Lubos is a brand of full oh shit that I did not know existed pre-internet days.

]]>Yuling:

That reminds me . . . redundant parameter can work fine in Gibbs and Metropolis (as in my paper with David van Dyk) but fail in HMC. Which is funny, because HMC is typically much faster than Gibbs or Metropolis. It’s just that HMC is a global method and, in some way, takes the joint posterior density “literally,” whereas Gibbs and Metropolis are, in different ways, local methods and don’t care if the joint density is improper. It’s one of these “What you don’t know won’t hurt you” situations.

]]>See

https://motls.blogspot.com/2011/07/why-is-sum-of-integers-equal-to-112.html

https://motls.blogspot.com/2014/01/sum-of-integers-and-oversold-common.html

The above reference even states:

The value −1/12 is really the right one and the rightness may be experimentally verified (using the Casimir effect).

https://terrytao.wordpress.com/2010/04/10/the-euler-maclaurin-formula-bernoulli-numbers-the-zeta-function-and-real-variable-analytic-continuation/

http://math.ucr.edu/home/baez/qg-winter2004/zeta.pdf

The question is really “How do we assign meaning to such an expression?” See the quote at the end of

https://slate.com/technology/2014/01/follow-up-the-infinite-series-and-the-mind-blowing-result.html.

Bob

]]>In terms of statistics, such embedding seems to work almost always fine– redundant parameter in Gibbs sampling, simulated tempering, continuous model expansion, etc. But in principle, I suspect we can have similar discontinuity paradox too. (e.g., what if there is a phase-transition at exactly temperature 0 in simulated tempering? )

]]>It didn’t even change the font when I tried the pre tag.

]]>if(TRUE){

print(“hello”)

}

Anon:

In html, use the “pre” tag for code.

]]>https://en.wikipedia.org/wiki/Basel_problem

If mathjax works here this is what a properly formatted solution looks like:

$$

\sum_{n=0}^\infty \frac{1}{n^2} = \frac{\pi^2}{6}

$$

(if I made no mistakes in the $\LaTeX$ since one can’t edit posts).

]]>It would be very useful to be able to post multi line code that preserves indentation as well. Last time I tried the code tag it didnt work right:

if(TRUE){

print("hello")

}

MathJax is enabled. Nothing to learn other than that

$latex e^x$

renders as

$latex e^x$

But somebody needs to *turn it on in comments*. I’ll add a p.s. to the post to show how it works there.

Zad:

Yes, we do have that feature on the blog. I’m just too lazy to learn it, and it’s very rare that it comes up. Bob Carpenter uses the feature sometimes in his posts.

]]>+1

]]>Might make a difference because it’ll be hard for some blog readers to read what you’re writing. I write and read in LaTeX, so not really an issue for me, but I remembered being overwhelmed when seeing scripts like that when I had no idea what LaTeX even was

]]>the same mistake as Gelman’s generating function attempt.

(I had misremembered the solution I read way back when.)

You have to think of 1/n^2 as the *square* of

a Fourier series coefficient 1/n.

Then you figure out that sin(nx)/n

converges to a piecewise polynomial function.

Then you integrate the *square* of that function. ]]>

In this case, sum_{n=1}^{infinity} 1/n^2 is the value of

the Fourier series sum_{n=1}^{infinity} cos(nx)/n^2 at x=0.

Now make an educated (or lucky) guess: this Fourier series converges

to a locally polynomial function. Then work out which polynomial. ]]>

Sounds like how Fisher should the hard question a good summary – good for what? – with sufficiency.

From https://phaneron0.files.wordpress.com/2015/08/thesisreprint.pdf

Fisher in a 1935 paper read at the Royal Statistical Society. In discussing overcoming the preliminary difficulty of multiple

criteria for judging estimates “better for what?” he argued Whatever other purpose our estimate may be wanted for, we may require at least that it shall be fit to use, in conjunction with the results drawn from other samples of a like kind, as a basis for making an improved estimate. On this basis, in fact, our enquiry becomes self contained, and capable of developing its own appropriate criteria, without

reference to extraneous or ulterior considerations. … where the real problem of finite samples is considered, the requirement that our

estimates from these samples may be wanted as materials for a subsequent process of estimation [combined somehow with results drawn from samples of a like e kind?] is found to supply the unequivocal criteria required.