docs: added code examples in potential class docstring

[Jocho-Smith]

This PR is inspired by #1763

In preparation of GSoC Project Idea 3 I investigated into the potential functions and wrote minimal examples to try them out.

Is it appreciated if we add these examples in the class docstrings? In the same way it appeared in #1534, this would enhance API references on the docs website.

Pre-commit hooks and fast tests passed

(sbi) schmidt@node-63:~/gsoc2026/sbi$ pre-commit run --all-files
ruff.....................................................................Passed
ruff-format..............................................................Passed
check for added large files..............................................Passed
check for merge conflicts................................................Passed
check toml...............................................................Passed
check yaml...............................................................Passed
fix end of files.........................................................Passed
mixed line ending........................................................Passed
trim trailing whitespace.................................................Passed

(update: I just realized I could have just run pytest -m "not slow and not gpu", there was no need for --bm)

(sbi) schmidt@node-63:~/gsoc2026/sbi$ pytest --bm
....................                                     [100%]
====================== mini SBIBM results ======================
Amortized inference:
          gaussian_linear  linear_mvg_2d     slcp     two_moons  
-----------------------------------------------------------------
FMPE{}         0.608           0.525        0.950       0.799    
NLE_A{}        0.565           0.570        0.888       0.637    
NPE_C{}        0.558           0.637        0.950       0.789    
NPSE{}         0.635           0.512        0.904       0.733    
NRE_B{}        0.605           0.514        0.954       0.812    
20 passed in 844.00s (0:14:04)

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 87.86%. Comparing base (3c60a97) to head (7445561).

Additional details and impacted files

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Flag	Coverage Δ
fast	82.72% <ø> (?)

Flags with carried forward coverage won't be shown. Click here to find out more.

Files with missing lines	Coverage Δ
...inference/potentials/likelihood_based_potential.py	82.10% <ø> (ø)
.../inference/potentials/posterior_based_potential.py	90.90% <ø> (ø)
sbi/inference/potentials/ratio_based_potential.py	100.00% <ø> (ø)

[Jocho-Smith]

I could also do that for the methods listed here: https://sbi.readthedocs.io/en/latest/api_reference/potentials.html

[dgedon]

I believe this is a very good start for the GSoC 2026 project 3 to get an overview. However, there are some issues:

• in the API reference we list the likelihood_estimator_based_potential function instead of the LikelihoodBasedPotential where your current examples are located. So they are never shown in the API reference
• more critical: the potentials are mostly used internally and have limited user-facing interaction. So examples have limited value
• With the re-design of the potential function, these examples would need a re-design as well.

Because of the second point, I think this PR is nice-to-have.

Changes that are necessary:

• add examples to the right location
• point out that the potentials can then be used for MCMC sampling, VI, ...