Archive for Cambridge

Britain, please stay!

Posted in Books, Kids, pictures, Running, University life with tags , , , , , , , , , on June 7, 2016 by xi'an

A love letter from some Europeans against Brexit that appeared in the Times Literary Supplement a few days ago, and which message I definitely support:

All of us in Europe respect the right of the British people to decide whether they wish to remain with us in the European Union. It is your decision, and we will all accept it. Nevertheless, if it will help the undecided to make up their minds, we would like to express how very much we value having the United Kingdom in the European Union. It is not just treaties that join us to your country, but bonds of admiration and affection. All of us hope that you will vote to renew them. Britain, please stay.

messages from Harvard

Posted in pictures, Statistics, Travel, University life with tags , , , , , , on March 24, 2016 by xi'an

As in Bristol two months ago, where I joined the statistics reading in the morning, I had the opportunity to discuss the paper on testing via mixtures prior to my talk with a group of Harvard graduate students. Which concentrated on the biasing effect of the Bayes factor against the more complex hypothesis/model. Arguing [if not in those terms!] that Occam’s razor was too sharp. With a neat remark that decomposing the log Bayes factor as

log(p¹(y¹,H))+log(p²(y²|y¹,H))+…

meant that the first marginal was immensely and uniquely impacted by the prior modelling, hence very likely to be very small for a larger model H, which would then take forever to recover from. And asking why there was such a difference with cross-validation

log(p¹(y¹|y⁻¹,H))+log(p²(y²|y⁻²,H))+…

where the leave-one out posterior predictor is indeed more stable. While the later leads to major overfitting in my opinion, I never spotted the former decomposition which does appear as a strong and maybe damning criticism of the Bayes factor in terms of long-term impact of the prior modelling.

Other points made during the talk or before when preparing the talk:

  1. additive mixtures are but one encompassing model, geometric mixtures could be fun too, if harder to process (e.g., missing normalising constant). Or Zellner’s mixtures (with again the normalising issue);
  2. if the final outcome of the “test” is the posterior on α itself, the impact of the hyper-parameter on α is quite relative since this posterior can be calibrated by simulation against limiting cases (α=0,1);
  3. for the same reason the different rate of accumulation near zero and one  when compared with a posterior probability is hardly worrying;
  4. what I see as a fundamental difference in processing improper priors for Bayes factors versus mixtures is not perceived as such by everyone;
  5. even a common parameter θ on both models does not mean both models are equally weighted a priori, which relates to an earlier remark in Amsterdam about the different Jeffreys priors one can use;
  6. the MCMC output also produces a sample of θ’s which behaviour is obviously different from single model outputs. It would be interesting to study further the behaviour of those samples, which are not to be confused with model averaging;
  7. the mixture setting has nothing intrinsically Bayesian in that the model can be processed in other ways.

Harvard snow sprinkle

Posted in Kids, pictures, Running, Travel, University life with tags , , , , , on March 22, 2016 by xi'an

glorious Boston sunrise

Posted in pictures, Travel, University life with tags , , , , , on March 21, 2016 by xi'an

seminar in Harvard

Posted in Statistics, Travel with tags , , , , , , , , , , on March 16, 2016 by xi'an

harvard2103Next week, I will be in Harvard Monday and Tuesday, visiting friends in the Department of Statistics and giving a seminar. The slides for the talk will be quite similar to those of my talk in Bristol, a few weeks ago. Hopefully, there will not be too much overlap between both audiences! And hopefully I’ll manage to get to my conclusion before all hell breaks loose (which is why I strategically set my conclusion in the early slides!)

on intelligent design…

Posted in Books, Kids, Travel with tags , , , , , , , on August 19, 2014 by xi'an

chicken In connection with Dawkins’ The God delusion, which review is soon to appear on the ‘Og, a poster at an exhibit on evolution in the Harvard Museum of Natural History, which illustrates one of Dawkins’ points on scientific agosticism. Namely, that refusing to take a stand on the logical and philosophical opposition between science and religion(s) is not a scientific position. The last sentence in the poster is thus worse than unnecessary…

JSM 2014, Boston

Posted in Books, Mountains, pictures, Running, Statistics, Travel, University life with tags , , , , , , , , , , , , on August 6, 2014 by xi'an

A new Joint Statistical meeting (JSM), first one since JSM 2011 in Miami Beach. After solving [or not] a few issues on the home front (late arrival, one lost bag, morning run, flat in a purely residential area with no grocery store nearby and hence no milk for tea!), I “trekked” to [and then through] the faraway and sprawling Boston Convention Centre and was there in (plenty of) time for Mathias Drton’s Medalion Lecture on linear structural equations. (The room was small and crowded and I was glad to be there early enough!, although there were no Cerberus [Cerberi?] to prevent additional listeners to sit on the ground, as in Washington D.C. a few years ago.) The award was delivered to Mathias by Nancy Reid from Toronto (and reminded me of my Medallion Lecture in exotic Fairbanks ten years ago). I had alas missed Gareth Roberts’ Blackwell Lecture on Rao-Blackwellisation, as I was still in the plane from Paris, trying to cut on my slides and to spot known Icelandic locations from glancing sideways at the movie The Secret Life of Walter Mitty played on my neighbour’s screen. (Vik?)

Mathias started his wide-ranging lecture by linking linear structural models with graphical models and specific features of covariance matrices. I did not spot a motivation for the introduction of confounding factors, a point that always puzzles me in this literature [as I must have repeatedly mentioned here]. The “reality check” slide made me hopeful but it was mostly about causality [another of or the same among my stumbling blocks]… What I have trouble understanding is how much results from the modelling and how much follows from this “reality check”. A novel notion revealed by the talk was the “trek rule“, expressing the covariance between variables as a product of “treks” (sequence of edges) linking those variables. This is not a new notion, introduced by Wright (1921), but it is a very elegant representation of the matrix inversion of (I-Λ) as a power series. Mathias made it sound quite intuitive even though I would have difficulties rephrasing the principle solely from memory! It made me [vaguely] wonder at computational implications for simulation of posterior distributions on covariance matrices. Although I missed the fundamental motivation for those mathematical representations. The last part of the talk was a series of mostly open questions about the maximum likelihood estimation of covariance matrices, from existence to unimodality to likelihood-ratio tests. And an interesting instance of favouring bootstrap subsampling. As in random forests.

I also attended the ASA Presidential address of Stephen Stigler on the seven pillars of statistical wisdom. In connection with T.E. Lawrence’s 1927 book. (Actually, 1922.) Itself in connection with Proverbs IX:1. Unfortunately wrongly translated as seven pillars rather than seven sages.  Here are Stephen’s pillars:

  1. aggregation, which leads to gain information by throwing away information, aka the sufficiency principle [one may wonder at the extension of this principleto non-exponantial families]
  2. information accumulating at the √n rate, aka precision of statistical estimates, aka CLT confidence [quoting our friend de Moivre at the core of this discovery]
  3. likelihood as the right calibration of the amount of information brought by a dataset [including Bayes’ essay]
  4. intercomparison [i.e. scaling procedures from variability within the data, sample variation], eventually leading to the bootstrap
  5. regression [linked with Darwin’s evolution of species, albeit paradoxically] as conditional expectation, hence as a Bayesian tool
  6. design of experiment [enters Fisher, with his revolutionary vision of changing all factors in Latin square designs]
  7. residuals [aka goodness of fit but also ABC!]

Maybe missing the positive impact of the arbitrariness of picking or imposing a statistical model upon an observed dataset. Maybe not as it is somewhat covered by #3, #4 and #7. The reliance on the reproducibility of the data could be the ground on which those pillars stand.

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