A Proof of Proposition 1

Since the size k of the observed set is randomly distributed given the observation time, the next lemma shows how this size concentrates around the mean. We start with the posterior mean. These conditions are necessary for the Taylor expansions of the logarithms to be converging. Again, this condition is necessary for the Taylor expansion of the logarithm to be converging. Using Lemma 2, we can show that r/ (1 r) is upper bounded by a constant in m with probability at least 1 δ .