E.J. Wagenmakers and his enthusiastic team of collaborators at University of Amsterdam and in the JASP software designing team have started a blog called Bayesian spectacles which I find a fantastic title. And not only because I wear glasses. Plus, they got their own illustrator, Viktor Beekman, which sounds like the epitome of sophistication! (Compared with resorting to vacation or cat pictures…)

In a most recent post they addressed the criticisms we made of the 72 author paper on p-values, one of the co-authors being E.J.! Andrew already re-addressed some of the address, but here is a disagreement he let me to chew on my own [and where the Abandoners are us!]:

Disagreement 2.The Abandoners’ critique the UMPBTs –the uniformly most powerful Bayesian tests– that features in the original paper. This is their right (see also the discussion of the 2013 Valen Johnson PNAS paper), but they ignore the fact that the original paper presented a series of other procedures that all point to the same conclusion: p-just-below-.05 results are evidentially weak. For instance, a cartoon on the JASP blog explains the Vovk-Sellke bound. A similar result is obtained using the upper bounds discussed in Berger & Sellke (1987) and Edwards, Lindman, & Savage (1963). We suspect that the Abandoners’ dislike of Bayes factors (and perhaps their upper bounds) is driven by a disdain for the point-null hypothesis. That is understandable, but the two critiques should not be mixed up. The first question is Given that we wish to test a point-null hypothesis, do the Bayes factor upper bounds demonstrate that the evidence is weak for p-just-below-.05 results? We believe they do, and in this series of blog posts we have provided concrete demonstrations.

Obviously, this reply calls for an examination of the entire BS blog series, but being short in time at the moment, let me point out that the upper lower bounds on the Bayes factors showing much more support for H⁰ than a p-value at 0.05 only occur in special circumstances. Even though I spend some time in my book discussing those bounds. Indeed, the [interesting] fact that the lower bounds are larger than the p-values does not hold in full generality. Moving to a two-dimensional normal with potentially zero mean is enough to see the order between lower bound and p-value reverse, as I found [quite] a while ago when trying to expand Berger and Sellker (1987, the same year as I was visiting Purdue where both had a position). I am not sure this feature has been much explored in the literature, I did not pursue it when I realised the gap was missing in larger dimensions… I must also point out I do not have the same repulsion for point nulls as Andrew! While considering whether a parameter, say a mean, is exactly zero [or three or whatever] sounds rather absurd when faced with the strata of uncertainty about models, data, procedures, &tc.—even in theoretical physics!—, comparing several [and all wrong!] models with or without some parameters for later use still makes sense. And my reluctance in using Bayes factors does not stem from an opposition to comparing models or from the procedure itself, which is quite appealing within a Bayesian framework [thus appealing *per se*!], but rather from the unfortunate impact of the prior [and its tail behaviour] on the quantity and on the delicate calibration of the thing. And on a lack of reference solution [to avoid the O and the N words!]. As exposed in the demise papers. (Which main version remains in a publishing limbo, the onslaught from the referees proving just too much for me!)

## Valen in Le Monde

Posted in Books, Statistics, University life with tags blogging, comments, False positive, Le Monde, Monsanto, p-values, Passeur de Sciences, statistical significance, UMPB test, uniformly most powerful tests, Valen Johnson on November 21, 2013 by xi'anValen Johnson made the headline inLe Monde, last week. (More precisely, to the scientific blogPasseur de Sciences. Thanks, Julien, for the pointer!) With the alarming title of “Une étude ébranle un pan de la méthode scientifique”(A study questions one major tool of the scientific approach). The reason for this French fame is Valen’s recent paper in PNAS,Revised standards for statistical evidence, where he puts forward his uniformly most powerful Bayesian tests (recently discussed on the ‘Og) to argue against the standard 0.05 significance level and in favour of “the 0.005 or 0.001 level of significance.”While I do plan to discuss the PNAS paper later (and possibly write a comment letter to PNAS with Andrew), I find interesting the way it made the headlines within days of its (early edition) publication: the argument suggesting to replace .05 with .001 to increase the proportion of reproducible studies is both simple and convincing for a scientific journalist. If only the issue with p-values and statistical testing could be that simple… For instance, the above quote from Valen is reproduced as “an [alternative] hypothesis that stands right below the significance level has in truth only 3 to 5 chances to 1 to be true”, the “truth” popping out of nowhere. (If you read French, the 300+ comments on the blog are also worth their weight in jellybeans…)## Share:

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