Stochastic monotonicity and realizable monotonicity
By James Allen Fill, Motoya Machida. 2000
65 citations recorded by the source corpus.
We explore and relate two notions of monotonicity, stochastic and realizable, for a system of probability measures on a common finite partially ordered set (poset) f when the measures are indexed by another poset A. We give counterexamples to show that the two notions are not always equivalent, but for various large classes of f we also present conditions on the poset A that are necessary and sufficient for equivalence. When A = f, the condition that the cover graph of f have no cycles is necessary and sufficient for equivalence. This case arises in comparing applicability of the perfect sampling algorithms of Propp and Wilson and the first author of the present paper.
Subfields: Economics and Econometrics, Geometry and Topology, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/130c40eefe77bb5d8bfb21fc9cbb7a40a9e64d11
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In Economics and Econometrics
In Geometry and Topology
In Statistics and Probability
Citations in the corpus
- Towards a theory of negative dependence (2000, background): “For the reason why this does not immediately follow from stochastic monotonicity in the boundary conditions, see Fill and Machida (1998).”