Update heteroskedastic Gaussian process notebook

[ckrapu]

Updates the notebook on using a Gaussian process with heteroskedastic variance to conform to the style guide and run successfully on v5.

Updates the code to use PyTensor and includes some edits for minor grammar issues.

Relevant issues: #795 #169 #723

• Notebook follows style guide https://docs.pymc.io/en/latest/contributing/jupyter_style.html
• PR description contains a link to the relevant issue:
  • a tracker one for existing notebooks (tracker issues have the "tracker id" label)
  • or a proposal one for new notebooks
• Check the notebook is not excluded from any pre-commit check: https://github.com/pymc-devs/pymc-examples/blob/main/.pre-commit-config.yaml

Helpful links

• https://github.com/pymc-devs/pymc-examples/blob/main/CONTRIBUTING.md

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[ckrapu]

One note on the style - Instead of using idata.posterior.stack, I used .reshape(-1, len(...)). If this should be changed, let me know.

[ckrapu]

This PR passes the pre-commit checks on GitHub Actions when changing python-version: '3.13' in pre-commit.yml.

@OriolAbril, I was seeing the same precommit failures as you mentioned on #822. As best as I can tell, it's a compatibility issue between Python 3.14.2 and pyupgrade.

[aloctavodia]

using stack is more idiomatic. I have updated pyupgrade so pre-commit works again.

[ckrapu]

Thanks, @aloctavodia. The notebook uses .stack now and runs without issue.