Fix Static check in Gaussian likelihood (#484)

* Fix passing Static obs_stddev to Gaussian likelihood

* Fix intro_to_kernels.py example

examples/intro_to_kernels.py

@@ -246,7 +246,7 @@ def forrester(x: Float[Array, "N"]) -> Float[Array, "N"]:  # noqa: F821
 prior = gpx.gps.Prior(mean_function=mean, kernel=kernel)
 
 likelihood = gpx.likelihoods.Gaussian(
-    num_datapoints=D.n, obs_stddev=PositiveReal(value=jnp.array(1e-3), tag="Static")
+    num_datapoints=D.n, obs_stdev=Static(jnp.array(1e-3))
 )  # Our function is noise-free, so we set the observation noise's standard deviation to a very small value
 
 no_opt_posterior = prior * likelihood

gpjax/likelihoods.py

@@ -28,7 +28,6 @@
     GHQuadratureIntegrator,
 )
 from gpjax.parameters import (
-    Parameter,
     PositiveReal,
     Static,
 )
@@ -152,10 +151,9 @@ def __init__(
                 likelihoods. Must be an instance of `AbstractIntegrator`. For the Gaussian likelihood, this defaults to
                 the `AnalyticalGaussianIntegrator`, as the expected log likelihood can be computed analytically.
         """
-        if isinstance(obs_stddev, Parameter):
-            self.obs_stddev = obs_stddev
-        else:
-            self.obs_stddev = PositiveReal(jnp.asarray(obs_stddev))
+        if not isinstance(obs_stddev, (PositiveReal, Static)):
+            obs_stddev = PositiveReal(jnp.asarray(obs_stddev))
+        self.obs_stddev = obs_stddev
 
         super().__init__(num_datapoints, integrator)