Constructing consonant belief functions from sample data using confidence sets of pignistic probabilities

A new method is proposed for building a predictive belief function from statistical data in the transferable belief model framework. The starting point of this method is the assumption that, if the probability distribution PX of a random variable X is known, then the belief function quantifying our belief regarding a future realization of X should have its pignistic probability distribution equal to PX. When PX is unknown but a random sample of X is available, it is possible to build a set P of probability distributions containing PX with some confidence level. Following the least commitment principle, we then look for a belief function less committed than all belief functions with pignistic probability distribution in P. Our method selects the most committed consonant belief function verifying this property. This general principle is applied to arbitrary discrete distributions as well as exponential and normal distributions. The efficiency of this approach is demonstrated using a simulated multi-sensor classification problem.