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SUMMARY:Global testing for dependent Bernoullis  - Sumit Mukherjee (Columb
 ia University)
DTSTART:20211008T150000Z
DTEND:20211008T160000Z
UID:TALK162121@talks.cam.ac.uk
CONTACT:Qingyuan Zhao
DESCRIPTION: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 n
 ull hypothesis that $p_i=\\frac{1}{2}$ for all $i$\, versus the alternativ
 e 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 underst
 ood\, both in the case when the signal is arbitrary\, and when the signal 
 is present in a segment.\n\nWe study the above questions when the Bernoull
 is are dependent\, and the dependence is modeled by a graphical model (Isi
 ng model). In this case\, contrary to what typically happens\, dependence 
 can allow detection of smaller signals than the independent case. This phe
 nomenon happens over a wide range of graphs\, for both arbitrary signals a
 nd segment signals. \n\nThis talk is based on joint work with Nabarun Deb\
 , Rajarshi Mukherjee\, and Ming Yuan
LOCATION:https://maths-cam-ac-uk.zoom.us/j/93998865836?pwd=VzVzN1VFQ0xjS3V
 DdlY0enBVckY5dz09
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