text: user8601: The following paragraph comes from the GSEA paper that explains how to obtain an enrichment score for a gene set. Note that the enrichment score is computed up to a position i in L. There are 2 things I don’t understand about this:
  1- first, the following image illustrating the method seems to suggest that that we score a gene set across the whole list of ranked genes, which conflicts with the idea of “up to a position i” in L
  2- second, if we’re only considering genes up to a position i, then how are we going to capture the genes that are underexpressed (appear at the bottom of the ranked list) for phenotype A?
  
  
  
  user8601: Actually I believe I get it now. i is not a constant. We vary it from i=1 to N and consider the i for which $P_{hit} - P_{miss}$  is largest in magnitude
  
original_text: 8601: <p>The following paragraph comes from the GSEA paper that explains how to obtain an enrichment score for a gene set. Note that the enrichment score is computed <strong>up to a position i</strong> in L. There are 2 things I don’t understand about this:</p>
  <p>1- first, the following image illustrating the method seems to suggest that that we score a gene set across the whole list of ranked genes, which conflicts with the idea of “up to a position i” in L</p>
  <p>2- second, if we’re only considering genes up to a position i, then how are we going to capture the genes that are underexpressed (appear at the bottom of the ranked list) for phenotype A?</p>
  <p><a href="https://i.stack.imgur.com/guDWR.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/guDWR.jpg" alt="enter image description here" /></a>
  <a href="https://i.stack.imgur.com/Wh35F.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/Wh35F.jpg" alt="enter image description here" /></a></p>
   8601: <p>Actually I believe I get it now. i is not a constant. We vary it from i=1 to N and consider the i for which <span class="math-container">$P_{hit} - P_{miss}$</span>  is largest in magnitude</p>
  