Imprecise Probability & Multiple Testing

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Abstractions about credal uncertainty, evidence combination, imprecise probabilities, correction for multiple comparisons, and probabilistic isolation arguments.

5 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Bonferroni Correction — Control the family-wise probability of any false rejection across m tests by comparing each p-value with alpha/m, or equivalently multiplying each p-value by m, without requiring independence.
• Credal Set — Represent imprecise probabilistic belief by a set of admissible probability measures, deriving lower and upper expectations as envelopes while keeping convexity, closure, conditioning, and independence choices explicit.
• Dempster–Shafer theory — Assign evidential mass to subsets of a frame of discernment, derive belief and plausibility bounds for propositions, and combine appropriately independent evidence with a declared conflict rule.
• Imprecise probability — Represent incomplete probabilistic commitment by a coherent set of admissible probability measures or equivalent lower and upper expectations, so conclusions expose a range and distinguish robust agreement from decisions that depend on an unresolved model choice.
• Isolation lemma — Assign independent random weights to elements of a finite set system so that, with a controlled positive probability, a nonempty family has a unique minimum-weight member.