Category: Math/Programming

As my time at Budapest comes to a close, I can’t help but be reminded of the times during honor band in high school.

For three days, sixty other musicians and you gel together and make beautiful music for the sake of music. Friendships are made, and is inevitably short-lived with the nature of gathering students from all over the state. During the last rehearsal of one such honor band, the conductor said something quite profound to me. He told me to look around and know that this is the last time this group of people will be assembled. Consequently, that was also the last time that particular sound associated with the ensemble was made in history.

After the concert, the sound of the ensemble is forever lost to history.

I guess BSM, or any other camp for that matter,  is something like that. That group of people will never be together again, and that synergy of relationships will be gone after the program. But as the saying goes, it is better to have loved than not loved at all.

And so, another happy chapter comes to a close in my life.

Done with my internship! I’m in Montana right now.

This should be a well known methodology by now, but it seems to not be.

In statistical work, one frequently sees the expression where the absolute value means determinant of covariance matrix . With large covariances, the calculations can easily overflow, but usually the finally value is a reasonable finite number.

The covariance is key, as it allows us to compute a Cholesky decomposition of first, which is quite numerically stable. We will have two triangular matrices whose determinants are the products of their diagonals (proof left as an exercise to the reader). Taking the log of that will transform the product to a sum!

Thus where is the diagonals of the matrices. You’ll find that this will rarely overflow, and possibly (depending on how sophisticated the determinant calculation is) speed up the work!

I went to the National Gallery today to take a final look before I leave next week. This particular series of painting caught my eye, especially the one above.

It just seems to reflect the drastic kick of reality I’ve been ingesting. When I was little, dreams were so lofty, ideas so wild and thoughts run carelessly. Now, the future seems perilous at times… what if my next steps are wrong?

I’m still looking forward to the next year though…. but what lies after Cornell truly scares me.

I’m starting to write solutions for the Larson’s problem book on Github. It’s just a small project I would like to keep adding on to it as I progress through the book…

Link is here: https://github.com/runiteking1/larsons_solution

At work, I had to generate random data to run logistic regressions on. In one unusual case, the slice sampler was performing far worse than expected. The code was simple, and contained no mistake; we thought something incredibly bad had happened with the whole testing framework.

What ended up happening was that our data matrix was generated by a uniform distribution from 0 to 1, but the reference runs were generated from -.5 to .5. The parameters of the logistical regressions are both generated from -0.5 to 0.5.

The logistic regression is a special case of GLMs, implying that we have a linear predictor of . Theoretically, in both cases they should be centered at 0. Somehow, it’s (almost) always true that shifting away from the 0 will cause the condition number to shift larger.

Maybe a small proof will come later? But this seems to have to do with the eigenvalues of the sum of two randomly distributed matrix… which is not entirely trivial.

Work is so tough. I thought it’ll be pretty chill and have tons of time to relax at night. Nope… too tired to do other stuff.

I’ll be posting some statistics soon though!