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.)

a fixation on food [U.S. airports survival guide]

Posted in Kids, Travel, Wines with tags , , , , , , , on January 30, 2016 by xi'an

In connection with the big snow storm of last weekend in the U.S. North-East, The New York Time published an airport survival guide that includes a comprehensive Best Dining section on each major airport. Sections that I find somewhat hilarious in turning what is just the thing to avoid (why would you need food before sitting in a plane for several hours?!) into a hype! Here are some particularly crunchy and savoury quotes (and a mention of the brewery that makes the famous Fat Tire!):

“Less healthy but perhaps more popular, Garrett Popcorn Shops, also in 2 and 3, specialize in the Garrett Mix, a blend of cheese and caramel popcorn.”

“At B Gates, Elway’s steakhouse is popular for its burger as well as Colorado-raised steaks, and New Belgium Hub serves microbrews from the Fort Collins brewer.”

“There is a strong Cuban accent in Miami’s airport restaurants, beginning with four Café Versailles, branches of the Little Havana landmark.”

“At its culinary rival, Terminal D, Bisoux will box your croque monsieurs and other bistro fare to go.”

(with the last one managing to stuff two French grammar mistakes in one line).