Last week, I received this new book of Deborah Mayo, which I was looking forward reading and annotating!, but thrice alas, the book had been sabotaged: except for the preface and acknowledgements, the entire book is printed upside down [a minor issue since the entire book is concerned] and with some part of the text cut on each side [a few letters each time but enough to make reading a chore!]. I am thus waiting for a tested copy of the book to start reading it in earnest!
As I was teaching my introduction to Bayesian Statistics this morning, ending up with the chapter on tests of hypotheses, I found reflecting [out loud] on the relative nature of posterior quantities. Just like when I introduced the role of priors in Bayesian analysis the day before, I stressed the relativity of quantities coming out of the BBB [Big Bayesian Black Box], namely that whatever happens as a Bayesian procedure is to be understood, scaled, and relativised against the prior equivalent, i.e., that the reference measure or gauge is the prior. This is sort of obvious, clearly, but bringing the argument forward from the start avoids all sorts of misunderstanding and disagreement, in that it excludes the claims of absolute and certainty that may come with the production of a posterior distribution. It also removes the endless debate about the determination of the prior, by making each prior a reference on its own. With an additional possibility of calibration by simulation under the assumed model. Or an alternative. Again nothing new there, but I got rather excited by this presentation choice, as it seems to clarify the path to Bayesian modelling and avoid misapprehensions.
Further, the curious case of the Bayes factor (or of the posterior probability) could possibly be resolved most satisfactorily in this framework, as the [dreaded] dependence on the model prior probabilities then becomes a matter of relativity! Those posterior probabilities depend directly and almost linearly on the prior probabilities, but they should not be interpreted in an absolute sense as the ultimate and unique probability of the hypothesis (which anyway does not mean anything in terms of the observed experiment). In other words, this posterior probability does not need to be scaled against a U(0,1) distribution. Or against the p-value if anyone wishes to do so. By the end of the lecture, I was even wondering [not so loudly] whether or not this perspective was allowing for a resolution of the Lindley-Jeffreys paradox, as the resulting number could be set relative to the choice of the [arbitrary] normalising constant. Continue reading →
This may be a coincidence, but a few days after the ASA statement got published, Yuri Gurevich and Vladimir Vovk arXived a note on the Fundamentals of p-values. Which actually does not contribute to the debate. The paper is written in a Q&A manner. And defines a sort of peculiar logic related with [some] p-values. A second and more general paper is in the making, which may shed more light on the potential appeal of this formalism…
It took a visit on FiveThirtyEight to realise the ASA statement I mentioned yesterday was followed by individual entries from most members of the panel, much more diverse and deeper than the statement itself! Without discussing each and all comments, some points I subscribe to
Last night I received an email from the ASA signed by Jessica Utts and Ron Wasserstein with the following sentence
“Widespread use of ‘statistical significance’ (generally interpreted as ‘p
In short, we envision a new era, in which the broad scientific community recognizes what statisticians have been advocating for many years. In this “post p
Is such an era beyond reach? We think not, but we need your help in making sure this opportunity is not lost.”
which is obviously missing important bits. The email was pointing out a free access American Statistician article warning about the misuses and over-interpretations of p-values. Which contains rather basic “principles” that p-values are not probabilities that the null is true, that there is no golden level against which to compare the p-value, that nominal p-values may be far from actual p-values, that they do not provide a measure of evidence per se, &tc. As written in the conclusion, “Nothing in the ASA statement is new”. But, besides calling for caution and the cumulative use of different assessments of evidence, this statement may leave the non-statistician completely nonplussed about how to proceed when testing hypotheses or comparing models. And make the decision of Basic and Applied Social Psychology of rejecting all arguments based on p-values sound sensible.
Incidentally, the article contains the completion of the first sentence [in red below], if not of the second:
“Widespread use of ‘statistical significance’ (generally interpreted as ‘p≤ 0.05”) as a license for making a claim of a scientific finding (or implied truth) leads to considerable distortion of the scientific process.“
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