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5 Jun 2020: i) There exists a sequence of deterministic hypothesis tests,{TN}, such that β(TN) eNAN for all N and:. ... a lower boundon the type-I error probability of the best feasible test.

5 Jun 2020: Counting the Primes Using Entropy. Ioannis KontoyiannisAthens U of Economics & Business.

5 Jun 2020: The set Cn is called the critical region, and the type-I andtype-II probabilities of error associated with the test are, respectively,. ... Combi-natorial Theory, 1:385–393, 1966. [5] W. Hoeffding. Asymptotically optimal tests for multinomial

5 Jun 2020: Department of Informatics, Athens University of Economics and Business, Patission 76, 104 34, Athens, Greece$ School of Applied Mathematical and Physical Sciences, National Technical University of Athens, 157 80, Athens, Greece. ... S. T. was supported

5 Jun 2020: test is imperfect (there is a certain chance wemight get a false positive or a false negative), is it better to testone person twice, or two people, once each? ... Again, althoughit may seem more reasonable to test two people independently,we find that

5 Jun 2020: of the spike count in the data (as quantified by the Fano factor).This conclusion is rigorously justified with a t-test with a p-value of 5 104. ... Fanofactors and the percentage drop is zero, and the test statisticis t = r.

5 Jun 2020: Athens University of Economics and Business, Athens, Greeceyiannis@aueb.gr. 6.

5 Jun 2020: Athens University of Economics and Business, Athens, Greeceyiannis@aueb.gr. 960 c THE MATHEMATICAL ASSOCIATION OF AMERICA [Monthly 115.

5 Jun 2020: Scenario (II): Dependence. In this case the asymptotic behavior of the test statisticI(n) is somewhat different. ... 3 Experimental Results. In this section we apply the mutual information test described above to biological data.

5 Jun 2020: Department of Informatics, Athens University of Economics and Business, Patission 76, Athens 10434, Greece.Email: yiannis@aueb.gr.