Likelihood Principle

Next Phil Stat Forum: January 7: D. Mayo: Putting the Brakes on the Breakthrough (or “How I used simple logic to uncover a flaw in …..statistical foundations”)

The fourth meeting of our New Phil Stat Forum*:

The Statistics Wars
and Their Casualties

January 7, 16:00 – 17:30  (London time)
11 am-12:30 pm (New York, ET)**
**note time modification and date change

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 G. Mayo

.

HOW TO JOIN US: SEE THIS LINK

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 posted an imaginary dialogue (here) with Allan Birnbaum at the stroke of midnight, New Year’s Eve, and this will be relevant for the talk.

The Phil Stat Forum schedule is at the Phil-Stat-Wars.com blog 


Readings:

One of the following 3 papers:

My earliest treatment via counterexample:

A deeper argument can be found in:

For an intermediate Goldilocks version (based on a presentation given at the JSM 2013):

This post from the Error Statistics Philosophy blog will get you oriented. (It has links to other posts on the LP & Birnbaum, as well as background readings/discussions for those who want to dive deeper into the topic.)


Slides and Video Links:

D. Mayo’s slides: “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’”

D. Mayo’s  presentation:

Discussion on Mayo’s presentation:


Mayo’s Memos: Any info or events that arise that seem relevant to share with y’all before the meeting.

You may wish to look at my rejoinder to a number of statisticians: Rejoinder “On the Birnbaum Argument for the Strong Likelihood Principle”. (It is also above in the link to the complete discussion in the 3rd reading option.)

I often find it useful to look at other treatments. So I put together this short supplement to glance through to clarify a few select points.


Please post comments on the Phil Stat Wars blog here.

 

 
 
 
Categories: Birnbaum, Birnbaum Brakes, Likelihood Principle | 5 Comments

Next Phil Stat Forum: January 7: D. Mayo: Putting the Brakes on the Breakthrough (or “How I used simple logic to uncover a flaw in …..statistical foundations”)

The fourth meeting of our New Phil Stat Forum*:

The Statistics Wars
and Their Casualties

January 7, 16:00 – 17:30  (London time)
11 am-12:30 pm (New York, ET)**
**note time modification and date change

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 G. Mayo

.

HOW TO JOIN US: SEE THIS LINK

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, and this will be relevant for the talk.

The Phil Stat Forum schedule is at the Phil-Stat-Wars.com blog 

 
 
 
Categories: Birnbaum, Birnbaum Brakes, Likelihood Principle | 1 Comment

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