diff --git a/examples/analytical_function/.ipynb_checkpoints/example_analytical_function-checkpoint.ipynb b/examples/analytical_function/.ipynb_checkpoints/example_analytical_function-checkpoint.ipynb
index 848932a6ff76756264309510e49881d54db655f5..e63948ddc4e636a1e0eef9834c706a40f5be6890 100644
--- a/examples/analytical_function/.ipynb_checkpoints/example_analytical_function-checkpoint.ipynb
+++ b/examples/analytical_function/.ipynb_checkpoints/example_analytical_function-checkpoint.ipynb
@@ -349,12 +349,12 @@
     "# inputParams = np.load('data/InputParameters_2.npy')\n",
     "\n",
     "# First parameter\n",
-    "# Inputs.addMarginals()\n",
+    "# Inputs.add_marginals()\n",
     "# Inputs.Marginals[0].name = '$X_1$'\n",
     "# Inputs.Marginals[0].input_data = inputParams[:, 0]\n",
     "\n",
     "# Second parameter\n",
-    "# Inputs.addMarginals()\n",
+    "# Inputs.add_marginals()\n",
     "# Inputs.Marginals[1].name = '$X_2$'\n",
     "# Inputs.Marginals[1].input_data = inputParams[:, 1]"
    ]
@@ -472,7 +472,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "Computing orth. polynomial coeffs: 100%|##########| 2/2 [00:03<00:00,  1.71s/it]"
+      "Computing orth. polynomial coeffs: 100%|##########| 2/2 [00:02<00:00,  1.42s/it]"
      ]
     },
     {
@@ -489,7 +489,8 @@
      "output_type": "stream",
      "text": [
       "\n",
-      "Running forward model : 100%|██████████| 100/100 [00:00<00:00, 7893.97it/s]\n"
+      "Running forward model : 100%|██████████| 100/100 [00:00<00:00, 6414.49it/s]\n",
+      "Fitting regression:   0%|          | 0/1 [00:00<?, ?it/s]"
      ]
     },
     {
@@ -505,7 +506,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "Fitting regression: 100%|██████████| 1/1 [00:05<00:00,  5.11s/it]"
+      "Fitting regression: 100%|██████████| 1/1 [00:04<00:00,  4.51s/it]"
      ]
     },
     {
@@ -579,10 +580,43 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 13,
    "id": "96e85fb9",
    "metadata": {},
    "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "   Time [s]        mean         std\n",
+      "0  0.000000  126.943408  170.920339\n",
+      "1  0.111111  126.941468  170.889593\n",
+      "2  0.222222  126.940664  170.880029\n",
+      "3  0.333333  126.940047  170.873950\n",
+      "4  0.444444  126.939527  170.869675\n",
+      "5  0.555556  126.939069  170.866553\n",
+      "6  0.666667  126.938655  170.864251\n",
+      "7  0.777778  126.938274  170.862569\n",
+      "8  0.888889  126.937919  170.861378\n",
+      "9  1.000000  126.937586  170.860589\n",
+      "\n",
+      ">>>>> Moments of Z <<<<<\n",
+      "\n",
+      "Index  |  Mean   |  Std. deviation\n",
+      "-----------------------------------\n",
+      "1  |  1.266e+02  |  1.705e+02\n",
+      "2  |  1.266e+02  |  1.705e+02\n",
+      "3  |  1.266e+02  |  1.705e+02\n",
+      "4  |  1.266e+02  |  1.705e+02\n",
+      "5  |  1.266e+02  |  1.705e+02\n",
+      "6  |  1.266e+02  |  1.705e+02\n",
+      "7  |  1.266e+02  |  1.705e+02\n",
+      "8  |  1.266e+02  |  1.705e+02\n",
+      "9  |  1.266e+02  |  1.705e+02\n",
+      "10  |  1.266e+02  |  1.705e+02\n",
+      "----------------------------------------\n"
+     ]
+    },
     {
      "data": {
       "text/html": [
@@ -597,10 +631,10 @@
        "        "
       ],
       "text/plain": [
-       "<IPython.lib.display.IFrame at 0x7fe078460ee0>"
+       "<IPython.lib.display.IFrame at 0x7f44a48ed670>"
       ]
      },
-     "execution_count": 12,
+     "execution_count": 13,
      "metadata": {},
      "output_type": "execute_result"
     },
@@ -616,7 +650,7 @@
    ],
    "source": [
     "# Compute the moments and compare with the Monte-Carlo reference\n",
-    "PostPCE.plotMoments()\n",
+    "PostPCE.plot_moments()\n",
     "# Show the pdf\n",
     "IFrame(\"./Outputs_PostProcessing_calib/Mean_Std_PCE.pdf\", width=900, height=600)"
    ]
@@ -639,7 +673,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 15,
    "id": "cfd42c02",
    "metadata": {},
    "outputs": [
@@ -647,7 +681,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "Running forward model valid: 100%|██████████| 3/3 [00:00<00:00, 15015.41it/s]\n"
+      "Running forward model valid: 100%|██████████| 3/3 [00:00<00:00, 3583.85it/s]\n"
      ]
     },
     {
@@ -664,10 +698,10 @@
        "        "
       ],
       "text/plain": [
-       "<IPython.lib.display.IFrame at 0x7fe0dc9e8ac0>"
+       "<IPython.lib.display.IFrame at 0x7f44a47a7bb0>"
       ]
      },
-     "execution_count": 13,
+     "execution_count": 15,
      "metadata": {},
      "output_type": "execute_result"
     },
@@ -683,7 +717,7 @@
    ],
    "source": [
     "# Plot to check validation visually.\n",
-    "PostPCE.validMetamodel(nValidSamples=3)\n",
+    "PostPCE.valid_metamodel(n_samples=3)\n",
     "# Show the pdf\n",
     "IFrame(\"./Outputs_PostProcessing_calib/Model_vs_PCEModel.pdf\", width=900, height=600)"
    ]
diff --git a/examples/analytical_function/example_analytical_function.ipynb b/examples/analytical_function/example_analytical_function.ipynb
index a1e1c0b1a413ad122b5ea3489eb3276b04134f10..e63948ddc4e636a1e0eef9834c706a40f5be6890 100644
--- a/examples/analytical_function/example_analytical_function.ipynb
+++ b/examples/analytical_function/example_analytical_function.ipynb
@@ -349,12 +349,12 @@
     "# inputParams = np.load('data/InputParameters_2.npy')\n",
     "\n",
     "# First parameter\n",
-    "# Inputs.addMarginals()\n",
+    "# Inputs.add_marginals()\n",
     "# Inputs.Marginals[0].name = '$X_1$'\n",
     "# Inputs.Marginals[0].input_data = inputParams[:, 0]\n",
     "\n",
     "# Second parameter\n",
-    "# Inputs.addMarginals()\n",
+    "# Inputs.add_marginals()\n",
     "# Inputs.Marginals[1].name = '$X_2$'\n",
     "# Inputs.Marginals[1].input_data = inputParams[:, 1]"
    ]
diff --git a/examples/analytical_function/AnalytFuncValid_Test.py b/examples/analytical_function/util/AnalytFuncValid_Test.py
similarity index 99%
rename from examples/analytical_function/AnalytFuncValid_Test.py
rename to examples/analytical_function/util/AnalytFuncValid_Test.py
index c10c9495c9ff42daaf6eebd8f3c131d47624784e..b172de0baf73399ad8a1180ab9e8cfe20b4fb7b8 100644
--- a/examples/analytical_function/AnalytFuncValid_Test.py
+++ b/examples/analytical_function/util/AnalytFuncValid_Test.py
@@ -73,7 +73,7 @@ if __name__ == "__main__":
     
     ndim = 2
     for i in range(ndim):
-        Inputs.addMarginals()
+        Inputs.add_marginals()
         Inputs.Marginals[i].Name = '$X_{%s}$'%(i+1)
         Inputs.Marginals[i].DistType = 'unif'
         Inputs.Marginals[i].Parameters =  [-5, 5]
diff --git a/examples/analytical_function/AnalyticFunc_Demo.py b/examples/analytical_function/util/AnalyticFunc_Demo.py
similarity index 100%
rename from examples/analytical_function/AnalyticFunc_Demo.py
rename to examples/analytical_function/util/AnalyticFunc_Demo.py
diff --git a/examples/analytical_function/dynamic_image.py b/examples/analytical_function/util/dynamic_image.py
similarity index 100%
rename from examples/analytical_function/dynamic_image.py
rename to examples/analytical_function/util/dynamic_image.py