[kalman] Update to JAX

[xuanguang-li]

This pull request makes updates to the kalman.md notebook, modernizing the codebase by switching from NumPy to JAX.

Key changes include:

• Replaced all numpy (np) operations with jax.numpy (jnp) and updated imports accordingly.
• Refactored the bivariate Gaussian plotting logic: replaced the custom bivariate_normal and gen_gaussian_plot_vals functions with a vectorized, JAX-based implementation using jax.vmap.
• Standardized the use of random seeds in simulations for reproducible results.
• Adding mystnb metadata blocks to each figure-generating code cell.
• Fixed minor typos and improved the clarity.

[github-actions]

📖 Netlify Preview Ready!

Preview URL: https://pr-611--sunny-cactus-210e3e.netlify.app (5be7a1f)

📚 Changed Lecture Pages: back_prop, bayes_nonconj, kalman, lqcontrol, mle, qr_decomp

[github-actions]

📖 Netlify Preview Ready!

Preview URL: https://pr-611--sunny-cactus-210e3e.netlify.app (b1629e8)

📚 Changed Lecture Pages: back_prop, bayes_nonconj, kalman, lqcontrol, mle, qr_decomp

[mmcky]

Thanks @xuanguang-li -- @HumphreyYang this is now ready for review.

[github-actions]

📖 Netlify Preview Ready!

Preview URL: https://pr-611--sunny-cactus-210e3e.netlify.app (533e30f)

📚 Changed Lecture Pages: back_prop, bayes_nonconj, kalman, lqcontrol, mle, qr_decomp

[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-611--sunny-cactus-210e3e.netlify.app/ currently returns 404.

Why previews are down (repo-wide findings)

1. This branch is stale — 193 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 ~193 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-611--sunny-cactus-210e3e.netlify.app/kalman.html

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This PR touches: kalman.md. Last CI build: success@2025-09-18. Branch: 193 commits behind main as of 2026-07-08.

[xuanguang-li]

@copilot resolve the merge conflicts in this pull request

[Copilot]

@copilot resolve the merge conflicts in this pull request

Resolved by merging origin/main into this branch and fixing the lectures/kalman.md conflicts. Commit: eeb3b74.