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The theory of belief functions is based on two ideas: the idea of obtaining degrees of belief for one question from subjective probabilities for a related question, and Dempster's rule for combining such degrees of belief when they are based on independent items of evidence.
Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.
Dempster–Shafer theory is a generalization of the Bayesian theory of subjective probability. Belief functions base degrees of belief (or confidence, or trust) for one question on the subjective probabilities for a related question.
Basic mechanisms for reasoning with belief functions extend both probabilistic operations (such as marginalization and conditioning) and set-theoretic operations (such as intersection and union). DS reasoning produces the same results as probabilistic reasoning or interval analysis when provided with the same information.
Let m0 be a mass function on expressing our beliefs about X in a context where we know that X 2 B. We want to build a mass function m verifying the constraint m( j B) = m0. Any m built from m0 by transferring each mass m0(A) to A [ C for some C B satisfies the constraint. 0 otherwise. X and Y.
Contents of this lecture 1 Historical perspective, motivations 2 Fundamental concepts: belief, plausibility, commonality, conditioning, basic combination rules 3 Some more advanced concepts: cautious rule, multidimensional belief functions, belief functions in infinite spaces Thierry Denœux Introduction to belief functions July 5, 2017 2 / 77
