Last modified: Thu Sep 29 13:56:22 EDT 2005 by Dean Foster

Statistical Data mining: Bonferroni

Admistrivia

• Homework due today. More homework due next week

So: Add all of them with a |t| > sqrt(2 log p)

• Called Bonferroni
  • Prove tail of the null: Phi(x) < phi(x) for x < -1.
  • Prove sum of events: P(U A_i) &le sum P(A_i)
• First suggested by Foster and George (for regression) / Donoho and Johnstone (for wavelets)

Started with "fit" ended with paranoia

• Back to first principles
• Goal is a good fit: Too poorly defined
• Goal is a good worst-case fit: Bad goal since encorages adding all variables
• Goal is good fit over each size model: Idea of Risk Inflation

Risk inflation

• Definition: ratio of risks to best
• Alternative definition: compared to oracle
• Look at table 2 from paper to see how some simple methods do

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