Statistical inference with belief functions: A survey
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AIPR assessment
Problem difficulty: this is a technically mature but still niche theoretical area, where the challenge is synthesis across several decades of scattered literature rather than empirical benchmarking. Compounding strengths: the taxonomy, definitions, and critique sections reinforce each other, so the survey is useful both as an entry point and as a comparative map. Compounding weaknesses: the lack of new results means there is no experimental or theoretical evidence beyond citation-based synthesis
Abstract
Belief functions are a powerful and popular framework for the mathematical characterisation of uncertainty, in particular in situations in which lack of data renders learning a probability distribution for the problem impractical. The first step in a reasoning chain based on belief functions is inference: how to learn a belief measure from the available data. In this survey we focus, in particular, on making inference from statistical data, and review the most significant contributions in the area.
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