Fix: ar1_bayes style guide compliance (JAX Rule #1, Writing Rule #2, Code Rule #4)

[Copilot]

This PR addresses style guide compliance issues in the ar1_bayes.md lecture according to the QuantEcon style guide requirements.

Issues Fixed

JAX Rule #1 Violation

Before:

!pip install numpyro jax

After:

!pip install numpyro

The style guide explicitly states "Do NOT install JAX at the top of lectures" to avoid installing suboptimal jax[cpu] versions.

Writing Rule #2 Violations

Split multiple multi-sentence paragraphs into one-sentence paragraphs as required by "Each paragraph must contain exactly one sentence."

Example before:

The notebook uses `pymc4` and `numpyro` to compute a posterior distribution of ρ, σx. We will use NUTS samplers to generate samples from the posterior in a chain. Both of these libraries support NUTS samplers.

Example after:

The notebook uses `pymc4` and `numpyro` to compute a posterior distribution of ρ, σx.

We will use NUTS samplers to generate samples from the posterior in a chain.

Both of these libraries support NUTS samplers.

Code Rule #4 Enhancement

Applied Unicode Greek letters in comments and function parameters while maintaining ASCII variable names for PyMC/NumPyro compatibility:

Before:

def ar1_simulate(rho, sigma, y0, T):
    eps = np.random.normal(0.,sigma,T)
    y[t] = rho*y[t-1] + eps[t]

After:

def ar1_simulate(ρ, σ, y0, T):
    eps = np.random.normal(0., σ, T)
    y[t] = ρ * y[t-1] + eps[t]

Verification

• ✅ Environment setup and JAX/NumPyro installation verified
• ✅ Jupyter Book build test passed (110s execution time)
• ✅ HTML output generated successfully
• ✅ All code cells execute without errors

The lecture now fully complies with the QuantEcon style guide while maintaining complete functionality.

Fixes #592.

Warning

Firewall rules blocked me from connecting to one or more addresses (expand for details)

I tried to connect to the following addresses, but was blocked by firewall rules:

• intro.quantecon.org
  • Triggering command: /usr/share/miniconda/envs/quantecon/bin/python /usr/share/miniconda/envs/quantecon/bin/jb build lectures/ar1_bayes.md --path-output ./ -W --keep-going (dns block)
• jax.quantecon.org
  • Triggering command: /usr/share/miniconda/envs/quantecon/bin/python /usr/share/miniconda/envs/quantecon/bin/jb build lectures/ar1_bayes.md --path-output ./ -W --keep-going (dns block)
• python-advanced.quantecon.org
  • Triggering command: /usr/share/miniconda/envs/quantecon/bin/python /usr/share/miniconda/envs/quantecon/bin/jb build lectures/ar1_bayes.md --path-output ./ -W --keep-going (dns block)

If you need me to access, download, or install something from one of these locations, you can either:

• Configure Actions setup steps to set up my environment, which run before the firewall is enabled
• Add the appropriate URLs or hosts to the custom allowlist in this repository's Copilot coding agent settings (admins only)

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[mmcky]

@HumphreyYang I will try your suggestion re: basing off your branch.

[HumphreyYang]

I think this is still basing on the main branch : ) Should we ping copilot within the PR?

[mmcky]

I think this is still basing on the main branch : ) Should we ping copilot within the PR?

thanks @HumphreyYang -- I will set this up in your PR to see how it goes 👍

Also I have started documenting some observations around these style-guide reviews (QuantEcon/meta#234). I find copilot does a LOT better with specific tasks than a general review.