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CATEGORIES:Statistics
SUMMARY:Global testing for dependent Bernoullis - Sumit M
ukherjee (Columbia University)
DTSTART;TZID=Europe/London:20211008T160000
DTEND;TZID=Europe/London:20211008T170000
UID:TALK162121AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/162121
DESCRIPTION:Suppose $(X_1\,\\ldots\,X_n)$ are independent Bern
oulli 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 se
gment.\n\nWe study the above questions when the Be
rnoullis are dependent\, and the dependence is mod
eled by a graphical model (Ising model). In this c
ase\, contrary to what typically happens\, depende
nce can allow detection of smaller signals than th
e independent case. This phenomenon happens over a
wide range of graphs\, for both arbitrary signals
and segment signals. \n\nThis talk is based on jo
int work with Nabarun Deb\, Rajarshi Mukherjee\, a
nd Ming Yuan
LOCATION:https://maths-cam-ac-uk.zoom.us/j/93998865836?pwd=
VzVzN1VFQ0xjS3VDdlY0enBVckY5dz09
CONTACT:Qingyuan Zhao
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