## Archive for Susie Bayarri

## Sancerre

Posted in Wines with tags French wines, Loire, Sancerre, Susie Bayarri, white wine on September 20, 2022 by xi'an## prior sensitivity of the marginal likelihood

Posted in Books, pictures, Statistics, University life with tags arXiv, Bayes factors, Bayesian model selection, blogging, expected posterior prior, flat prior, fractional Bayes factor, Harold Jeffreys, improper priors, intrinsic Bayes factor, Madrid, marginal likelihood, parameterisation, Susie Bayarri on June 27, 2022 by xi'an**F**ernando Llorente and (Madrilene) coauthors have just arXived a paper on the safe use of prior densities for Bayesian model selection. Rather than blaming the Bayes factor, or excommunicating some improper priors, they consider in this survey solutions to design “objective” priors in model selection. (Writing this post made me realised I had forgotten to arXive a recent piece I wrote on the topic, based on short courses and blog pieces, for an incoming handbook on Bayesian advance(ment)s! Soon to be corrected.)

While intrinsically interested in the topic and hence with the study, I somewhat disagree with the perspective adopted by the authors. They for instance stick to the notion that a flat prior over the parameter space is appropriate as “the maximal expression of a non-informative prior” (despite depending on the parameterisation). Over bounded sets at least, while advocating priors “with great scale parameter” otherwise. They also refer to Jeffreys (1939) priors, by which they mean *estimation priors* rather than *testing priors*. As uncovered by Susie Bayarri and Gonzalo Garcia-Donato. Considering asymptotic consistency, they state that “in the asymptotic regime, Bayesian model selection is more sensitive to the sample size D than to the prior specifications”, which I find both imprecise and confusing, as my feeling is that the prior specification remains overly influential as the sample size increases. (In my view, consistency is a minimalist requirement, rather than “comforting”.) The argument therein that a flat prior is *informative* for model choice stems from the fact that the marginal likelihood goes to zero as the support of the prior goes to infinity, which may have been an earlier argument of Jeffreys’ (1939), but does not carry much weight as the property is shared by many other priors (as remarked later). Somehow, the penalisation aspect of the marginal is not exploited more deeply in the paper. In the “objective” Bayes section, they adhere to the (convenient but weakly supported) choice of a common prior on the nuisance parameters (shared by different models). Their main argument is to develop (heretic!) “data-based priors”, from Aitkin (1991, not cited) double use of the data (or setting the likelihood to the power two), all the way to the intrinsic and fractional Bayes factors of Tony O’Hagan (1995), Jim Berger and Luis Pericchi (1996), and to the *expected posterior priors* of Pérez and Berger (2002) on which I worked with Juan Cano and Diego Salmeròn. (While the presentation is made against a flat prior, nothing prevents the use of another reference, improper, prior.) A short section also mentions the X-validation approach(es) of Aki Vehtari and co-authors.

## Jeffreys priors for hypothesis testing [Bayesian reads #2]

Posted in Books, Statistics, University life with tags Arnold Zellner, Bayes factor, Bayesian tests of hypotheses, CDT, class, classics, Gaussian mixture, improper priors, Jeffreys prior, JRSSB, Kullback-Leibler divergence, Oxford, PhD course, Saint Giles cemetery, Susie Bayarri, Theory of Probability, University of Oxford on February 9, 2019 by xi'anA second (re)visit to a reference paper I gave to my OxWaSP students for the last round of this CDT joint program. Indeed, this may be my first complete read of Susie Bayarri and Gonzalo Garcia-Donato 2008 Series B paper, inspired by Jeffreys’, Zellner’s and Siow’s proposals in the Normal case. *(Disclaimer: I was not the JRSS B editor for this paper.) *Which I saw as a talk at the O’Bayes 2009 meeting in Phillie.

The paper aims at constructing formal rules for objective proper priors in testing embedded hypotheses, in the spirit of Jeffreys’ Theory of Probability “hidden gem” (Chapter 3). The proposal is based on symmetrised versions of the Kullback-Leibler divergence κ between null and alternative used in a transform like an inverse power of 1+κ. With a power large enough to make the prior proper. Eventually multiplied by a reference measure (i.e., the arbitrary choice of a dominating measure.) Can be generalised to any intrinsic loss (not to be confused with an intrinsic prior à la Berger and Pericchi!). Approximately Cauchy or Student’s t by a Taylor expansion. To be compared with Jeffreys’ original prior equal to the derivative of the atan transform of the root divergence (!). A delicate calibration by an effective sample size, lacking a general definition.

At the start the authors rightly insist on having the nuisance parameter v to differ for each model but… as we all often do they relapse back to having the “same ν” in both models for integrability reasons. Nuisance parameters make the definition of the divergence prior somewhat harder. Or somewhat arbitrary. Indeed, as in reference prior settings, the authors work first conditional on the nuisance then use a prior on ν that may be improper by the “same” argument. (Although *conditioning* is not the proper term if the marginal prior on ν is improper.)

The paper also contains an interesting case of the translated Exponential, where the prior is L¹ Student’s t with 2 degrees of freedom. And another one of mixture models albeit in the simple case of a location parameter on one component only.

## Altos de Losada [guest wine post by Susie]

Posted in pictures, Travel, University life, Wines with tags Altos de Losada, Leon, Spanish wines, Susie Bayarri, València, wine tasting on June 20, 2015 by xi'an[Here is a wine criticism written by Susie Bayarri in 2013 about a 2008 bottle of Altos de Losada, a wine from Leon:]

**T**he cork is fantastic. Very good presentation and labelling of the bottle. The wine color is like dark cherry, I would almost say of the color of blood. Very bright although unfiltered. The cover is d16efinitely high. The tear is very nice (at least in my glass), slow, wide, through parallel streams… but it does not dye my glass at all.

The bouquet is its best feature… it is simply voluptuous… with ripe plums as well as vanilla, some mineral tone plus a smoky hint. I cannot quite detect which wood is used… I have always loved the bouquet of this wine…

In mouth, it remains a bit closed. Next time, I will make sure I decant it (or I will use that Venturi device) but it is nonetheless excellent… the wine is truly fruity, but complex as well (nothing like grape juice). The tannins are definitely present, but tamed and assimilated (I think they will continue to mellow) and it has just a hint of acidity… Despite its alcohol content, it remains light, neither overly sweet nor heavy. The after-taste offers a pleasant bitterness… It is just delicious, an awesome wine!