A0766
Title: Global testing for dependent Bernoullis
Authors: Nabarun Deb - Columbia University (United States)
Rajarshi Mukherjee - Harvard T.H. Chan School of Public Health (United States)
Ming Yuan - Columbia University (United States)
Sumit Mukherjee - Columbia University (United States) [presenting]
Abstract: Suppose $(X_1,\ldots,X_n)$ are independent Bernoulli random variables with $\mathbb{E}(X_i)= p_i$, and we want to test the global null hypothesis that $p_i=\frac{1}{2}$ for all $i$, versus the alternative that there is a sparse set of size $s$ on which $p_i\ge \frac{1}{2}+A$. The detection boundary of this test in terms of $(s,A)$ is well understood, both in the case when the signal is arbitrary, and when the signal is present in a segment. We study the above questions when the Bernoullis are dependent, and the dependence is modeled by a graphical model (Ising model). In this case, contrary to what typically happens, dependence can allow the detection of smaller signals than in the independent case. This phenomenon happens over a wide range of graphs, for both arbitrary signals and segment signals.
