Positive Influence and Negative Dependence
We study negative dependence properties of a sampling process due to Srinivasan to produce distributions on level sets with given marginals. We give a simple proof that the distribution satisfies negative association. We also show that under a linear match schedule it satisfies the stronger condition of conditional negative association via a non-trivial application of the Feder–Mihail theorem. This method involves the notion of a variable of positive influence. We give some results and related counter-examples which might shed some light on its role in a theory of negative dependence.(Received June 30 2004)
(Revised July 6 2005)
1 Work done partly while the author was visiting BRICS.
2 Work supported by the Swedish Research Council.
3 Work done partly while the author was visiting the Max–Planck–Institut für Informatik and BRICS.
4 Work partially supported by the ESPRIT Basic Research Actions Program of the EC under contract No. 7141 (project ALCOM II).