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:
- 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]
- 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]
- likelihood as the right calibration of the amount of information brought by a dataset [including Bayes’ essay]
- intercomparison [i.e. scaling procedures from variability within the data, sample variation], eventually leading to the bootstrap
- regression [linked with Darwin’s evolution of species, albeit paradoxically] as conditional expectation, hence as a Bayesian tool
- design of experiment [enters Fisher, with his revolutionary vision of changing all factors in Latin square designs]
- 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.