diff --git a/docs/examples/oceanmodelling.py b/docs/examples/oceanmodelling.py
index 77f125b12..5d3490495 100644
--- a/docs/examples/oceanmodelling.py
+++ b/docs/examples/oceanmodelling.py
@@ -195,16 +195,14 @@ def dataset_3d(pos, vel):
 
 
 # %%
-
-
-@dataclass
 class VelocityKernel(gpx.kernels.AbstractKernel):
-    kernel0: gpx.kernels.AbstractKernel = field(
-        default_factory=lambda: gpx.kernels.RBF(active_dims=[0, 1])
-    )
-    kernel1: gpx.kernels.AbstractKernel = field(
-        default_factory=lambda: gpx.kernels.RBF(active_dims=[0, 1])
-    )
+    def __init__(
+        self,
+        kernel0: gpx.kernels.AbstractKernel = gpx.kernels.RBF(active_dims=[0, 1]),
+        kernel1: gpx.kernels.AbstractKernel = gpx.kernels.RBF(active_dims=[0, 1]),
+    ):
+        self.kernel0 = kernel0
+        self.kernel1 = kernel1
 
     def __call__(
         self, X: Float[Array, "1 D"], Xp: Float[Array, "1 D"]
diff --git a/docs/examples/yacht.py b/docs/examples/yacht.py
index b5d7fd0dc..c1d0958aa 100644
--- a/docs/examples/yacht.py
+++ b/docs/examples/yacht.py
@@ -31,6 +31,7 @@
 
 from jax import jit
 import jax.random as jr
+import jax.numpy as jnp
 from jaxtyping import install_import_hook
 import matplotlib as mpl
 import matplotlib.pyplot as plt
@@ -169,8 +170,8 @@
 n_train, n_covariates = scaled_Xtr.shape
 kernel = gpx.kernels.RBF(
     active_dims=list(range(n_covariates)),
-    variance=np.var(scaled_ytr),
-    lengthscale=0.1 * np.ones((n_covariates,)),
+    variance=jnp.var(scaled_ytr),
+    lengthscale=0.1 * jnp.ones((n_covariates,)),
 )
 meanf = gpx.mean_functions.Zero()
 prior = gpx.gps.Prior(mean_function=meanf, kernel=kernel)
@@ -188,14 +189,15 @@
 # %%
 training_data = gpx.Dataset(X=scaled_Xtr, y=scaled_ytr)
 
-negative_mll = jit(gpx.objectives.ConjugateMLL(negative=True))
-
 opt_posterior, history = gpx.fit_scipy(
     model=posterior,
-    objective=negative_mll,
+    # we use the negative mll as we are minimising
+    objective=lambda p, d: -gpx.objectives.conjugate_mll(p, d),
     train_data=training_data,
 )
 
+print(-gpx.objectives.conjugate_mll(opt_posterior, training_data))
+
 # %% [markdown]
 # ## Prediction
 #