On Transforming Belief Function Models to Probability Models
Prakash Shenoy2003
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Abstract
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This paper explores methods for transforming belief function models, specifically Dempster-Shafer models, into equivalent Bayesian probability models. It argues for the significance of such transformations, highlighting advantages such as facilitating reasoning within complex models containing both belief and probability functions, providing coherent decision-making frameworks, and enhancing understanding of belief function theory through probabilistic semantics. The authors critique existing transformation methods, emphasizing that a correct approach can yield qualitatively consistent results between belief and probability models.
Key takeaways
- Section 3 describes the pignistic and plausibility methods of transforming belief functions to probability functions.
- The plausibility probability function and pignistic probability function for each of these bpa's are exactly the same, with probabilities 1/3 for each element in the state space.
- Smets [2002] says that the pignistic probability function is more appropriate than the plausibility probability function.
- First, we will represent the evidence from the 30 sensors by bpa's and compute the joint belief function for T. Next, we will represent the evidence by probability functions using the pignistic transformation and compute the joint probability function for T. Finally, we will represent the evidence by probability functions obtained using the plausibility transformation and compute the joint probability function for T. Table 4.2 along with the corresponding plausibility function.
- Next, consider the probability model for the target identification problem obtained from the belief function model using the plausibility transformation.
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