bayes_nonconj: declare the truncated log-normal prior's (0, 1] support (numpyro 0.22)

[mmcky]

Since numpyro 0.22.0 (PyPI, 2026-09-18), bayes_nonconj fails wherever it is executed. The lecture installs numpyro unpinned, and 0.22.0 validates distribution arguments by default. truncated_lognormal() returned a TransformedDistribution(TruncatedNormal(high=0), ExpTransform()), whose declared support is (0, ∞) rather than (0, 1], so NUTS initialisation could propose θ > 1 and dist.Binomial(n, θ) raised ValueError: BinomialProbs distribution got invalid probs parameter. at mcmc_ln = run_nuts(binomial_model, prior_ln, k, n).

This already broke this repo's weekly cache build: run 35557364600 (2026-09-21, the first after the release) failed with bayes_nonconj as the only failing notebook. The 2026-09-22 publish still went green, presumably because it reused an earlier execution cache.

Change. truncated_lognormal() now returns a small TransformedDistribution subclass whose support is constraints.interval(0.0, 1.0), with a two-line comment saying why. Nothing else in the lecture changes. Two alternatives were ruled out (details in the linked comment): init_strategy=init_to_median gets NUTS through but the later SVI/AutoNormal cell fails with the same error, and pinning numpyro<0.22 in the !pip install cell would downgrade the shared environment for every later numpyro lecture in the build.

Verification. I executed the whole lecture (jupytext → jupyter nbconvert --execute) in clean Python 3.13 venvs with jax 0.11.2 and arviz 1.3.0:

Lecture	numpyro	Result
main (unfixed)	0.22.0	fails: BinomialProbs … invalid probs parameter at run_nuts(…, prior_ln, …)
main (unfixed)	0.21.0	17/17 cells, 8 figures
this PR	0.21.0	17/17 cells, 8 figures, ~18 s
this PR	0.22.0	17/17 cells, 8 figures, ~18 s

The log-normal posterior is statistically unchanged: mcmc_ln θ mean 0.4506 / sd 0.101 before, 0.4532 / sd 0.102 after (sampling noise from the new unconstrained parameterisation), with no draw above 1. The fixed version gives identical draws under 0.21.0 and 0.22.0. The PR preview should show the posterior plots rendered.

Found while diagnosing QuantEcon/actions#159; full write-up in this comment. This PR leaves the lecture's build time alone: that is QuantEcon/actions#196.

Assisted-by: Claude Code (Claude Opus 5.5)

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[Copilot]

Copilot review overview

🟢 Approval recommended

The change is minimal, localized to the prior construction, and directly addresses the reported NumPyro 0.22 support/initialization failure mode.

Review effort: Lite
Findings: None

What changed in this PR

This PR fixes execution failures in the bayes_nonconj lecture under NumPyro ≥ 0.22 by making the truncated log-normal prior correctly declare unit-interval support, so inference initialization doesn’t propose invalid binomial probabilities.

Changes:

• Update truncated_lognormal() to return a small TransformedDistribution subclass that sets support = constraints.interval(0.0, 1.0).
• Add a brief inline comment explaining why the explicit support declaration is needed.

File	Description
lectures/​bayes_nonconj.md	Ensures the truncated log-normal prior advertises unit-interval support so NUTS/VI initialization won’t produce θ > 1 under NumPyro 0.22 validation.

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[mmcky]

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