Transferable belief model

Transferable belief model

Consider the following classical problem of information fusion. A patient has an illness that can be caused by three different factors "A", "B" and "C". Doctor 1 says that the patient's illness is very likely to be caused by A (very likely, meaning probability "p" = 0.95), but "B" is also possible but not likely ("p" = 0.05). Doctor 2 says that the cause is very likely "C" ("p" = 0.95), but "B" is also possible but not likely ("p" = 0.05). How is one to make one's own opinion from this ?

Bayesian updating the first opinion with the second (or the other way round) implies certainty that the cause is "B". Dempster's rule of combination lead to the same result. This can be seen as paradoxical, since although the two doctors point at different causes "A" and "C", they both agree that "B" is not likely. (For this reason the standard Bayesian approach is to adopt Cromwell's rule and avoid the use of 0 or 1 as prior probabilities.)

The transferable belief model (TBM) is an elaboration on the Dempster-Shafer theory of evidence developed by the late Dr. Philippe Smets, based on the intuition that in the situation above, the result should allocate most of the belief weight to the empty set (i.e. neither "A", "B", nor "C"). Technically, this would be done by using the TBM conjunction rule for non-interactive sources of information, which is the same as Dempster's rule of combination without renormalization.

While most other theories adhere to the axiom "the probability (or belief mass) of the empty set is always zero", there is another intuitive reason to drop this axiom: the open-world assumption. It applies when the frame of reference is not exhaustive, so there are reason to believe that an event not described in this frame of reference will occur. For example, when tossing a coin one usually assumes that Head or Tail will occur, so that scriptstyle Pr(mathrm{Head})+Pr(mathrm{Tail})=1. The open-world assumption is that the coin can be stolen in mid-air, disappear, break apart or otherwise fall sideway so that neither Head nor Tail occurs, so that scriptstyle Pr(varnothing)+Pr(mathrm{Head})+Pr(mathrm{Tail})=1.

ee also

* Dempster-Shafer theory

External links

* [http://iridia.ulb.ac.be/Projects/trans.html "The Transferable Belief Model"]
* [http://iridia.ulb.ac.be/~psmets/AABPapers.html "Publications on TBM"]
* [http://iridia.ulb.ac.be/~psmets/#G "Software for TBM in Matlab"]


Wikimedia Foundation. 2010.

Игры ⚽ Поможем сделать НИР

Look at other dictionaries:

  • Modele des Croyances Transferables (MCT) — Modèle des croyances transférables La mesure d une grandeur physique par un capteur est généralement entachée d incertitude et d imprécision liées aux conditions de fonctionnement du capteur ainsi qu à ses limitations. Afin de prendre en compte… …   Wikipédia en Français

  • Modèle des Croyances Transférables (MCT) — Modèle des croyances transférables La mesure d une grandeur physique par un capteur est généralement entachée d incertitude et d imprécision liées aux conditions de fonctionnement du capteur ainsi qu à ses limitations. Afin de prendre en compte… …   Wikipédia en Français

  • Modèle des croyances transférables — Le MCT ou Modèle des croyances transférables est un modèle non probabiliste de « raisonnement incertain » reposant sur la théorie des fonctions de croyance. Il a été proposé et développé par Philippe Smets au début des années 90 Quand… …   Wikipédia en Français

  • Modèle des croyances transférables (mct) — Modèle des croyances transférables La mesure d une grandeur physique par un capteur est généralement entachée d incertitude et d imprécision liées aux conditions de fonctionnement du capteur ainsi qu à ses limitations. Afin de prendre en compte… …   Wikipédia en Français

  • Possibility theory — is a mathematical theory for dealing with certain types of uncertainty and is an alternative to probability theory. Professor Lotfi Zadeh first introduced possibility theory in 1978 as an extension of his theory of fuzzy sets and fuzzy logic. D.… …   Wikipedia

  • Dempster-Shafer theory — The Dempster Shafer theory is a mathematical theory of evidenceShafer, Glenn; A Mathematical Theory of Evidence , Princeton University Press, 1976, ISBN 0 608 02508 9] based on belief functions and plausible reasoning , which is used to combine… …   Wikipedia

  • Pignistic probability — A pignistic probability is a probability that a rational person will assign to an option when required to make a decision. A person may have, at one level certain beliefs or a lack of knowledge, or uncertainty, about the options and their actual… …   Wikipedia

  • Dempster–Shafer theory — Prof Arthur P. Dempster at the workshop on Belief Function Theory (Brest 1 april 2010). The Dempster–Shafer theory (DST) is a mathematical theory of evidence.[1] It allows …   Wikipedia

  • List of probability topics — This is a list of probability topics, by Wikipedia page. It overlaps with the (alphabetical) list of statistical topics. There are also the list of probabilists and list of statisticians.General aspects*Probability *Randomness, Pseudorandomness,… …   Wikipedia

  • List of mathematics articles (T) — NOTOC T T duality T group T group (mathematics) T integration T norm T norm fuzzy logics T schema T square (fractal) T symmetry T table T theory T.C. Mits T1 space Table of bases Table of Clebsch Gordan coefficients Table of divisors Table of Lie …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”