From imprecise probability assessments to conditional probabilities with quasi additive classes of conditioning events
This work addresses foundational issues in probability theory for researchers in imprecise probability, but it is incremental as it builds on existing g-coherence results.
The paper tackles the problem of constructing coherent conditional probabilities from imprecise interval-valued assessments on finite families of conditional events, achieving consistency by defining a sequence of conditional probabilities using solutions to linear systems.
In this paper, starting from a generalized coherent (i.e. avoiding uniform loss) intervalvalued probability assessment on a finite family of conditional events, we construct conditional probabilities with quasi additive classes of conditioning events which are consistent with the given initial assessment. Quasi additivity assures coherence for the obtained conditional probabilities. In order to reach our goal we define a finite sequence of conditional probabilities by exploiting some theoretical results on g-coherence. In particular, we use solutions of a finite sequence of linear systems.