (or equivalently the odds ratios) as random variables themselves. An application to binary data is presented. 1 Statement of problem Combining information from different sources is a difficult problem occurring over many different disciplines. Consider that we wish to assess our knowledge about an event A. Here A could be as complex as presence/absence of a set of connected fractures close to a well or it could be the binary event that the average porosity of a given region in the subsurface is lesser than a given threshold value. Typically, we get information about the unknown event from, say, n different sources namely D 1 , D 2 , ..., D n. Each datum event D i can be quite complex involving different variables and multiple sample locations in space.