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<Paper uid="W04-3243">
  <Title>On Log-Likelihood-Ratios and the Significance of Rare Events</Title>
  <Section position="11" start_page="8" end_page="8" type="ackno">
    <SectionTitle>
8 Acknowledgements
</SectionTitle>
    <Paragraph position="0"> Thanks to Ken Church, Joshua Goodman, David Heckerman, Mark Johnson, Chris Meek, Ted Pedersen, and Chris Quirk for many valuable discussions of the issues raised in this paper. Thanks especially to Joshua Goodman for pointing out the existence of fast numerical approximations for the factorial function, and to Mark Johnson for helping to track down previous results on the relationship between log-likelihood-ratios and mutual information.</Paragraph>
  </Section>
class="xml-element"></Paper>