diff --git a/tests/unit_tests/test_hetGP.py b/tests/unit_tests/test_hetGP.py
index 427e714..c06560d 100644
--- a/tests/unit_tests/test_hetGP.py
+++ b/tests/unit_tests/test_hetGP.py
@@ -30,10 +30,10 @@ def test_fit():
     test_model = emulator(x=X, theta=np.array([0]), f=Y, method="hetGP")
     test_model.fit()
 
-    assert test_model._info["ll"] == reference_model["ll"]
-    assert test_model._info["theta"] == reference_model["theta"]
-    assert test_model._info["g"] == reference_model["g"]
-    assert test_model._info["beta0"] == reference_model["beta0"]
+    assert np.allclose(test_model._info["ll"], reference_model["ll"])
+    assert np.allclose(test_model._info["theta"], reference_model["theta"])
+    assert np.allclose(test_model._info["g"], reference_model["g"])
+    assert np.allclose(test_model._info["beta0"], reference_model["beta0"])
     assert np.allclose(test_model._info["Delta"], reference_model["Delta"])
     assert np.allclose(test_model._info["Lambda"], reference_model["Lambda"])
 
@@ -56,10 +56,10 @@ def test_matern():
     )
     test_model.fit()
 
-    assert test_model._info["ll"] == reference_model["ll"]
-    assert test_model._info["theta"] == reference_model["theta"]
-    assert test_model._info["g"] == reference_model["g"]
-    assert test_model._info["beta0"] == reference_model["beta0"]
+    assert np.allclose(test_model._info["ll"], reference_model["ll"])
+    assert np.allclose(test_model._info["theta"], reference_model["theta"])
+    assert np.allclose(test_model._info["g"], reference_model["g"])
+    assert np.allclose(test_model._info["beta0"], reference_model["beta0"])
     assert np.allclose(test_model._info["Delta"], reference_model["Delta"])
     assert np.allclose(test_model._info["Lambda"], reference_model["Lambda"])
 
@@ -114,10 +114,10 @@ def test_hetGP_update_kriging_believer():
     test_model.fit()
     test_model.update(Xnew)
 
-    assert test_model._info["ll"] == reference_model["ll"]
-    assert test_model._info["theta"] == reference_model["theta"]
-    assert test_model._info["g"] == reference_model["g"]
-    assert test_model._info["beta0"] == reference_model["beta0"]
+    assert np.allclose(test_model._info["ll"], reference_model["ll"])
+    assert np.allclose(test_model._info["theta"], reference_model["theta"])
+    assert np.allclose(test_model._info["g"], reference_model["g"])
+    assert np.allclose(test_model._info["beta0"], reference_model["beta0"])
 
 
 def test_hetGP_update():
@@ -132,16 +132,22 @@ def test_hetGP_update():
     test_model.fit()
     test_model.update(x=Xnew, Y=Ypred)
 
-    assert test_model._info["ll"] == reference_model["ll"]
-    assert test_model._info["theta"] == reference_model["theta"]
-    assert test_model._info["g"] == reference_model["g"]
-    assert test_model._info["beta0"] == reference_model["beta0"]
+    assert np.allclose(test_model._info["ll"], reference_model["ll"])
+    assert np.allclose(test_model._info["theta"], reference_model["theta"])
+    assert np.allclose(test_model._info["g"], reference_model["g"])
+    assert np.allclose(test_model._info["beta0"], reference_model["beta0"])
 
 
 def test_conversion_to_homGP():
     # should return homoskedastic GP
     X = np.linspace(0, 1, 20).reshape(-1, 1)
-    Y = X
+    rand = np.random.default_rng(2)
+    reps = rand.choice(len(X), size=len(X))
+    X = X[reps, :]
+    Y = np.sin(X).squeeze()
+    noise = 0.2 * rand.normal(size=Y.shape[0])
+    Y += noise
+    Y = Y.reshape(-1, 1)
     model = emulator(x=X, theta=np.array([0]), f=Y, method="hetGP")
     Xp = np.linspace(X.min(), X.max(), 100).reshape(-1, 1)
     preds = model.predict(Xp)
diff --git a/tests/unit_tests/test_homGP.py b/tests/unit_tests/test_homGP.py
index f5ce2d1..ca72d09 100644
--- a/tests/unit_tests/test_homGP.py
+++ b/tests/unit_tests/test_homGP.py
@@ -31,10 +31,10 @@ def test_fit():
     test_model = emulator(x=X, theta=np.array([0]), f=Y, method="homGP")
     test_model.fit()
 
-    assert test_model._info["ll"] == reference_model["ll"]
-    assert test_model._info["theta"] == reference_model["theta"]
-    assert test_model._info["g"] == reference_model["g"]
-    assert test_model._info["beta0"] == reference_model["beta0"]
+    assert np.allclose(test_model._info["ll"], reference_model["ll"])
+    assert np.allclose(test_model._info["theta"], reference_model["theta"])
+    assert np.allclose(test_model._info["g"], reference_model["g"])
+    assert np.allclose(test_model._info["beta0"], reference_model["beta0"])
 
 
 def test_predict():
@@ -93,10 +93,10 @@ def test_matern():
     )
     test_model.fit()
 
-    assert test_model._info["ll"] == reference_model["ll"]
-    assert test_model._info["theta"] == reference_model["theta"]
-    assert test_model._info["g"] == reference_model["g"]
-    assert test_model._info["beta0"] == reference_model["beta0"]
+    assert np.allclose(test_model._info["ll"], reference_model["ll"])
+    assert np.allclose(test_model._info["theta"], reference_model["theta"])
+    assert np.allclose(test_model._info["g"], reference_model["g"])
+    assert np.allclose(test_model._info["beta0"], reference_model["beta0"])
 
 
 def test_homGP_update_kriging_believer():
@@ -111,10 +111,10 @@ def test_homGP_update_kriging_believer():
     test_model.fit()
     test_model.update(Xnew)
 
-    assert test_model._info["ll"] == reference_model["ll"]
-    assert test_model._info["theta"] == reference_model["theta"]
-    assert test_model._info["g"] == reference_model["g"]
-    assert test_model._info["beta0"] == reference_model["beta0"]
+    assert np.allclose(test_model._info["ll"], reference_model["ll"])
+    assert np.allclose(test_model._info["theta"], reference_model["theta"])
+    assert np.allclose(test_model._info["g"], reference_model["g"])
+    assert np.allclose(test_model._info["beta0"], reference_model["beta0"])
 
 
 def test_homGP_update():
@@ -129,10 +129,10 @@ def test_homGP_update():
     test_model.fit()
     test_model.update(x=Xnew, Y=Ypred)
 
-    assert test_model._info["ll"] == reference_model["ll"]
-    assert test_model._info["theta"] == reference_model["theta"]
-    assert test_model._info["g"] == reference_model["g"]
-    assert test_model._info["beta0"] == reference_model["beta0"]
+    assert np.allclose(test_model._info["ll"], reference_model["ll"])
+    assert np.allclose(test_model._info["theta"], reference_model["theta"])
+    assert np.allclose(test_model._info["g"], reference_model["g"])
+    assert np.allclose(test_model._info["beta0"], reference_model["beta0"])
 
 
 if __name__ == "__main__":
diff --git a/tests/unit_tests/test_multihetGP.py b/tests/unit_tests/test_multihetGP.py
index 15ee070..61c9dbd 100644
--- a/tests/unit_tests/test_multihetGP.py
+++ b/tests/unit_tests/test_multihetGP.py
@@ -8,11 +8,12 @@
 from copy import deepcopy
 
 # create some noise 2D data
+np.random.seed(1)
 rng = np.random.default_rng(1)
 lhs = qmc.LatinHypercube(d=2, rng=rng)
 
 X = lhs.random(n=100)
-reps = rng.choice(len(X), size=100, replace=True)
+reps = rng.choice(len(X), size=5000, replace=True)
 X = X[reps,]
 # prediction grid
 Xp = lhs.random(n=100)
@@ -20,7 +21,7 @@
 Y[:, 0] = np.sin(X[:, 0])
 Y[:, 1] = np.cos(X[:, 1])
 # varying noise field
-noise = rng.normal(size=Y.shape) * np.exp(-(X**2))
+noise = rng.normal(size=Y.shape)
 noise *= 2
 
 Y += noise
@@ -41,7 +42,7 @@
 }
 NOISECONTROL = {"k_theta_g_bounds": (1, 100), "g_max": 1e2, "g_bounds": (1e-6, 1)}
 
-MAXIT = 100
+MAXIT = 200
 
 
 def test_fit():