Mathematical Theory of Evidence Versus Evidence
This work is incremental, refining theoretical foundations in uncertainty reasoning for researchers in AI and statistics.
The paper addresses weaknesses in Shafer's probabilistic interpretation of the Mathematical Theory of Evidence (MTE) and proposes a new interpretation that aligns with belief function definitions and Dempster's rule, showing that Shaferian conditioning can be viewed as data modification based on beliefs.
This paper is concerned with the apparent greatest weakness of the Mathematical Theory of Evidence (MTE) of Shafer \cite{Shafer:76}, which has been strongly criticized by Wasserman \cite{Wasserman:92ijar}. Weaknesses of Shafer's proposal \cite{Shafer:90b} of probabilistic interpretation of MTE belief functions is demonstrated. Thereafter a new probabilistic interpretation of MTE conforming both to definition of belief function and to Dempster's rule of combination of independent evidence. It is shown that shaferian conditioning of belief functions on observations \cite{Shafer:90b} may be treated as selection combined with modification of data, that is data is not viewed as it is but it is casted into one's beliefs in what it should be like.