AI and fundamental stats
In my upcoming introductory stat class I am planning to include "critical evaluation of AI analyses" as a core learning objective. Starting to explore how ChatGPT 4.0 handles some of my favorite questions and it turns out that it does rather well.
The Great Gatsby Curve
Greater income mobility is correlated with less income inequality. The opportunity for mathematical modeling comes in being able to study questions of causation of the correlation.
Asymptotic behavior of the heat equation in free space
I always appreciate self-contained efforts to summarize thinking on basic topics. In contrast to textbooks, which by necessity need to address a broad set of techniques, a deep dive on one familiar topic can reveal the strengths and weaknesses of various mathematical perspectives.
Bayesian consistency, or (again) lack thereof
In applied math, the model is almost always mis-specified, and so we have to ask “if the truth is complicated and I apply Bayesian procedures to my simplified model, what kind of mistakes am I likely (or not likely) to make?”
Wilks’ phenomenon, or lack thereof
I commonly find myself in a situation where I want to decide whether or not a certain mechanism is present in an applied problem.
Happy Solstice, to those who celebrate.
“And so it seems every year that the shortening of the days tracks with a shortening of spirit.”