## an infinite regress of hierarchical priors

Posted in Statistics with tags , , , , on October 22, 2020 by xi'an

An interesting musing posted on X validated about the impact of perpetuating prior models on the parameters of closer priors till infinity. Using a hierarchy of exponential priors and an exponential sampling distribution. If the (temporary) top prior at level d is Exp(1), the marginal distribution of the exponential sample corresponds to a ratio of two independent products of Exp(1) random variables

$X= \frac{\epsilon_{2\lfloor d/2 \rfloor}\cdots \epsilon_0}{\epsilon_{2\lfloor (d-1)/2 \rfloor+1}\cdots \epsilon_1}$

And both terms converge almost surely to zero with d (by Kakutani’s product martingale theorem). Thus ending up in an indeterminate ratio. Hierarchy has to stop somewhere! (Or, assuming an expectation of one everywhere, the variability at each level has to decrease fast enough.)

## Denver snapshot [jatp]

Posted in pictures, Travel, Wines with tags , , , , , , , , , on July 28, 2019 by xi'an

## ultimum optimum prior

Posted in pictures, Travel, Wines with tags , , , , , , on May 8, 2016 by xi'an

## Trip to Louvain (and back)

Posted in Kids, pictures, Running, Statistics, Travel, University life, Wines with tags , , , , , , , , , , on October 24, 2015 by xi'an

Apart from the minor initial inconvenience that I missed my train to Brussels thanks to the SNCF train company dysfunctional automata [but managed to switch to one half-an-hour later], my Belgian trip to Louvain-la-Neuve was quite enjoyable! I met with several local faculty [UCL] members I had not seen for several years, I gave my talk for the World Statistics Day in front of a large audience, maybe not the most appropriate talk for that day since it was somewhat skeptical about the nature of statistical tests, I got sharp questions, comments, and suggestions on the mixture approach to testing [incl. a challenging one about the Bernoulli B(p) case], I had a superb and animated and friendly dinner in a local restaurant—where everyone kindly spoke French although I was the only native French speaker—, I met the next morning with two PhD students from KU Leuven (the “other” part of the former Leuven university, albeit in the Flemmish side of the border) about functional ABC and generalised Jeffreys priors, I had a few more interesting discussions, and I managed to grab a few bags of Belgian waffles in Brussels before heading home! (In case you wonder from the above pixture, the crowds in the pedestrian streets of Louvain-la-Neuve were not connected to my visit!, but to a student festival centred at beer a 24 hour bike relay that attracted around 50,000 students, for less than a hundred bikes!)

## beer factory

Posted in pictures, Travel, Wines with tags , , , , , on April 19, 2014 by xi'an