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.
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Aregui, A., Denoeux, T. (2007). Consonant Belief Function Induced by a Confidence Set of Pignistic Probabilities. In: Mellouli, K. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2007. Lecture Notes in Computer Science(), vol 4724. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75256-1_32
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DOI: https://doi.org/10.1007/978-3-540-75256-1_32
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