[likelihood_bayes] Update lecture according to the style guide

[HumphreyYang]

This PR corrects some notations and update likelihood_bayes according to the style guide.

[github-actions]

📖 Netlify Preview Ready!

Preview URL: https://pr-651--sunny-cactus-210e3e.netlify.app (af66993)

📚 Changed Lecture Pages: likelihood_bayes

[github-actions]

📖 Netlify Preview Ready!

Preview URL: https://pr-651--sunny-cactus-210e3e.netlify.app (d0f515f)

📚 Changed Lecture Pages: likelihood_bayes, likelihood_ratio_process, likelihood_ratio_process_2

[jstac]

🤖 Status note for a future session — from a maintainer investigation on 2026-07-08 into why open-PR previews 404. Context only, not instructions.

Netlify preview: https://pr-651--sunny-cactus-210e3e.netlify.app/ currently returns 404.

Why previews are down (repo-wide findings)

1. This branch is stale — 164 commits behind main. A preview build compiles the whole site from this branch. This branch's lectures/house_auction.md still has unpinned !pip install prettytable, which now breaks on a wcwidth incompatibility. main fixed this on 2026-06-28 by pinning prettytable<3.18 (#939). This alone fails any rebuild of this branch until it's updated to main.

2. The arviz failure was a red herring — do NOT pin arviz or rewrite plotting. A 2026-07-07 rebuild also failed in ar1_bayes/ar1_turningpts with an arviz_plots figsize ValueError. That was a transient bug in an intermediate arviz-plots 1.x release, already fixed in arviz 1.2.0. Verified locally on a clean latest-stack venv: the real az.plot_trace(trace) cell (pymc + numpyro InferenceData) runs green. The lectures use only 1.x-compatible arviz APIs (plot_trace, summary, from_numpyro, compare).

Recommended first step for this PR

Update this branch to main (merge or rebase — pulls in #939 plus ~164 other commits), then let CI rebuild. On today's latest libraries the site builds clean, so the preview should return. house_auction is the known blocker; updating also picks up other since-merged fixes — rebuild and address any remaining per-lecture failures. Verify with:

curl -sI https://pr-651--sunny-cactus-210e3e.netlify.app/likelihood_bayes.html

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This PR touches: likelihood_bayes.md, likelihood_ratio_process.md, likelihood_ratio_process_2.md. Last CI build: success@2025-10-29. Branch: 164 commits behind main as of 2026-07-08.