2013/01/21
bounding overlaps
A Venn diagram gives a schematic view of joint counts on a set of n categories, e.g. c(Sn1=sn1) where si∈{0,1}. Each “patch” of the diagram corresponds to one of 2n possible values of sn1.
If we have the total count C≜, then we can take the counts as probabilities by normalizing with p(S_1^n=s_1^n)=c(S_1^n=s_1^n)/C.
Suppose we are given only singleton marginals p(S_i=1)\triangleq \sum_{s_j: j\in \{1,…,n\}\backslash i} p(S_1^n=s_1^n), then we can bound the other probabilities by imposing universal constraints on probabilities to be between 0 and 1.
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