Putting the Brakes on the Breakthrough, or “How I used simple logic to uncover a flaw in a controversial 60-year old ‘theorem’ in statistical foundations”

Deborah Mayo (Virginia Tech)

ABSTRACT: An essential component of inference based on familiar frequentist (error statistical) notions p-values, statistical significance and confidence levels, is the relevant sampling distribution (hence the term sampling theory). This results in violations of a principle known as the strong likelihood principle (SLP), or just the likelihood principle (LP), which says, in effect, that outcomes other than those observed are irrelevant for inferences within a statistical model. Now Allan Birnbaum was a frequentist (error statistician), but he found himself in a predicament: He seemed to have shown that the LP follows from uncontroversial frequentist principles! Bayesians, such as Savage, heralded his result as a “breakthrough in statistics”! But there’s a flaw in the “proof”, and that’s what I aim to show in my presentation by means of 3 simple examples:.

• Example 1: Trying and Trying Again
• Example 2: Two instruments with different precisions
  (you shouldn’t get credit/blame for something you didn’t do)
• The Breakthrough: Don’t Birnbaumize that data my friend

As in the last 9 years, I will post an imaginary dialogue with Allan Birnbaum at the stroke of midnight, New Year’s Eve, on errorstatistics.com, and this will be relevant for the talk.