Yea, I shall return with the tide. - Khalil Gibran
Hello again! It’s been over a year since my last post, and I’ve spent every day of it aching to get back to posting! Not really though, I mostly spent it with my head between the pages Casella and Berger’s Statistical Inference. The first year of my Ph.D. has been… eventful. I was too busy trying to absorb all that I’d learned to keep up with this blog, so I figure now that I finally have some time again I should update this blog with what I’ve been learning and what my plans are for this blog in the future.
I’ve been learning a lot about Bayesian statistics in Austin. Turns out, it’s not all linear algebra! I’ve gotten super involved in Bayesian inference on graphical models, specifically pairwise Markov random fields. As part of that research, I studied a recent paper Sampling Algorithms for Discrete Markov Random Fields and Related Graphical Models (2021) by Alan Julian Izenman. I spent much of my summer working on implementations of the sampling algorithms reviews in that paper, and have more news about that to share in dedicated posts.
I also did some work on constrained nuclear norm maximization which took me down a rabbit hole that seems to have ended at subgradient methods. With good progress, you can expect posts about that in the future as well.
The last project on the desk right now is experimenting with Bayesian predictive resampling as in On Recursive Bayesian Predictive Distributions (2018) by P. Richard Hahn, Ryan Martin, and one of my very own professors Stephen G. Walker. I’ve only just begun this work but as I come to understand this kind of sampling scheme I’ll surely be trying to make some kind of overview or tutorial post because I think this can become an incredibly useful and popular method for Bayesian prediction.
Going forward, I hope to update this blog at least monthly, but having just moved out to Austin I’m still getting a handle on my routines here and might not be all that consistent. To push consistency, I plan on making some small personal or non-statistical posts every now and then between big project updates. I’ll probably disregard my previous posts, specifically what was going to be the “Generalizing Linear Models” series, because it’ll take enough time just to catch y’all up on my projects. So consider this a reboot!
I’m looking forward to sharing more with you all soon!
Thank you,
Blake