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RAPLER / dst-1

Combine basic probability assignments with Dempster's rule of combination
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Feature request: export all hypotheses whose belief values is greater than some threshold (& visualize with plot) #19

Closed garyzhubc closed 10 months ago

garyzhubc commented 1 year ago

I think it's reasonable to report "credible sets" instead of current belplau result, that are, all hypotheses whose belief values is greater than some threshold.

garyzhubc commented 1 year ago

An idea to visualize the "credible sets": plot basic mass assignment for masses that support the credible sets in a lattice (optional, can just use singleton sets), and colour the credible sets. This can also be easily contrasted with a Bayesian model of marginal / joint probabilities.

The idea is inspired by Glenn Shafer's work Constructive probability, where he contrasted: $$P(A)=\sum{\theta\in A}p(\theta)$$ and $$Bel(A)=\sum{B\subset A}m(B)$$ to illustrate the difference between the two.

garyzhubc commented 10 months ago

This turns out to be a wrong understanding of belief functions, as beliefs encode much more information than probabilities; therefore such comparison is meaningless. Alternatively we provided evaluation methods in the package better suited for such purpose.