Dempster-Shafer Theory¶
Dempster-Shafer Theory (DST), also known as evidence theory or belief function theory, is a mathematical framework for representing and reasoning about uncertainty. Developed by Dempster and extended by Shafer, DST generalizes Bayesian probability theory by allowing beliefs to be assigned not just to single outcomes but to sets of outcomes.
The theory is particularly useful for situations where information is incomplete, conflicting, or comes from multiple potentially unreliable sources. Unlike Bayesian approaches which require prior probabilities, DST only requires evidence without assuming a fixed probability distribution over outcomes.
Key concepts¶
- Basic Probability Assignment (BPA): Assigns belief mass to sets in the frame of discernment
- Belief and Plausibility functions: Lower and upper bounds on probability
- Dempster's Rule of Combination: Classic rule for fusing evidence from independent sources
- Conflict handling: Methods for managing conflicting evidence
Key papers¶
- Belief Evolution Network-based Probability Transformation and Fusion — proposes improved combination rules and probability transformation methods
Related topics¶
- Belief Functions (foundational concept)
- Information Fusion (primary application domain)
- Uncertainty Quantification (broader framework)