Consonant Belief Function Induced by a Confidence Set of Pignistic Probabilities

Abstract

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 ℙ X 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 ℙ X . When PX is unknown but a random sample of X is available, it is possible to build a set \(\mathcal{P}\) of probability distributions containing ℙ X 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 \(\mathcal{P}\). Our method selects the most committed consonant belief function verifying this property. This general principle is applied to the case of the normal distribution.KeywordsDempster-Shafer theoryEvidence theoryTransferable BeliefModelpossibility distributionstatistical data