6

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 these "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.

I also asked the same question on stats.stackexchange.com, as I want to confront points of view.

(edit, typo)

Michael Hardy
  • 1
Dju
  • 61
  • I have nothing to say about the merits of these theories. At ay rate, I think the "official" Wikipedia page https://en.wikipedia.org/wiki/Dempster–Shafer_theory makes sense. – Christian Blatter Nov 10 '16 at 09:36
  • DST and the TBM are very deep and important fields with firm philosophical and mathematical foundations. Start with Wikipedia, then Google--there is a vast body of literature on both the theory and applications, especially DST. – E. Douglas Jensen Jul 09 '18 at 19:38

1 Answers1

1

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.

Bjørn Kjos-Hanssen
  • 2,915