LLM-generated Stan case study on Galielo’s inclined plane experiment

This post is from Bob. I’ve been planning for at least a couple years to generate a case study around Galielo’s use of an inclined plane instrumented with water clocks to estimate the terrestrial gravitational constant. Here are some photographs of a replica in the Museo Galileo (click to blow them up). And here’s a video simulation of the experiment. We replace his clever pendulum apparatus explained in the video and the web page with simple Bayesian statistics so we can actually estimate the gravitational constant. The case study Here is a draft. Bob Carpenter. 2026. Estimating g from Galileo’s Water Clock: A scientific Bayesian inverse problem with Stan and CmdStanPy. GitHub. I list myself as the author here because I’m responsible and AIs can’t own copyright in the U.S., but 100% of the text and code was written by Claude Opus 4.8 (medium or high effort, but I can’t recall which). I used the desktop app, which doesn’t allow sharing, but you can try it yourself. The prompt Here’s…