George H. W. Bush (2) vs. William Carlos Willams; Mel Brooks advances

All of yesterday’s comments favored Mr. Blazing Saddles. Jeff had a good statistics-themed comment:

Mel Brooks created Get Smart (along with Buck Henry), which suggests a number of seminar topics of interest to readers of this blog.

“Missed It By That Much: Why Predictive Models Don’t Always Pick the Winner”

“Sorry About That, Chief: Unconscious Researcher Biases”

“I Asked You Not to Tell Me That: How Not to Respond to Replication Failures”

And Jrc has the pithy summary:

Mel Brooks: EGOT

Chris Christie: GTFO

I’d rather see the guy who came up with the line, It’s good to be the king, than the guy who really was king—of New Jersey—and all he did with it was hog a beach.

As for today’s matchup . . . G. H. W. Bush is seeded #2 in the Magicians category but not because of any talent at performing magic; he’s just the second-most-famous person in that category. And William Carlos Williams is an unseeded Jerseyite. It’s your choice: you could get stories about the secret service, Iran-Contra, etc., or some modernist poetry. The winner will probably get wiped out in the second round, as he’ll have to face either David Sedaris or Stanislaw Ulam.

Again, the full bracket is here, and here are the rules:

We’re trying to pick the ultimate seminar speaker. I’m not asking for the most popular speaker, or the most relevant, or the best speaker, or the deepest, or even the coolest, but rather some combination of the above.

I’ll decide each day’s winner not based on a popular vote but based on the strength and amusingness of the arguments given by advocates on both sides. So give it your best!

Chris Christie (2) vs. Mel Brooks; Boris Karloff advances

We had some good arguments in favor of Karloff. If I had to choose just one, it would be from J Storrs Hall, who writes:

Well, the main problem with Anastasia is … she’s dead. However, we can be relatively certain that 31 or so pretenders would show up in her place. One of them might be Godunov.

Karloff is of course also dead. Yet one has faith that if we were to patch him back together and expose him to a little lightning, he would be good to go. All we’d need would be hooks, and some wire.

Today’s matchup is the #2 seed from New Jersey, a man once jocularly referred to as a possible future Secretary of Transportation, versus an unseeded wit. Who do you want to hear from? Sure, Bridgegate is old news—but the 2000-year-old-man, that’s even older news. Either one would have lots of stories, I’m sure.

Again, the full bracket is here, and here are the rules:

We’re trying to pick the ultimate seminar speaker. I’m not asking for the most popular speaker, or the most relevant, or the best speaker, or the deepest, or even the coolest, but rather some combination of the above.

I’ll decide each day’s winner not based on a popular vote but based on the strength and amusingness of the arguments given by advocates on both sides. So give it your best!

Boris Karloff (3) vs. Anastasia Romanoff; Lance Armstrong advances

I’m still feeling bad about my ruling the other day. . . . I mean, sure, Robin Williams doing Elmer Fudd doing Bruce Springsteen was amazing, but Veronica Geng—she was one of a kind.

Anyway, yesterday’s winner is another dark horse. There’s little doubt in my mind that Bobby Fischer, if in a good mood, could give a much more interesting talk than Lance Armstrong, but then there was this argument from Diana:

Zbicyclist gave such a strong argument for him that zchessplayer appeared out of nowhere—a testament to the generative potential of an Armstrong seminar.

You’ll have to read the whole thread to see where she was coming from here.

Also, Lance has his own statistical principle.

Today we have a battle of two people whose names end in f: the original Frankenstein and the original lost princess. Check out Karloff’s wikipedia entry, where you’ll learn a few of interesting things: he was related to an English diplomat, he was part-Indian, and he wasn’t actually named Karloff. Anastasia you know all about, I’m sure.

Again, the full bracket is here, and here are the rules:

We’re trying to pick the ultimate seminar speaker. I’m not asking for the most popular speaker, or the most relevant, or the best speaker, or the deepest, or even the coolest, but rather some combination of the above.

I’ll decide each day’s winner not based on a popular vote but based on the strength and amusingness of the arguments given by advocates on both sides. So give it your best!

Bobby Fischer (4) vs. Lance Armstrong; Riad Sattouf advances

Our best argument from the last one comes from Bobbie:

I used to believe that Euler could draw circles around anyone but after some investigation I now believe that Sattouf could draw anything around anyone (and write about it beautifully as well).

And today we have a battle of two GOATs, with Fischer seeded fourth and Armstrong unseeded. I have a horrible feeling that either one would come off as a whiny victim, with Bobby complaining about how the Russians conspired against him, and Armstrong complaining about all those damn reporters. But, hey, they’re both GOATs, so there’s that!

Again, the full bracket is here, and here are the rules:

We’re trying to pick the ultimate seminar speaker. I’m not asking for the most popular speaker, or the most relevant, or the best speaker, or the deepest, or even the coolest, but rather some combination of the above.

I’ll decide each day’s winner not based on a popular vote but based on the strength and amusingness of the arguments given by advocates on both sides. So give it your best!

Transforming parameters in a simple time-series model; debugging the Jacobian

So. This one is pretty simple. But the general idea could be useful to some of you. So here goes.

We were fitting a model with an autocorrelation parameter, rho, which was constrained to be between 0 and 1. The model looks like this:

eta_t ~ normal(rho*eta_{t-1}, sigma_res), for t = 2, 3, ... T

To make this work out, you need the following marginal distribution for the first element in the series:

eta_1 ~ normal(0, sigma_res/sqrt(1 - rho^2)).

In case you’re wondering, eta is a vector of latent parameters deep inside the model. In addition to these autocorrelated error terms, the model also has linear predictors, independent errors, and all sorts of other things. But here we’re focusing on the etas.

It’s easy enough to write the above model in Stan, either by computing the T x T covariance matrix and using the multivariate normal, or by simply building up the distribution one step at a time, as above, which is how we did it.

When fitting the model there was some slow mixing, and we decided it could work better to reparameterize in terms of the marginal variance rather than the residual variance.

Thus, we defined:

sigma = sigma_res/sqrt(1 - rho^2)

And then the above model became:

eta_1 ~ normal(0, sigma)
eta_t ~ normal(rho*eta_{t-1}, sigma*sqrt(1 - rho^2)), for t = 2, 3, ... T

But then there were also issues with rho, having to do with posterior mass piling up near rho = 1. This is a situation that experienced time-series modelers will be familiar with, the so-called unit root problem, that time series often seem to want to be nonstationary. This sort of data issue should be respected, and it typically is a sign that the model needs more structure, for example long-term trends. Here, though, we wanted first to deal with awkward nonlinearity in the posterior dependence of rho and sigma, and we decided to reparameterize as follows:

xi = 1/(1 - rho^2)

When rho ranges from 0 to 1, xi varies from 1 to infinity. So now we don’t have to worry about the density piling up at the boundary.

So, in Stan:

parameters { real xi; real sigma; vector[T] eta;
}
transformed parameters { real rho; vector[T] M; vector[T] S; rho = sqrt(1 - 1/xi); M[1] = 0; S[1] = sigma; for (t in 2:T){ M[t] = rho*eta[t-1] S[t] = sigma*sqrt(1 - square(rho)); }
}
model { eta ~ normal(M, S);
}

There are various ways the code could be cleaner, especially with future language improvements. For example, I’d like M and S to not have to be named variables; instead they could be attributes of eta in some way.

But that discussion is for another time.

For now, let’s continue with this model. For computational reasons, it is convenient for xi, not rho, to be the parameter in the Stan model. But suppose we want to put a prior on the scale of rho. For example, the model above has an implicit flat prior on xi, but that implies a big mass on high values, as xi is unconstrained on the high end.

To put a flat prior on rho, when the above model is parameterized in terms of xi, we need to add the log Jacobian to the log posterior density, or target function in Stan.

The Jacobian is the absolute value of the derivative of the transformation:

J = |d(xi)/d(rho)| = 2*rho/(1-rho^2)^2

But I always get confused which direction to include the Jacobian, also I’m always worried that I get my algebra wrong.

So I write a little test program, “transformation_test.stan”:

parameters { real xi;
}
transformed parameters { real rho; rho = sqrt(1 - 1/xi);
}
model { target += log(rho) - 2*log(1 - square(rho));
}

And then I run this R script:

library("rstan")
options(mc.cores = parallel::detectCores())
rstan_options(auto_write = TRUE) fit <- stan("transformation_test.stan")
print(fit)

And here's what we get:

Inference for Stan model: transformation_test.
4 chains, each with iter=2000; warmup=1000; thin=1; post-warmup draws per chain=1000, total post-warmup draws=4000. mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
xi 1.076634e+16 2.917436e+14 4.410165e+15 3.446772e+15 6.921461e+15 1.086366e+16 1.463243e+16 1.765822e+16 229 1.03
rho 1.000000e+00 0.000000e+00 0.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 749 1.00
lp__ 1.088500e+02 4.000000e-02 6.900000e-01 1.064800e+02 1.085600e+02 1.090100e+02 1.093100e+02 1.095000e+02 338 1.02

Damn! I guess I did the Jacobian in the wrong direction.

Let's try again:

parameters { real xi;
}
transformed parameters { real rho; rho = sqrt(1 - 1/xi);
}
model { target += - log(rho) + 2*log(1 - square(rho));
}

And now:

 mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
xi 6.33 2.48 93.92 1.00 1.07 1.36 2.25 17.34 1430 1
rho 0.50 0.01 0.29 0.02 0.26 0.51 0.75 0.97 1358 1
lp__ -1.60 0.03 0.91 -4.23 -1.83 -1.25 -1.02 -0.96 712 1

Yesssss! It works. rho has a uniform distribution, which was our goal.

The whole procedure, including several debugging steps not shown here, took about 10 minutes. (In contrast, it took half hour to write all this up.)

OK, we've succeeded in implementing the trivial. So what?

I'm not claiming this is some great accomplishment. Rather, this is the sort of thing we need to do sometimes. And so it's good to have a way to check our work.

Now that we've succeeded in the reparameterization, we can add a prior on rho directly. For example, if we want normal(0.7, 0.2), we just add it to the model block:

 rho ~ normal(0.7, 0.2);

Or, equivalently:

 target += normal(rho | 0.7, 0.2);

In either case, the constraint to the range [0, 1] is implicit, having already been achieved in the declaration step.

And now we can move on and continue with the rest of our modeling.

Riad Sattouf (1) vs Leonhard Euler; Springsteen advances

I really wanted to go with Geng, partly because I’m a big fan of hers and partly because of Dzhaughn’s Geng-tribute recommendation:

In the way that many search their memories for significant aromas when they read Proust, re-reading Geng led me to recollect my youth in Speech Club, of weekends of interpretive readings and arguments about Mr. Reagan.

But then I continued to read Dzhaughn’s comment and came to this link. And now all I want, more than anything in the world, is to see Bruce do Robin doing Elmer doing Bruce.

And today we begin the second half of the bracket, with a match between the top seed in the “People whose name ends with f” category and an unseeded mathematician. The Mathematicians category is deep, though, and even today’s unseeded entry is one of the all-time greats.

Personally, I’m rooting for Sattouf. The guy is just brilliant, both his drawing and his storytelling. Indeed, the whole category of “People whose names end in f” exists entirely because I wanted an excuse to put Sattouf into this competition. But if you can put in a good argument for the King of Imaginary Numbers, he could squeak through. Your best bet might be something connected to those seven bridges. Power series are cool too, but maybe too sophisticated for the seminar audience.

Again, the full bracket is here, and here are the rules:

We’re trying to pick the ultimate seminar speaker. I’m not asking for the most popular speaker, or the most relevant, or the best speaker, or the deepest, or even the coolest, but rather some combination of the above.

I’ll decide each day’s winner not based on a popular vote but based on the strength and amusingness of the arguments given by advocates on both sides. So give it your best!

Bruce Springsteen (1) vs. Veronica Geng; Monty Python advances

Yesterday’s contest wasn’t particularly close, as it pitted a boring guy who got lucky with one famous book, vs. some very entertaining wits. I saw Life of Brian when it came out, and I think I laughed harder at that spaceship scene than any other time in my life. In any case, Ethan brings it home with the comment, “I want to hear Monty Python riff on pystan,” and Dzhaughn seals it with, “How many at Hormel owe their terrible disgusting jobs to this comedy troupe? Canned meat was dead in the water. Literally. But now “Spam” is on everyone’s lips. . . .” And this, from Tom: “There is the opportunity here for a seminar ending with a hall full of people singing ‘Always look on the bright side . . .’ It is that or listen to someone whose name ends in F.” f, actually, as we’re not shouting here. Whatever.

Today we conclude the first half of the draw with the top seeded person from New Jersey, against another person from our Wits category. Unseeded or not, Veronica Geng was very witty. The Boss would pull in the crowds, but maybe Geng works better for a university audience. What do you all think?

Again, the full bracket is here, and here are the rules:

We’re trying to pick the ultimate seminar speaker. I’m not asking for the most popular speaker, or the most relevant, or the best speaker, or the deepest, or even the coolest, but rather some combination of the above.

I’ll decide each day’s winner not based on a popular vote but based on the strength and amusingness of the arguments given by advocates on both sides. So give it your best!

Darrell Huff (4) vs. Monty Python; Frank Sinatra advances

In yesterday’s battle of the Jerseys, Jonathan offered this comment:

Sinatra is an anagram of both artisan and tsarina. Apgar has no English anagram. Virginia is from New Jersey. Sounds confusing.

And then we got this from Dzhaughn:

I got as far as “Nancy’s ancestor,” and then a Youtube clip of Joey Bishop told me, pal, stop he’s a legend, he don’t need no backronym from you or anybody. He don’t need no google doodle, although it would have been a respectful gesture on his 100th birthday, but nevermind. He’s a legend, and he’s against someone who puts people to sleep. Professionally.

Good point. As much as I’d love to see Apgar, we can’t have a seminar speaker who specializes in putting people to sleep. So it will be Frank facing Julia in the second round.

Today, we have the #4 seed in the “People whose name ends in f” category, vs. an unseeded entry in the Wits category. (Yes, Monty Python is an amazing group, but the Wits category is a tough one; seedings are hard to come by when you’re competing with the likes of Oscar Wilde and Dorothy Parker.)

Darrell Huff is a bit of a legend in statistics, or used to be, based on his incredibly successful book from 1954, How to Lie with Statistics. But the guy didn’t really understand statistics; he was a journalist who wrote that one book and then went on to other things, most notoriously working on a book, How to Lie with Smoking Statistics, which was paid for by the cigarette industry but was never completed, or at least never published. Huff could talk about how to lie with statistics firsthand—but I suspect his knowledge of statistics was simplistic enough that he might not have even known what he was doing.

As for Monty Python: You know who they are. I have nothing to add on that account.

Again, the full bracket is here, and here are the rules:

We’re trying to pick the ultimate seminar speaker. I’m not asking for the most popular speaker, or the most relevant, or the best speaker, or the deepest, or even the coolest, but rather some combination of the above.

I’ll decide each day’s winner not based on a popular vote but based on the strength and amusingness of the arguments given by advocates on both sides. So give it your best!

Frank Sinatra (3) vs. Virginia Apgar; Julia Child advances

My favorite comment from yesterday came from Ethan, who picked up on the public TV/radio connection and rated our two candidate speakers on their fundraising abilities. Very appropriate for the university—I find myself spending more and more time raising money for Stan, myself. A few commenters picked up on Child’s military experience. I like the whole shark repellent thing, as it connects to the whole “shark attacks determine elections” story. Also, Jeff points out that “a Julia win would open at least the possibility of a Wilde-Child semifinal,” and Diana brings up the tantalizing possibility that Julia Grownup would show up. That would be cool. I looked up Julia Grownup and it turns out she was on Second City too!

As for today’s noontime matchup . . . What can I say? New Jersey’s an amazing place. Hoboken’s own Frank Sinatra is only the #3 seed of our entries from that state, and he’s pitted against Virginia Apgar, an unseeded Jerseyite. Who do you want to invite for our seminar: the Chairman of the Board, or a pioneering doctor who’s a familiar name to all parents of newborns?

Here’s an intriguing twist: I looked up Apgar on wikipedia and learned that she came from a musical family! Meanwhile, Frank Sinatra had friends who put a lot of people in the hospital. So lots of overlap here.

You can evaluate the two candidates on their own merits, or based on who has a better chance of besting Julia Child in round 2.

Again, the full bracket is here, and here are the rules:

We’re trying to pick the ultimate seminar speaker. I’m not asking for the most popular speaker, or the most relevant, or the best speaker, or the deepest, or even the coolest, but rather some combination of the above.

I’ll decide each day’s winner not based on a popular vote but based on the strength and amusingness of the arguments given by advocates on both sides. So give it your best!

Julia Child (2) vs. Ira Glass; Dorothy Parker advances

Yesterday we got this argument from Manuel in favor of Biles:

After suffering so many bad gymnastics (mathematical, logical, statistical, you name it) at seminars, to have some performed by a true champion would be a welcome change.

But Parker takes it away, based on this formidable contribution of Dzhaughn:

Things I Have Learned From the Contest So Far:
(Cf. “Resume” by Dorothy Parker)

Thorpe’s 1/8th hashtag
Babe’s just a champ
Oscar is all Gray
Hotdogs cause cramp
Serena’s a whiner
Erdos sylvan
Jeff’s gone ballistic
I might as well win.

Today’s contest features the second seed in the Creative Eaters category against an unseeded magician. (Regular listeners to This American Life will recall that Glass did magic shows when he was about 12 years old, I think it was.) Both have lots of experience performing in front of an audience. So what’ll it be? Public TV or public radio? In either case, the winner will be facing someone from New Jersey in the second round.

Again, the full bracket is here, and here are the rules:

We’re trying to pick the ultimate seminar speaker. I’m not asking for the most popular speaker, or the most relevant, or the best speaker, or the deepest, or even the coolest, but rather some combination of the above.

I’ll decide each day’s winner not based on a popular vote but based on the strength and amusingness of the arguments given by advocates on both sides. So give it your best!