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Something seems off with equation (5).

Just imagining Monte Carlo sampling it, the middle expectation will have a bunch of zeros due to the indicator function and the right expectation won’t.

I can make the middle expectation be as close to zero as I like by making the success threshold sufficiently high.

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Ah yes you are right the rhs was meant to be proportional to the middle expectation (see the equation below), for equality the rhs needs to be multiplied by a normalization constant independent of theta. Note this doesn't affect the bounds as the constant is the same across equations. Will update the paper to incorporate.

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