Just wanted to share some of my writing since my last update earlier this year.
I finished up my introduction to regression analyses from a probabilistic modeling perspective with two more case studies. First (Co)variations On A Theme introduces the foundational assumptions behind regression models (hint: they’re just curve fitting models). The two new case studies go into common models for those curves within certain neighborhoods, starting with lines in Taylor Regression Models and warped lines in General Taylor Models. In particular these last two pieces use the theory of Taylor approximation to understand why these might be useful models in so many applications and how to verify when they are useful in practice. By the end you’ll learn how to build meaningful prior models for logistic regression.
Beyond this regression suite I also put out:
Outwit, Outlast, Outmodel (Survival Modeling)
Some Ruminations on Containment Prior Modeling (Experimenting with a few nontraditional prior models)
Bridge Over Troubled Processes (Brownian Bridges)
https://betanalpha.github.io/assets/case_studies/conditional_probability.pdf (Preview of expanded introduction to conditional probability theory)
Markov Chain Monte Carlo Basics (Preview of expanded Markov chain Monte Carlo material)
As always you can find my writing at Writing - betanalpha.github.io as soon as each piece is released. If you’re interested in early access or supporting my work then consider supporting me on Patreon, Michael Betancourt is creating case studies for principled statistical analyses. | Patreon.