[likelihood_ratio_process_2.md] Update np.random → Generator API

[Chihiro2000GitHub]

Summary

This PR migrates legacy NumPy random API usage in likelihood_ratio_process_2.md as part of QuantEcon/meta#299.

All np.random.* draws are replaced with an explicit rng = np.random.default_rng().

Related PRs and issues

I checked for open PRs and issues related to this lecture. No open issue concerns it, and the only open PR that touches the file (#651, a likelihood_bayes style-guide PR) changes a single unrelated prose line — nothing overlaps with this migration.

Details

• In the main text, rng is defined once in the imports cell and reused in the later main-text cells.
• Each solution block (lr_ex4, lr_ex5, lr_ex6, lr_ex7) defines its own rng so the block stays self-contained.
• Replacements: np.random.beta(...) → rng.beta(...), and np.random.rand(N, T) → rng.random((N, T)) (note the shape tuple).
• No fixed seed is introduced, since the lecture did not seed before.

Numba notes. The two @jit(parallel=True) functions (compute_posterior_three_models, simulate_three_model_allocation) take pre-generated s_seq arrays as input and do not draw random numbers inside their prange loops, so no random draws occur inside the parallel loops.

The one jitted draw is in simulate (@jit), migrated by passing rng in as an explicit argument (w = rng.beta(a, b)). Note that simulate is not called anywhere in this lecture, so it is never compiled — the build therefore does not exercise that particular line. Flagging for reviewer judgment.

Hi @mmcky and @HumphreyYang, I'd be grateful if you could take a look when you have time.

[github-actions]

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📚 Changed Lectures

• likelihood_ratio_process_2

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