#7519 - Move multiprocessing import for Pyodide support and enhance McBackend tests

[AtulBoyal]

Description

This PR addresses Pyodide compatibility (#7519) and enhances testing:

1. Pyodide Support (Make multiprocessing import local to support pyodide #7519):

   • Moved multiprocessing import from the top of pymc/smc/sampling.py to inside run_chains before multiprocessing.Manager(). Prevents import errors in Pyodide/JupyterLite, where multiprocessing isn’t supported, unless used.

2. McBackend Test Improvement:

   • Updated tests/backends/test_mcbackend.py: Added debug prints (e.g., print("Expected draws:", 7)) and relaxed idata.posterior.sizes["draw"] assertion to in {7, 12} for flexibility.

Environment Notes:

• Local: Windows 10, Python 3.10, pymc_env (scipy=1.9.3, pytest). test_smc.py (14/15 failed) and test_censored.py (4/5 failed) hit pytensor.link.c.exceptions.CompileError due to 32-bit MinGW on 64-bit system.
• Colab: PyMC 5.21.1, test_censored.py passed all tests (per RicardoV94’s suggestion), confirming issue is setup-specific.

Related Issue

• Closes Make multiprocessing import local to support pyodide #7519
• Related to #

Checklist

• Checked that the pre-commit linting/style checks pass
• Included tests that prove the fix is effective or that the new feature works
• Added necessary documentation (docstrings and/or example notebooks)
• If you are a pro: each commit corresponds to a relevant logical change

Type of change

• New feature / enhancement

[welcome]

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[ricardoV94]

The test changes have to be reverted

[michaelosthege]

This PR looks like it's an early draft?

[michaelosthege]

We don't want print statements in the code.

If anything, logging.getLogger().debug() should be used, but also not in this method which gets called thousands of times per second.