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I have to review an article for a conference. This article deals with Transferable belief model and Pignistic probability, concepts that were previously unknown to me (CS background).

I dived into thes "theories" and all this came to me as a complete pseudo-science with very unclear concepts, out-of-the blue definitions and overly complexed vocabularies. Reading the wikipedia talk pages on Transferable belief model and Dempster–Shafer_theory conforted my opinion. Plus the fact that these articles are noted as of low importance.

However, I'm no expert in statistics and decision theory so I ask the community if these theories are backed by a rigorous background and if they have a proven track-record of applications and reproducible results ? As a researcher, I won't be convinced by a high number of citations of research articles.

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  • $\begingroup$ did not hear about these things before, but reading the Dempster–Shafer theory wiki article it did not seem like pseudo-science to me at all. $\endgroup$
    – Steffen Moritz
    Commented Nov 17, 2016 at 0:33
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    $\begingroup$ To be honest, don't you think it would be a good idea to refuse the review..? Which is no shame, nobody can be an expert in all fields. I mean if the basics on which the author bases his research are already completely far away from your expertise, how will you be able to actually assess his research. $\endgroup$
    – Steffen Moritz
    Commented Nov 17, 2016 at 0:38

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Imagine you have a stock whose value at time 0 is $S_0$ and at time 1 can take one of two possible values, $S_1\in\{a,b\}$ (corresponding to up-tick and down-tick in the price). Now you also have another financial security $V_1$ that depends on the value $S_1$ (for example, a call option). Since any two points determine a straight line, $V_1$ is a linear function of $S_1$. This allows us to find $V_0$, the price of the security at time 0, from $S_0$ using the linearity of pricing (the price of two cars is $2$ $\times$ the price of one car).

This is known as risk-neutral pricing and is a central part of mathematical finance. Now suppose that $S_1\in\{a,b,c\}$ (three possible values) instead. Then the above type of argument only gives an interval for $V_0$, rather than an exact value.

While I don't know for sure, it seems that the theory of belief functions in Dempster-Shafer theory is related to this -- so we have some belief in a proposition $p$ without assigning an exact Bayesian probability to $p$. Here $V_0$ could be equal to 1 if $p$ is true and 0 otherwise.

In conclusion, this is certainly not pseudo-science, but seems like a useful way of organizing inconclusive evidence.

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