Abstract
Risk, or the probability of loss, depends on the amount of information available to predict outcomes, as well as the essentially random characteristics of the process. Probabilities calculated by traditional methods do not reflect information content directly. Therefore, traditional probabilities must be reported along with confidence intervals, particularly in situations in which information is limited. Interpretation of risk-expressed as a degree of confidence in a probability of some loss-is difficult. In this paper, information theory was used to estimate conditional probability distributions, representing risks, for which no data were available but one or two statistics (such as mean values) were known. The resulting distributions expressed information content directly. Revision of these distributions with additional information resulted in narrower distributions, in contrast with traditional approaches. Probabilities of cadmium removal efficiencies experienced for various durations were estimated from knowledge of total annual flow and residue. The complete particle-size distribution for a sand filter bed was predicted satisfactorily from knowledge of clear water headloss, verifying the method, and providing the basis for a rapid quality-control test for particle-size separators.
