Negative Dependence in Sampling


Johan Jonasson, Department of Mathematics, Chalmers University of Technology and Göteborg University, 412 96 Gothenburg, Sweden.


Abstract.  The strong Rayleigh property is a new and robust negative dependence property that implies negative association; in fact it implies conditional negative association closed under external fields (CNA+). Suppose that inline image and inline image are two families of 0-1 random variables that satisfy the strong Rayleigh property and let inline image. We show that {Zi} conditioned on inline image is also strongly Rayleigh; this turns out to be an easy consequence of the results on preservation of stability of polynomials of Borcea & Brändén (Invent. Math., 177, 2009, 521–569). This entails that a number of important πps sampling algorithms, including Sampford sampling and Pareto sampling, are CNA+. As a consequence, statistics based on such samples automatically satisfy a version of the Central Limit Theorem for triangular arrays.