Negative Dependence in Sampling

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 and are two families of 0‐1 random variables that satisfy the strong Rayleigh property and let . We show that {Z_i} conditioned on 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 π ps 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.