Run pre-commit and mypy on oldest supported Python version (#6969)

* Run pre-commit and mypy on oldest supported Python version

* Fix type hints invalid with Python 3.9

Author: ricardoV94

.github/workflows/pre-commit.yml

@@ -13,6 +13,8 @@ jobs:
     steps:
     - uses: actions/checkout@b4ffde65f46336ab88eb53be808477a3936bae11
     - uses: actions/setup-python@v4
+      with:
+        python-version: "3.9"  # Run pre-commit on oldest supported Python version
     - uses: pre-commit/action@v3.0.0
   mypy:
     runs-on: ubuntu-latest
@@ -50,7 +52,7 @@ jobs:
           activate-environment: pymc-test
           channel-priority: strict
           environment-file: conda-envs/environment-test.yml
-          python-version: 3.9
+          python-version: "3.9"  # Run pre-commit on oldest supported Python version
           use-mamba: true
           use-only-tar-bz2: false # IMPORTANT: This may break caching of conda packages! See https://github.com/conda-incubator/setup-miniconda/issues/267
       - name: Install-pymc and mypy dependencies

pymc/sampling/jax.py

@@ -184,7 +184,7 @@ def _device_put(input, device: str):
 def _postprocess_samples(
     jax_fn: Callable,
     raw_mcmc_samples: List[TensorVariable],
-    postprocessing_backend: Literal["cpu", "gpu"] | None = None,
+    postprocessing_backend: Optional[Literal["cpu", "gpu"]] = None,
     postprocessing_vectorize: Literal["vmap", "scan"] = "scan",
 ) -> List[TensorVariable]:
     if postprocessing_vectorize == "scan":
@@ -239,7 +239,7 @@ def _blackjax_stats_to_dict(sample_stats, potential_energy) -> Dict:
 def _get_log_likelihood(
     model: Model,
     samples,
-    backend: Literal["cpu", "gpu"] | None = None,
+    backend: Optional[Literal["cpu", "gpu"]] = None,
     postprocessing_vectorize: Literal["vmap", "scan"] = "scan",
 ) -> Dict:
     """Compute log-likelihood for all observations"""