What is the intuition for dependence assumption in Benjamini and Hochberg (1995)? For dealing with multiple testing, Benjamini and Hochberg (1995) assume that the tests are independent. Benjamini and Yekutieli (2001) show that (1) the 1995 result also holds under (I think) weaker conditions and that (2) including the factor $\Sigma^m_{i=1}\frac{1}{i}$ makes the procedure applicable for any dependence structure (see Theorem 1.3). Since this summation is greater than or equal to 1, it would make the procedure more conservative.
My question is why is independent tests not the worst case assumption? Is there some simple example to illustrate why not? Does it involve a negative dependence structure of some sort?
Maybe my understanding is faulty, but I thought that the Bonferroni adjustment 
(for the familywise error) worked for any dependence and that independence is the worst case assumption. Perhaps this is not correct and hence my confusion with BH. 
 A: Independence is more like a best-case assumption than a worst-case assumption.  Loosely, when data are independent, each datum contains as much information as possible.  If data were dependent, because their values can be predicted from other data, each additional datum must have less new information to contribute (the part that could have been predicted you already knew in some sense).  The situation can be similar with multiple testing.  In terms of simple alpha correction strategies, if the tests are independent, the Dunn-Sidak correction can be used:
$$
\alpha_{\rm DS} = 1 - (1-\alpha)^{1/k}
$$
but if the tests are not independent, the Bonferroni correction must be used:
$$
\alpha_{\rm B} = \frac{\alpha}{k}
$$
As is clear from the formulas, $\alpha_{\rm DS}\ge \alpha_{\rm B}$.  
A: Gung is incorrect that Dunn-Sidak should be used under independence and Bonferroni must be used under dependence. In fact, Dunn-Sidak controls the FWER not only under independence, but also under positive dependence. And Bonferroni controls the FWER for any dependence structure--including independence.
To answer your question, the reason independence isn't the "worst case" is that in certain situations, you can theoretically have negative dependence.
