## Archive for The University of Texas at Austin

## U of T sunset [jatp]

Posted in pictures, Running, Travel, University life with tags Austin, jatp, sunset, Texas, The University of Texas at Austin, USA on December 14, 2017 by xi'an## Au’Bayes 17

Posted in Statistics, Travel, University life with tags ABC, Austin, BNP12, canoe, Hyvärinen score, misspecified model, NIPS 2017, O'Ba, O'Bayes 2019, O-Bayes 2017, objective Bayes, safe Bayes, Sardinia, Texas, The University of Texas at Austin, University of Oxford, University of Warwick, Wikiprevia on December 14, 2017 by xi'anSome notes scribbled during the O’Bayes 17 conference in Austin, not reflecting on the highly diverse range of talks. And many new faces and topics, meaning O’Bayes is alive and evolving. With all possible objectivity, a fantastic conference! (Not even mentioning the bars where Peter Müller hosted the poster sessions, a feat I would have loved to see duplicated for the posters of ISBA 2018… Or the Ethiopian restaurant just around the corner with the right amount of fierce spices!)

The wiki on objective, reference, vague, neutral [or whichever label one favours] priors that was suggested at the previous O’Bayes meeting in Valencià, was introduced as Wikiprevia by Gonzalo Garcia-Donato. It aims at classifying recommended priors in most of the classical models, along with discussion panels, and it should soon get an official launch, when contributors will be welcome to include articles in a wiki principle. I wish the best to this venture which, I hope, will induce O’Bayesians to contribute actively.

In a brilliant talk that quickly reverted my jetlag doziness, Peter Grünwald returned to the topic he presented last year in Sardinia, namely safe Bayes or powered-down likelihoods to handle some degree of misspecification, with a further twist of introducing an impossible value `o’ that captures missing mass (to be called Peter’s demon?!), which absolute necessity I did not perceive. Food for thoughts, definitely. (But I feel that the only safe Bayes is the dead Bayes, as protecting against all kinds of mispecifications means no action is possible.)

I also appreciated Cristiano Villa’s approach to constructing prior weights in model comparison from a principled and decision-theoretic perspective even though I felt that the notion of ranking parameter importance required too much input to be practically feasible. (Unless I missed that point.)

Laura Ventura gave her talk on using for ABC various scores or estimating equations as summary statistics, rather than the corresponding M-estimators, which offers the appealing feature of reducing computation while being asymptotically equivalent. (A feature we also exploited for the regular score function in our ABC paper with Gael, David, Brendan, and Wonapree.) She mentioned the Hyvärinen score [of which I first heard in Padova!] as a way to bypass issues related to doubly intractable likelihoods. Which is a most interesting proposal that bypasses (ABC) simulations from such complex targets by exploiting a pseudo-posterior.

Veronika Rockova presented a recent work on concentration rates for regression tree methods that produce a rigorous analysis of these methods. Showing that the spike & slab priors plus BART [equals spike & tree] achieve sparsity and optimal concentration. In an oracle sense. With a side entry on assembling partition trees towards creating a new form of BART. Which made me wonder whether or not this was also applicable to random forests. Although they are not exactly Bayes. Demanding work in terms of the theory behind but with impressive consequences!

Just before I left O’Bayes 17 for Houston airport, Nick Polson, along with Peter McCullach, proposed an intriguing notion of sparse Bayes factors, which corresponds to the limit of a Bayes factor when the prior probability υ of the null goes to zero. When the limiting prior is replaced with an exceedance measure that can be normalised into a distribution, but does it make the limit a special prior? Linking υ with the prior under the null is not an issue (this was the basis of my 1992 Lindley paradox paper) but the sequence of priors indexed by υ need be chosen. And reading from the paper at Houston airport, I could not spot a construction principle that would lead to a reference prior of sorts. One thing that Nick mentioned during his talk was that we observed directly realisations of the data marginal, but this is generally not the case as the observations are associated with a given value of the parameter, not one for each observation.The next edition of the O’Bayes conference will be in… Warwick on June 29-July 2, as I volunteered to organise this edition (16 years after O’Bayes 03 in Aussois!) just after the BNP meeting in Oxford on June 23-28, hopefully creating the environment for fruitful interactions between both communities! (And jumping from Au’Bayes to Wa’Bayes.)

## O’Bayes 2017 group photograph

Posted in pictures, Statistics, Travel, University life with tags Austin, conference, group picture, ISBA, O'Bayes17, objective Bayes, Texas, The University of Texas at Austin, USA on December 13, 2017 by xi'an## off to Austin!

Posted in Books, Kids, Statistics, Travel, University life, Wines with tags Austin, conference, ISBA, O'Bayes17, objective Bayes, Objective Bayesian hypothesis testing, Robert Dedman, Texas, The University of Texas at Austin, USA on December 9, 2017 by xi'an**T**oday I am flying to Austin, Texas, on the occasion of the O’Bayes 2017 conference, the 12th meeting in the series. In complete objectivity (I am a member of the scientific committee!), the scientific program looks quite exciting, with new themes and new faces. (And Peter Müller concocted a special social program as well!) As indicated above [with an innovative spelling of my first name!] I will give my “traditional” tutorial on O’Bayes testing and model choice tomorrow, flying back to Paris on Wednesday (and alas missing the final talks, including Better together by Pierre!). A nice pun is that the conference centre is located on Robert De[a]dman Drive, which I hope is not premonitory of a fatal ending to my talk there..!

## priors without likelihoods are like sloths without…

Posted in Books, Statistics with tags Austin, Bayes factors, Bayesian Analysis, identifiability, improper priors, noninformative priors, O'Bayes17, Pierre Simon Laplace, posterior predictive, reference priors, sloth, The American Statistician, The University of Texas at Austin on September 11, 2017 by xi'an

“The idea of building priors that generate reasonable data may seem like an unusual idea…”

**A**ndrew, Dan, and Michael arXived a opinion piece last week entitled “The prior can generally only be understood in the context of the likelihood”. Which connects to the earlier Read Paper of Gelman and Hennig I discussed last year. I cannot state strong disagreement with the positions taken in this piece, actually, in that I do not think prior distributions ever occur as *a given* but are rather chosen as a reference measure to probabilise the parameter space and eventually prioritise regions over others. If anything I find myself even further on the prior agnosticism gradation. (Of course, this lack of disagreement applies to the likelihood understood as a function of both the data and the parameter, rather than of the parameter only, conditional on the data. Priors cannot be depending on the data without incurring disastrous consequences!)

“…it contradicts the conceptual principle that the prior distribution should convey only information that is available before the data have been collected.”

The first example is somewhat disappointing in that it revolves as so many Bayesian textbooks (since Laplace!) around the [sex ratio] Binomial probability parameter and concludes at the strong or long-lasting impact of the Uniform prior. I do not see much of a contradiction between the use of a Uniform prior and the collection of prior information, if only because there is not standardised way to transfer prior information into prior construction. And more fundamentally because a parameter rarely makes sense by itself, alone, without a model that relates it to potential data. As for instance in a regression model. More, following my epiphany of last semester, about the relativity of the prior, I see no damage in the prior being relevant, as I only attach a *relative* meaning to statements based on the posterior. Rather than trying to limit the impact of a prior, we should rather build assessment tools to measure this impact, for instance by prior predictive simulations. And this is where I come to quite agree with the authors.

“…non-identifiabilities, and near nonidentifiabilites, of complex models can lead to unexpected amounts of weight being given to certain aspects of the prior.”

Another rather straightforward remark is that non-identifiable models see the impact of a prior remain as the sample size grows. And I still see no issue with this fact in a relative approach. When the authors mention (p.7) that purely mathematical priors perform more poorly than weakly informative priors it is hard to see what they mean by this “performance”.

“…judge a prior by examining the data generating processes it favors and disfavors.”

Besides those points, I completely agree with them about the fundamental relevance of the prior as a generative process, only when the likelihood becomes available. And simulatable. (This point is found in many references, including our response to the American Statistician paper *Hidden dangers of specifying noninformative priors*, with Kaniav Kamary. With the same illustration on a logistic regression.) I also agree to their criticism of the marginal likelihood and Bayes factors as being so strongly impacted by the choice of a prior, if treated as absolute quantities. I also if more reluctantly and somewhat heretically see a point in using the posterior predictive for assessing whether a prior is relevant for the data at hand. At least at a conceptual level. I am however less certain about how to handle improper priors based on their recommendations. In conclusion, it would be great to see one [or more] of the authors at O-Bayes 2017 in Austin as I am sure it would stem nice discussions there! (And by the way I have no prior idea on how to conclude the comparison in the title!)