Archive for Normandy

learning optimal summary statistics

Posted in Books, pictures, Statistics with tags , , , , , , , , , on July 27, 2022 by xi'an

Despite the pursuit of the holy grail of sufficient statistics, most applications will have to settle for the weakest concept of optimal statistics.”Quiz #1: How does Bayes sufficiency [which preserves the posterior density] differ from sufficiency [which preserves the likelihood function]?

Quiz #2: How does Fisher-information sufficiency [which preserves the information matrix] differ from standard sufficiency [which preserves the likelihood function]?

Read a recent arXival by Till Hoffmann and Jukka-Pekka Onnela that I frankly found most puzzling… Maybe due to the Norman train where I was traveling being particularly noisy.

The argument in the paper is to find a summary statistic that minimises the [empirical] expected posterior entropy, which equivalently means minimising the expected Kullback-Leibler distance to the full posterior.  And maximizing the mutual information between parameters θ and summaries t(.). And maximizing the expected surprise. Which obviously requires breaking the sample into iid components and hence considering the gain brought by a specific transform of a single observation. The paper also contains a long comparison with other criteria for choosing summaries.

“Minimizing the posterior entropy would discard the sufficient statistic t such that the posterior is equal to the prior–we have not learned anything from the data.”

Furthermore, the expected aspect of the criterion takes us away from a proper Bayes analysis (and exhibits artifacts as the one above), which somehow makes me question the relevance of comparing entropies under different distributions. It took me a long while to realise that the collection of summaries was set by the user and quite limited. Like a neural network representation of the posterior mean. And the intractable posterior is further approximated by a closed-form function of the parameter θ and of the summary t(.). Using there a neural density estimator. Or a mixture density network.

35 years ago…

Posted in Books, Kids, Statistics, Travel, University life with tags , , , , , , , , on July 2, 2022 by xi'an

78 years ago

Posted in Statistics with tags , , , , , , , , , , on June 6, 2022 by xi'an

angelic visit to Mt St Michel

Posted in pictures, Travel with tags , , , , , , on May 24, 2022 by xi'an

the last duel [not a film review]

Posted in Books, Kids, pictures, Travel with tags , , , , , , , , , , , , , on September 23, 2021 by xi'an

The incoming film, The last duel, directed by Ridley Scott, is about one of the last trials by combat (ordalie) in France, in 1386 under the mad king Charles VI. Where the Norman knight Jehan de Carrouges fought a Norman squire, Jacques Le Gris, who stood accused of the rape of Marguerite de Carrouges, Jehan’s second wife. It is inspired from Eric Jager’s book on this story and I found it of some personal interest in that the original events take place in Normandy, near my wife’s hometown… Although the film was shot in completely different locations, including Ireland and the south of France! The rape story is presented there from three perspectives, as in Kurosawa’s (immense) Rashomon, but without the ambiguity of the later,

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