You know how in that recent movie, “Midnight in Paris,” the main character (I forget who plays it, I saw it on a plane) is a writer finishing a novel, and he steps into a cab that mysteriously picks him up at midnight and transports him back in time where he gets to run his work by such famous authors as Hemingway and Virginia Wolf? He is impressed when his work earns their approval and he comes back each night in the same mysterious cab…Well, imagine an error statistical philosopher is picked up in a mysterious taxi at midnight (new Year’s Eve 2011) and is taken back fifty years and, lo and behold, finds herself in the company of Allan Birnbaum.[i] Continue reading
Monthly Archives: December 2011
Fortunately, we have Jim Berger interpreting himself this evening (see December 11)
Jim Berger writes:
A few comments:
1. Objective Bayesian priors are often improper (i.e., have infinite total mass), but this is not a problem when they are developed correctly. But not every improper prior is satisfactory. For instance, the constant prior is known to be unsatisfactory in many situations. The ‘solution’ pseudo-Bayesians often use is to choose a constant prior over a large but bounded set (a ‘weakly informative’ prior), saying it is now proper and so all is well. This is not true; if the constant prior on the whole parameter space is bad, so will be the constant prior over the bounded set. The problem is, in part, that some people confuse proper priors with subjective priors and, having learned that true subjective priors are fine, incorrectly presume that weakly informative proper priors are fine. Continue reading
My efficient Errorstat Blogpeople1 have put forward the following 3 reader-contributed interpretive efforts2 as a result of the “deconstruction” exercise from December 11, (mine, from the earlier blog, is at the end) of what I consider:
“….an especially intriguing remark by Jim Berger that I think bears upon the current mindset (Jim is aware of my efforts):
Too often I see people pretending to be subjectivists, and then using “weakly informative” priors that the objective Bayesian community knows are terrible and will give ridiculous answers; subjectivism is then being used as a shield to hide ignorance. . . . In my own more provocative moments, I claim that the only true subjectivists are the objective Bayesians, because they refuse to use subjectivism as a shield against criticism of sloppy pseudo-Bayesian practice. (Berger 2006, 463)” (From blogpost, Dec. 11, 2011) Continue reading
First people deny a thing.
Then they belittle it.
Then they say they knew it all along.
I don’t know who was first to state it in one form or another. Here’s Schopenhauer with a slightly different variant:
“All truth passes through three stages: First, it is ridiculed; Second, it is violently opposed; and Third, it is accepted as self-evident.” – Arthur Schopenhauer
After recently presenting my paper criticizing the Birnbaum result on the likelihood principle (LP) the reception of my analysis seems somewhere around stage two, in some cases, moving into stage three (see my blogposts of December 6 and 7, 2011). Continue reading
Some time in 2006 (shortly after my ERROR06 conference), the trickle of irony and sometime flood of family feuds issuing from Bayesian forums drew me back into the Bayesian-frequentist debates.1 2 Suddenly sparks were flying, mostly kept shrouded within Bayesian walls, but nothing can long be kept secret even there. Spontaneous combustion is looming. The true-blue subjectivists were accusing the increasingly popular “objective” and “reference” Bayesians of practicing in bad faith; the new O-Bayesians (and frequentist-Bayesian unificationists) were taking pains to show they were not subjective; and some were calling the new Bayesian kids on the block “pseudo Bayesian.” Then there were the Bayesians somewhere in the middle (or perhaps out in left field) who, though they still use the Bayesian umbrella, were flatly denying the very idea that Bayesian updating fits anything they actually do in statistics.3 Obeisance to Bayesian reasoning remained, but on some kind of a priori philosophical grounds. Doesn’t the methodology used in practice really need a philosophy of its own? I say it does, and I want to provide this. Continue reading
This is a first draft of part II of the presentation begun in the December 6 blog post. This completes the proposed presentation. I expecterrors, and I will be grateful for feedback! (NOTE: I did not need to actually rip a cover of EGEK to obtain this effect!)
SEVEN:NOW FOR THE BREAKTHROUGH
You have observed y”, the .05 significant result from E”,the optional stopping rule, ending at n = 100.
Birnbaum claims he can show that you, as a frequentist error statistician, must grant that it is equivalent to having fixed n= 100 at the start (i.e., experiment E’)
The (strong) LikelihoodPrinciple (LP) is a universal conditional claim:
If two data sets y’and y” from experiments E’ and E” respectively, have likelihood functions which are functions of the same parameter(s) µ
and are proportional to each other, then y’ and y”should lead to identical inferential conclusions about µ Continue reading
I am going to post a FIRST draft (for a brief presentation next week in Madrid). [I thank David Cox for the idea!] I expect errors, and I will be very grateful for feedback! This is part I; part II will be posted tomorrow. These posts may disappear once I’ve replaced them with a corrected draft. I’ll then post the draft someplace.
If you wish to share queries/corrections please post as a comment or e-mail: email@example.com. (ignore Greek symbols that are not showing correctly, I await fixes by Elbians.) Thanks much!
ONE: A Conversation between Sir David Cox and D. Mayo (June, 2011)
Toward the end of this exchange, the issue of the Likelihood Principle (LP) arose:
COX: It is sometimes claimed that there are logical inconsistencies in frequentist theory, in particular surrounding the strong Likelihood Principle (LP). I know you have written about this, what is your view at the moment.
MAYO: What contradiction?
COX: Well, that frequentist theory does not obey the strong LP. Continue reading
|Ruler at the Bottom of Ocean|
Senator: But you conceded that whenever your measuring tool showed dangerous or ambiguous readings, you continually lowered the pressure, and that the stringent “cement bond log” test was entirely skipped. Continue reading