From 61a67c0af7ea040a065d399f1462842e1c2d8fd8 Mon Sep 17 00:00:00 2001
From: beckynevin <beckynevin@gmail.com>
Date: Fri, 20 Oct 2023 13:01:06 -0600
Subject: [PATCH] now have three dfs, hierarchical, unpooled and
 non-hierarchical (different ag value for each pendulum)

---
 notebooks/save_dataframe.ipynb | 884 +++++++++++++++++++++++++--------
 1 file changed, 689 insertions(+), 195 deletions(-)

diff --git a/notebooks/save_dataframe.ipynb b/notebooks/save_dataframe.ipynb
index 7a1e0c0..10897a7 100644
--- a/notebooks/save_dataframe.ipynb
+++ b/notebooks/save_dataframe.ipynb
@@ -37,12 +37,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 24,
    "id": "4ca50a6f-8f0e-469f-9993-e1e082133a7f",
    "metadata": {},
    "outputs": [],
    "source": [
-    "def save_thetas_and_xs_hierarchical(params_in):\n",
+    "def save_thetas_and_xs_hierarchical(params_in, noises, time):\n",
     "    # this function creates the fully hierarchical dataset\n",
     "    # note that μ_a_g and σ_a_g are inputs and a_g is drawn from these\n",
     "    \n",
@@ -64,17 +64,17 @@
     "                    starting_angle_radians=float(thetas[i]),\n",
     "                    acceleration_due_to_gravity=float(ags[i]),\n",
     "                    noise_std_percent={\n",
-    "                        \"pendulum_arm_length\": 0.0,\n",
-    "                        \"starting_angle_radians\": 0.1,\n",
-    "                        \"acceleration_due_to_gravity\": 0.0,\n",
+    "                        \"pendulum_arm_length\": noises[0],\n",
+    "                        \"starting_angle_radians\": noises[1],\n",
+    "                        \"acceleration_due_to_gravity\": noises[2],\n",
     "                    },\n",
     "                )\n",
-    "        x = pendulum.create_object(0.75, noiseless=False)\n",
+    "        x = pendulum.create_object(time, noiseless=False)\n",
     "        xs.append(x)\n",
     "        del pendulum\n",
     "    return ags, xs\n",
     "\n",
-    "def save_thetas_and_xs_non_hierarchical(params_in):\n",
+    "def save_thetas_and_xs_unpooled(params_in, noises, time):\n",
     "    # this function creates the fully hierarchical dataset\n",
     "    # note that μ_a_g and σ_a_g are inputs and a_g is drawn from these\n",
     "    \n",
@@ -96,20 +96,45 @@
     "                    starting_angle_radians=float(thetas[i]),\n",
     "                    acceleration_due_to_gravity=float(ags[i]),\n",
     "                    noise_std_percent={\n",
-    "                        \"pendulum_arm_length\": 0.0,\n",
-    "                        \"starting_angle_radians\": 0.1,\n",
-    "                        \"acceleration_due_to_gravity\": 0.0,\n",
+    "                        \"pendulum_arm_length\": noises[0],\n",
+    "                        \"starting_angle_radians\": noises[1],\n",
+    "                        \"acceleration_due_to_gravity\": noises[2],\n",
     "                    },\n",
     "                )\n",
-    "        x = pendulum.create_object(0.75, noiseless=False)\n",
+    "        x = pendulum.create_object(time, noiseless=False)\n",
     "        xs.append(x)\n",
     "        del pendulum\n",
-    "    return ags, xs"
+    "    return ags, xs\n",
+    "\n",
+    "def save_thetas_and_xs_non_hierarchical(params_in, noises, time):\n",
+    "    # this function creates the fully hierarchical dataset\n",
+    "    # note that μ_a_g and σ_a_g are inputs and a_g is drawn from these\n",
+    "    \n",
+    "    lengths, thetas, ags = params_in\n",
+    "\n",
+    "    \n",
+    "    xs = []\n",
+    "    for i in range(len(lengths)):\n",
+    "        #print(lengths[i], thetas[i], ags[i])\n",
+    "        pendulum = Pendulum(\n",
+    "                    pendulum_arm_length=float(lengths[i]),\n",
+    "                    starting_angle_radians=float(thetas[i]),\n",
+    "                    acceleration_due_to_gravity=float(ags[i]),\n",
+    "                    noise_std_percent={\n",
+    "                        \"pendulum_arm_length\": noises[0],\n",
+    "                        \"starting_angle_radians\": noises[1],\n",
+    "                        \"acceleration_due_to_gravity\": noises[2],\n",
+    "                    },\n",
+    "                )\n",
+    "        x = pendulum.create_object(time, noiseless=False)\n",
+    "        xs.append(x)\n",
+    "        del pendulum\n",
+    "    return xs"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 42,
    "id": "9fdc1f49-e453-4526-b18b-814b68f92aca",
    "metadata": {},
    "outputs": [],
@@ -118,14 +143,16 @@
     "length_percent_error_all = 0.0\n",
     "theta_percent_error_all = 0.1\n",
     "a_g_percent_error_all = 0.0\n",
+    "noises = [length_percent_error_all, \n",
+    "          theta_percent_error_all,\n",
+    "          a_g_percent_error_all]\n",
     "pos_err = 0.0\n",
     "\n",
     "time = 0.75\n",
     "\n",
     "total_length = 1000\n",
-    "length_df = int(total_length/4) # divide by four because we want the same total size as above\n",
-    "\n",
     "pendulums_per_planet = 100\n",
+    "n_planets = int(total_length/pendulums_per_planet) # 10 planets\n",
     "\n",
     "# and we get four pendulums per iteration of the below\n",
     "thetas = np.zeros((total_length, 5))\n",
@@ -136,27 +163,31 @@
     "#y_noisy = []\n",
     "\n",
     "    \n",
-    "rs = np.random.RandomState(666)# \n",
+    "rs = np.random.RandomState(667)# \n",
     "\n",
+    "# repeat 10 times because the same pendulums will exist on each planet\n",
+    "lengths_draw = np.tile(abs(rs.normal(loc=5, scale=2, size = pendulums_per_planet)), n_planets)\n",
+    "thetas_draw = np.tile(abs(rs.normal(loc=jnp.pi/100, scale=jnp.pi/500, size = pendulums_per_planet)), n_planets)\n",
     "\n",
-    "lengths_draw = abs(rs.normal(loc=5, scale=2, size = pendulums_per_planet))\n",
-    "thetas_draw = abs(rs.normal(loc=jnp.pi/100, scale=jnp.pi/500, size = pendulums_per_planet))\n",
+    "μ_a_g = abs(rs.normal(loc=10, scale=3))\n",
+    "σ_a_g = abs(rs.normal(loc=3, scale=0.5))\n",
     "\n",
-    "μ_a_g = abs(rs.normal(loc=10, scale=2))\n",
-    "σ_a_g = abs(rs.normal(loc=1, scale=0.5))\n",
+    "# these will be the same for all pendulums in this universe (read: dataframe)\n",
+    "μ_a_gs_draw = np.repeat(μ_a_g, total_length)\n",
+    "σ_a_gs_draw = np.repeat(σ_a_g, total_length)\n",
     "\n",
     "\n",
     "params_in = [lengths_draw,\n",
     "             thetas_draw,\n",
     "             μ_a_g, σ_a_g]\n",
     "\n",
-    "a_gs, xs_out = save_thetas_and_xs_hierarchical(params_in)\n",
+    "a_gs, xs_out = save_thetas_and_xs_hierarchical(params_in, noises, time)\n",
     "\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 43,
    "id": "9714134e-53a2-42df-b254-e942a2a41314",
    "metadata": {},
    "outputs": [
@@ -184,6 +215,8 @@
        "      <th>length</th>\n",
        "      <th>theta</th>\n",
        "      <th>a_g</th>\n",
+       "      <th>μ_a_g</th>\n",
+       "      <th>σ_a_g</th>\n",
        "      <th>time</th>\n",
        "      <th>pos</th>\n",
        "    </tr>\n",
@@ -191,43 +224,53 @@
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
-       "      <td>6.648376</td>\n",
-       "      <td>0.035245</td>\n",
-       "      <td>6.656893</td>\n",
+       "      <td>2.165523</td>\n",
+       "      <td>0.032737</td>\n",
+       "      <td>9.819111</td>\n",
+       "      <td>10.045455</td>\n",
+       "      <td>2.31817</td>\n",
        "      <td>0.75</td>\n",
-       "      <td>0.159997</td>\n",
+       "      <td>-0.001759</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
-       "      <td>5.959932</td>\n",
-       "      <td>0.035125</td>\n",
-       "      <td>6.656893</td>\n",
+       "      <td>4.874339</td>\n",
+       "      <td>0.034706</td>\n",
+       "      <td>9.819111</td>\n",
+       "      <td>10.045455</td>\n",
+       "      <td>2.31817</td>\n",
        "      <td>0.75</td>\n",
-       "      <td>0.164784</td>\n",
+       "      <td>0.082037</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
-       "      <td>7.346936</td>\n",
-       "      <td>0.027426</td>\n",
-       "      <td>6.656893</td>\n",
+       "      <td>0.517525</td>\n",
+       "      <td>0.029102</td>\n",
+       "      <td>9.819111</td>\n",
+       "      <td>10.045455</td>\n",
+       "      <td>2.31817</td>\n",
        "      <td>0.75</td>\n",
-       "      <td>0.148472</td>\n",
+       "      <td>-0.015782</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
-       "      <td>6.818096</td>\n",
-       "      <td>0.043121</td>\n",
-       "      <td>6.656893</td>\n",
+       "      <td>5.967690</td>\n",
+       "      <td>0.031120</td>\n",
+       "      <td>9.819111</td>\n",
+       "      <td>10.045455</td>\n",
+       "      <td>2.31817</td>\n",
        "      <td>0.75</td>\n",
-       "      <td>0.224570</td>\n",
+       "      <td>0.083749</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
-       "      <td>3.856557</td>\n",
-       "      <td>0.025951</td>\n",
-       "      <td>6.656893</td>\n",
+       "      <td>3.583923</td>\n",
+       "      <td>0.038289</td>\n",
+       "      <td>9.819111</td>\n",
+       "      <td>10.045455</td>\n",
+       "      <td>2.31817</td>\n",
        "      <td>0.75</td>\n",
-       "      <td>0.058967</td>\n",
+       "      <td>0.053290</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>...</th>\n",
@@ -236,70 +279,82 @@
        "      <td>...</td>\n",
        "      <td>...</td>\n",
        "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th>95</th>\n",
-       "      <td>8.139616</td>\n",
-       "      <td>0.021888</td>\n",
-       "      <td>6.431957</td>\n",
+       "      <th>995</th>\n",
+       "      <td>6.314215</td>\n",
+       "      <td>0.043477</td>\n",
+       "      <td>14.262585</td>\n",
+       "      <td>10.045455</td>\n",
+       "      <td>2.31817</td>\n",
        "      <td>0.75</td>\n",
-       "      <td>0.118812</td>\n",
+       "      <td>0.104018</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th>96</th>\n",
-       "      <td>4.816909</td>\n",
-       "      <td>0.032708</td>\n",
-       "      <td>6.431957</td>\n",
+       "      <th>996</th>\n",
+       "      <td>2.532752</td>\n",
+       "      <td>0.029214</td>\n",
+       "      <td>14.262585</td>\n",
+       "      <td>10.045455</td>\n",
+       "      <td>2.31817</td>\n",
        "      <td>0.75</td>\n",
-       "      <td>0.097864</td>\n",
+       "      <td>-0.016758</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th>97</th>\n",
-       "      <td>3.206136</td>\n",
-       "      <td>0.033854</td>\n",
-       "      <td>6.431957</td>\n",
+       "      <th>997</th>\n",
+       "      <td>4.698081</td>\n",
+       "      <td>0.032854</td>\n",
+       "      <td>14.262585</td>\n",
+       "      <td>10.045455</td>\n",
+       "      <td>2.31817</td>\n",
        "      <td>0.75</td>\n",
-       "      <td>0.058675</td>\n",
+       "      <td>0.034580</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th>98</th>\n",
-       "      <td>7.266712</td>\n",
-       "      <td>0.023045</td>\n",
-       "      <td>6.431957</td>\n",
+       "      <th>998</th>\n",
+       "      <td>3.241587</td>\n",
+       "      <td>0.032211</td>\n",
+       "      <td>14.262585</td>\n",
+       "      <td>10.045455</td>\n",
+       "      <td>2.31817</td>\n",
        "      <td>0.75</td>\n",
-       "      <td>0.113172</td>\n",
+       "      <td>-0.000247</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th>99</th>\n",
-       "      <td>8.444094</td>\n",
-       "      <td>0.040042</td>\n",
-       "      <td>6.431957</td>\n",
+       "      <th>999</th>\n",
+       "      <td>7.656012</td>\n",
+       "      <td>0.029380</td>\n",
+       "      <td>14.262585</td>\n",
+       "      <td>10.045455</td>\n",
+       "      <td>2.31817</td>\n",
        "      <td>0.75</td>\n",
-       "      <td>0.302359</td>\n",
+       "      <td>0.099346</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
-       "<p>100 rows × 5 columns</p>\n",
+       "<p>1000 rows × 7 columns</p>\n",
        "</div>"
       ],
       "text/plain": [
-       "      length     theta       a_g  time       pos\n",
-       "0   6.648376  0.035245  6.656893  0.75  0.159997\n",
-       "1   5.959932  0.035125  6.656893  0.75  0.164784\n",
-       "2   7.346936  0.027426  6.656893  0.75  0.148472\n",
-       "3   6.818096  0.043121  6.656893  0.75  0.224570\n",
-       "4   3.856557  0.025951  6.656893  0.75  0.058967\n",
-       "..       ...       ...       ...   ...       ...\n",
-       "95  8.139616  0.021888  6.431957  0.75  0.118812\n",
-       "96  4.816909  0.032708  6.431957  0.75  0.097864\n",
-       "97  3.206136  0.033854  6.431957  0.75  0.058675\n",
-       "98  7.266712  0.023045  6.431957  0.75  0.113172\n",
-       "99  8.444094  0.040042  6.431957  0.75  0.302359\n",
+       "       length     theta        a_g      μ_a_g    σ_a_g  time       pos\n",
+       "0    2.165523  0.032737   9.819111  10.045455  2.31817  0.75 -0.001759\n",
+       "1    4.874339  0.034706   9.819111  10.045455  2.31817  0.75  0.082037\n",
+       "2    0.517525  0.029102   9.819111  10.045455  2.31817  0.75 -0.015782\n",
+       "3    5.967690  0.031120   9.819111  10.045455  2.31817  0.75  0.083749\n",
+       "4    3.583923  0.038289   9.819111  10.045455  2.31817  0.75  0.053290\n",
+       "..        ...       ...        ...        ...      ...   ...       ...\n",
+       "995  6.314215  0.043477  14.262585  10.045455  2.31817  0.75  0.104018\n",
+       "996  2.532752  0.029214  14.262585  10.045455  2.31817  0.75 -0.016758\n",
+       "997  4.698081  0.032854  14.262585  10.045455  2.31817  0.75  0.034580\n",
+       "998  3.241587  0.032211  14.262585  10.045455  2.31817  0.75 -0.000247\n",
+       "999  7.656012  0.029380  14.262585  10.045455  2.31817  0.75  0.099346\n",
        "\n",
-       "[100 rows x 5 columns]"
+       "[1000 rows x 7 columns]"
       ]
      },
-     "execution_count": 6,
+     "execution_count": 43,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -310,6 +365,8 @@
     "    'length': lengths_draw,\n",
     "    'theta': thetas_draw,\n",
     "    'a_g': a_gs,\n",
+    "    'μ_a_g': μ_a_gs_draw,\n",
+    "    'σ_a_g': σ_a_gs_draw,\n",
     "    'time': np.repeat(time, len(lengths_draw)),\n",
     "    'pos': xs_out,\n",
     "    \n",
@@ -331,7 +388,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 46,
    "id": "482e2844-2ea2-4a8c-868b-8b798a36b296",
    "metadata": {},
    "outputs": [
@@ -359,6 +416,8 @@
        "      <th>length</th>\n",
        "      <th>theta</th>\n",
        "      <th>a_g</th>\n",
+       "      <th>μ_a_g</th>\n",
+       "      <th>σ_a_g</th>\n",
        "      <th>time</th>\n",
        "      <th>pos</th>\n",
        "      <th>pos_err</th>\n",
@@ -367,48 +426,58 @@
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
-       "      <td>6.648376</td>\n",
-       "      <td>0.035245</td>\n",
-       "      <td>6.656893</td>\n",
+       "      <td>2.165523</td>\n",
+       "      <td>0.032737</td>\n",
+       "      <td>9.819111</td>\n",
+       "      <td>10.045455</td>\n",
+       "      <td>2.31817</td>\n",
        "      <td>0.75</td>\n",
-       "      <td>0.159997</td>\n",
-       "      <td>0.017132</td>\n",
+       "      <td>-0.001759</td>\n",
+       "      <td>0.000186</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
-       "      <td>5.959932</td>\n",
-       "      <td>0.035125</td>\n",
-       "      <td>6.656893</td>\n",
+       "      <td>4.874339</td>\n",
+       "      <td>0.034706</td>\n",
+       "      <td>9.819111</td>\n",
+       "      <td>10.045455</td>\n",
+       "      <td>2.31817</td>\n",
        "      <td>0.75</td>\n",
-       "      <td>0.164784</td>\n",
-       "      <td>0.014691</td>\n",
+       "      <td>0.082037</td>\n",
+       "      <td>0.008203</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
-       "      <td>7.346936</td>\n",
-       "      <td>0.027426</td>\n",
-       "      <td>6.656893</td>\n",
+       "      <td>0.517525</td>\n",
+       "      <td>0.029102</td>\n",
+       "      <td>9.819111</td>\n",
+       "      <td>10.045455</td>\n",
+       "      <td>2.31817</td>\n",
        "      <td>0.75</td>\n",
-       "      <td>0.148472</td>\n",
-       "      <td>0.015226</td>\n",
+       "      <td>-0.015782</td>\n",
+       "      <td>0.001494</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
-       "      <td>6.818096</td>\n",
-       "      <td>0.043121</td>\n",
-       "      <td>6.656893</td>\n",
+       "      <td>5.967690</td>\n",
+       "      <td>0.031120</td>\n",
+       "      <td>9.819111</td>\n",
+       "      <td>10.045455</td>\n",
+       "      <td>2.31817</td>\n",
        "      <td>0.75</td>\n",
-       "      <td>0.224570</td>\n",
-       "      <td>0.021679</td>\n",
+       "      <td>0.083749</td>\n",
+       "      <td>0.010618</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
-       "      <td>3.856557</td>\n",
-       "      <td>0.025951</td>\n",
-       "      <td>6.656893</td>\n",
+       "      <td>3.583923</td>\n",
+       "      <td>0.038289</td>\n",
+       "      <td>9.819111</td>\n",
+       "      <td>10.045455</td>\n",
+       "      <td>2.31817</td>\n",
        "      <td>0.75</td>\n",
-       "      <td>0.058967</td>\n",
-       "      <td>0.005529</td>\n",
+       "      <td>0.053290</td>\n",
+       "      <td>0.004438</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>...</th>\n",
@@ -418,75 +487,100 @@
        "      <td>...</td>\n",
        "      <td>...</td>\n",
        "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th>95</th>\n",
-       "      <td>8.139616</td>\n",
-       "      <td>0.021888</td>\n",
-       "      <td>6.431957</td>\n",
+       "      <th>995</th>\n",
+       "      <td>6.314215</td>\n",
+       "      <td>0.043477</td>\n",
+       "      <td>14.262585</td>\n",
+       "      <td>10.045455</td>\n",
+       "      <td>2.31817</td>\n",
        "      <td>0.75</td>\n",
-       "      <td>0.118812</td>\n",
-       "      <td>0.013999</td>\n",
+       "      <td>0.104018</td>\n",
+       "      <td>0.011780</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th>96</th>\n",
-       "      <td>4.816909</td>\n",
-       "      <td>0.032708</td>\n",
-       "      <td>6.431957</td>\n",
+       "      <th>996</th>\n",
+       "      <td>2.532752</td>\n",
+       "      <td>0.029214</td>\n",
+       "      <td>14.262585</td>\n",
+       "      <td>10.045455</td>\n",
+       "      <td>2.31817</td>\n",
        "      <td>0.75</td>\n",
-       "      <td>0.097864</td>\n",
-       "      <td>0.010197</td>\n",
+       "      <td>-0.016758</td>\n",
+       "      <td>0.001535</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th>97</th>\n",
-       "      <td>3.206136</td>\n",
-       "      <td>0.033854</td>\n",
-       "      <td>6.431957</td>\n",
+       "      <th>997</th>\n",
+       "      <td>4.698081</td>\n",
+       "      <td>0.032854</td>\n",
+       "      <td>14.262585</td>\n",
+       "      <td>10.045455</td>\n",
+       "      <td>2.31817</td>\n",
        "      <td>0.75</td>\n",
-       "      <td>0.058675</td>\n",
-       "      <td>0.005284</td>\n",
+       "      <td>0.034580</td>\n",
+       "      <td>0.004028</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th>98</th>\n",
-       "      <td>7.266712</td>\n",
-       "      <td>0.023045</td>\n",
-       "      <td>6.431957</td>\n",
+       "      <th>998</th>\n",
+       "      <td>3.241587</td>\n",
+       "      <td>0.032211</td>\n",
+       "      <td>14.262585</td>\n",
+       "      <td>10.045455</td>\n",
+       "      <td>2.31817</td>\n",
        "      <td>0.75</td>\n",
-       "      <td>0.113172</td>\n",
-       "      <td>0.012745</td>\n",
+       "      <td>-0.000247</td>\n",
+       "      <td>0.000025</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th>99</th>\n",
-       "      <td>8.444094</td>\n",
-       "      <td>0.040042</td>\n",
-       "      <td>6.431957</td>\n",
+       "      <th>999</th>\n",
+       "      <td>7.656012</td>\n",
+       "      <td>0.029380</td>\n",
+       "      <td>14.262585</td>\n",
+       "      <td>10.045455</td>\n",
+       "      <td>2.31817</td>\n",
        "      <td>0.75</td>\n",
-       "      <td>0.302359</td>\n",
-       "      <td>0.026810</td>\n",
+       "      <td>0.099346</td>\n",
+       "      <td>0.011700</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
-       "<p>100 rows × 6 columns</p>\n",
+       "<p>1000 rows × 8 columns</p>\n",
        "</div>"
       ],
       "text/plain": [
-       "      length     theta       a_g  time       pos   pos_err\n",
-       "0   6.648376  0.035245  6.656893  0.75  0.159997  0.017132\n",
-       "1   5.959932  0.035125  6.656893  0.75  0.164784  0.014691\n",
-       "2   7.346936  0.027426  6.656893  0.75  0.148472  0.015226\n",
-       "3   6.818096  0.043121  6.656893  0.75  0.224570  0.021679\n",
-       "4   3.856557  0.025951  6.656893  0.75  0.058967  0.005529\n",
-       "..       ...       ...       ...   ...       ...       ...\n",
-       "95  8.139616  0.021888  6.431957  0.75  0.118812  0.013999\n",
-       "96  4.816909  0.032708  6.431957  0.75  0.097864  0.010197\n",
-       "97  3.206136  0.033854  6.431957  0.75  0.058675  0.005284\n",
-       "98  7.266712  0.023045  6.431957  0.75  0.113172  0.012745\n",
-       "99  8.444094  0.040042  6.431957  0.75  0.302359  0.026810\n",
+       "       length     theta        a_g      μ_a_g    σ_a_g  time       pos  \\\n",
+       "0    2.165523  0.032737   9.819111  10.045455  2.31817  0.75 -0.001759   \n",
+       "1    4.874339  0.034706   9.819111  10.045455  2.31817  0.75  0.082037   \n",
+       "2    0.517525  0.029102   9.819111  10.045455  2.31817  0.75 -0.015782   \n",
+       "3    5.967690  0.031120   9.819111  10.045455  2.31817  0.75  0.083749   \n",
+       "4    3.583923  0.038289   9.819111  10.045455  2.31817  0.75  0.053290   \n",
+       "..        ...       ...        ...        ...      ...   ...       ...   \n",
+       "995  6.314215  0.043477  14.262585  10.045455  2.31817  0.75  0.104018   \n",
+       "996  2.532752  0.029214  14.262585  10.045455  2.31817  0.75 -0.016758   \n",
+       "997  4.698081  0.032854  14.262585  10.045455  2.31817  0.75  0.034580   \n",
+       "998  3.241587  0.032211  14.262585  10.045455  2.31817  0.75 -0.000247   \n",
+       "999  7.656012  0.029380  14.262585  10.045455  2.31817  0.75  0.099346   \n",
        "\n",
-       "[100 rows x 6 columns]"
+       "      pos_err  \n",
+       "0    0.000186  \n",
+       "1    0.008203  \n",
+       "2    0.001494  \n",
+       "3    0.010618  \n",
+       "4    0.004438  \n",
+       "..        ...  \n",
+       "995  0.011780  \n",
+       "996  0.001535  \n",
+       "997  0.004028  \n",
+       "998  0.000025  \n",
+       "999  0.011700  \n",
+       "\n",
+       "[1000 rows x 8 columns]"
       ]
      },
-     "execution_count": 7,
+     "execution_count": 46,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -495,7 +589,7 @@
     "df['pos_err'] = analysis.calc_error_prop(df['length'],\n",
     "                         df['theta'],\n",
     "                         df['a_g'],\n",
-    "                         0.1*df['theta'],\n",
+    "                         noises[1]*df['theta'],\n",
     "                         df['time'],\n",
     "                         wrt='theta_0')\n",
     "df"
@@ -512,13 +606,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 47,
    "id": "1cbd3f6f-26f6-4786-bb8c-f9fc220da8b4",
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -536,9 +630,17 @@
     "plt.show()"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "c4d4dabe-7bbd-41f1-8da6-dff4f6d2d439",
+   "metadata": {},
+   "source": [
+    "There are multiple points (10) at the same $\\theta_0$ value because there's one per planet and there are 10 planets."
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 48,
    "id": "44c6292d-fea9-4693-9173-913fd396bbd5",
    "metadata": {},
    "outputs": [],
@@ -553,74 +655,466 @@
    "id": "5b2c4470-fc92-4c9b-882b-ebe58cce2431",
    "metadata": {},
    "source": [
-    "## Make the static dataframe for the non-hierarchical case\n"
+    "## Make the static dataframe for the unpooled case"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 49,
    "id": "be3710d9-4708-4dfd-b718-dc534acffdf4",
    "metadata": {},
+   "outputs": [],
+   "source": [
+    "# this needs to have the extra 1 so that SBI is happy\n",
+    "xs = np.zeros((total_length,1))\n",
+    "\n",
+    "# use same rs as above, which is:    \n",
+    "#rs = np.random.RandomState(667)# \n",
+    "\n",
+    "\n",
+    "lengths_draw = np.tile(abs(rs.normal(loc=5, scale=2, size = pendulums_per_planet)), n_planets)\n",
+    "thetas_draw = np.tile(abs(rs.normal(loc=jnp.pi/100, scale=jnp.pi/500, size = pendulums_per_planet)), n_planets)\n",
+    "\n",
+    "params_in = [lengths_draw,\n",
+    "             thetas_draw]\n",
+    "\n",
+    "a_gs, xs_out = save_thetas_and_xs_unpooled(params_in, noises, time)\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 52,
+   "id": "f13bcfcb-8281-4def-aa3c-6739fffe27e3",
+   "metadata": {},
    "outputs": [
     {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "ag0 9.74335976685576 ag1 10.666861788545654\n"
-     ]
-    },
-    {
-     "ename": "NameError",
-     "evalue": "name 'STOP' is not defined",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
-      "Cell \u001b[0;32mIn[12], line 28\u001b[0m\n\u001b[1;32m     23\u001b[0m thetas_draw \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mabs\u001b[39m(rs\u001b[38;5;241m.\u001b[39mnormal(loc\u001b[38;5;241m=\u001b[39mjnp\u001b[38;5;241m.\u001b[39mpi\u001b[38;5;241m/\u001b[39m\u001b[38;5;241m100\u001b[39m, scale\u001b[38;5;241m=\u001b[39mjnp\u001b[38;5;241m.\u001b[39mpi\u001b[38;5;241m/\u001b[39m\u001b[38;5;241m500\u001b[39m, size \u001b[38;5;241m=\u001b[39m pendulums_per_planet))\n\u001b[1;32m     25\u001b[0m params_in \u001b[38;5;241m=\u001b[39m [lengths_draw,\n\u001b[1;32m     26\u001b[0m              thetas_draw]\n\u001b[0;32m---> 28\u001b[0m a_gs, xs_out \u001b[38;5;241m=\u001b[39m \u001b[43msave_thetas_and_xs_non_hierarchical\u001b[49m\u001b[43m(\u001b[49m\u001b[43mparams_in\u001b[49m\u001b[43m)\u001b[49m\n",
-      "Cell \u001b[0;32mIn[10], line 42\u001b[0m, in \u001b[0;36msave_thetas_and_xs_non_hierarchical\u001b[0;34m(params_in)\u001b[0m\n\u001b[1;32m     40\u001b[0m ag1 \u001b[38;5;241m=\u001b[39m rs\u001b[38;5;241m.\u001b[39mnormal(loc\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m10\u001b[39m, scale\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m1\u001b[39m)\n\u001b[1;32m     41\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mag0\u001b[39m\u001b[38;5;124m'\u001b[39m, ag0, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mag1\u001b[39m\u001b[38;5;124m'\u001b[39m, ag1)\n\u001b[0;32m---> 42\u001b[0m \u001b[43mSTOP\u001b[49m\n\u001b[1;32m     43\u001b[0m ags \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39marray([np\u001b[38;5;241m.\u001b[39mrepeat(ag0,\u001b[38;5;28mint\u001b[39m(\u001b[38;5;28mlen\u001b[39m(lengths)\u001b[38;5;241m/\u001b[39m\u001b[38;5;241m2\u001b[39m)), np\u001b[38;5;241m.\u001b[39mrepeat(ag1,\u001b[38;5;28mint\u001b[39m(\u001b[38;5;28mlen\u001b[39m(lengths)\u001b[38;5;241m/\u001b[39m\u001b[38;5;241m2\u001b[39m))])\u001b[38;5;241m.\u001b[39mflatten()\n\u001b[1;32m     44\u001b[0m \u001b[38;5;66;03m#ags = np.array([rs.normal(loc=μ_a_g, scale=σ_a_g, size = int(len(lengths)/2)),\u001b[39;00m\n\u001b[1;32m     45\u001b[0m \u001b[38;5;66;03m#       rs.normal(loc=μ_a_g, scale=σ_a_g, size = int(len(lengths)/2))]).flatten()\u001b[39;00m\n",
-      "\u001b[0;31mNameError\u001b[0m: name 'STOP' is not defined"
-     ]
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>length</th>\n",
+       "      <th>theta</th>\n",
+       "      <th>a_g</th>\n",
+       "      <th>time</th>\n",
+       "      <th>pos</th>\n",
+       "      <th>pos_err</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>5.004154</td>\n",
+       "      <td>0.036652</td>\n",
+       "      <td>10.368171</td>\n",
+       "      <td>0.75</td>\n",
+       "      <td>0.074302</td>\n",
+       "      <td>0.008651</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>1.747232</td>\n",
+       "      <td>0.035067</td>\n",
+       "      <td>10.368171</td>\n",
+       "      <td>0.75</td>\n",
+       "      <td>-0.013108</td>\n",
+       "      <td>0.001553</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>4.113416</td>\n",
+       "      <td>0.039330</td>\n",
+       "      <td>10.368171</td>\n",
+       "      <td>0.75</td>\n",
+       "      <td>0.055574</td>\n",
+       "      <td>0.006001</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>5.508872</td>\n",
+       "      <td>0.038332</td>\n",
+       "      <td>10.368171</td>\n",
+       "      <td>0.75</td>\n",
+       "      <td>0.113731</td>\n",
+       "      <td>0.010889</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>4.287381</td>\n",
+       "      <td>0.032765</td>\n",
+       "      <td>10.368171</td>\n",
+       "      <td>0.75</td>\n",
+       "      <td>0.067875</td>\n",
+       "      <td>0.005528</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>...</th>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>995</th>\n",
+       "      <td>3.901779</td>\n",
+       "      <td>0.037532</td>\n",
+       "      <td>9.117351</td>\n",
+       "      <td>0.75</td>\n",
+       "      <td>0.059792</td>\n",
+       "      <td>0.006028</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>996</th>\n",
+       "      <td>4.619160</td>\n",
+       "      <td>0.023126</td>\n",
+       "      <td>9.117351</td>\n",
+       "      <td>0.75</td>\n",
+       "      <td>0.052637</td>\n",
+       "      <td>0.005281</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>997</th>\n",
+       "      <td>4.619737</td>\n",
+       "      <td>0.033381</td>\n",
+       "      <td>9.117351</td>\n",
+       "      <td>0.75</td>\n",
+       "      <td>0.081090</td>\n",
+       "      <td>0.007624</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>998</th>\n",
+       "      <td>6.278292</td>\n",
+       "      <td>0.030860</td>\n",
+       "      <td>9.117351</td>\n",
+       "      <td>0.75</td>\n",
+       "      <td>0.117798</td>\n",
+       "      <td>0.011983</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>999</th>\n",
+       "      <td>6.675469</td>\n",
+       "      <td>0.033984</td>\n",
+       "      <td>9.117351</td>\n",
+       "      <td>0.75</td>\n",
+       "      <td>0.129194</td>\n",
+       "      <td>0.014512</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "<p>1000 rows × 6 columns</p>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "       length     theta        a_g  time       pos   pos_err\n",
+       "0    5.004154  0.036652  10.368171  0.75  0.074302  0.008651\n",
+       "1    1.747232  0.035067  10.368171  0.75 -0.013108  0.001553\n",
+       "2    4.113416  0.039330  10.368171  0.75  0.055574  0.006001\n",
+       "3    5.508872  0.038332  10.368171  0.75  0.113731  0.010889\n",
+       "4    4.287381  0.032765  10.368171  0.75  0.067875  0.005528\n",
+       "..        ...       ...        ...   ...       ...       ...\n",
+       "995  3.901779  0.037532   9.117351  0.75  0.059792  0.006028\n",
+       "996  4.619160  0.023126   9.117351  0.75  0.052637  0.005281\n",
+       "997  4.619737  0.033381   9.117351  0.75  0.081090  0.007624\n",
+       "998  6.278292  0.030860   9.117351  0.75  0.117798  0.011983\n",
+       "999  6.675469  0.033984   9.117351  0.75  0.129194  0.014512\n",
+       "\n",
+       "[1000 rows x 6 columns]"
+      ]
+     },
+     "execution_count": 52,
+     "metadata": {},
+     "output_type": "execute_result"
     }
    ],
    "source": [
-    "length_percent_error_all = 0.0\n",
-    "theta_percent_error_all = 0.1\n",
-    "a_g_percent_error_all = 0.0\n",
-    "pos_err = 0.0\n",
-    "\n",
-    "time = 0.75\n",
-    "\n",
-    "total_length = 1000\n",
-    "length_df = int(total_length/4) # divide by four because we want the same total size as above\n",
-    "\n",
-    "pendulums_per_planet = 100\n",
+    "# now make it into a dataframe\n",
+    "data_params = {\n",
+    "    'length': lengths_draw,\n",
+    "    'theta': thetas_draw,\n",
+    "    'a_g': a_gs,\n",
+    "    'time': np.repeat(time, len(lengths_draw)),\n",
+    "    'pos': xs_out,\n",
+    "    \n",
+    "}\n",
     "\n",
-    "# and we get four pendulums per iteration of the below\n",
-    "thetas = np.zeros((total_length, 3))\n",
+    "## create the DataFrame\n",
+    "df_unpooled = pd.DataFrame(data_params)\n",
+    "df_unpooled['pos_err'] = analysis.calc_error_prop(df_unpooled['length'],\n",
+    "                         df_unpooled['theta'],\n",
+    "                         df_unpooled['a_g'],\n",
+    "                         noises[1]*df_unpooled['theta'],\n",
+    "                         df_unpooled['time'],\n",
+    "                         wrt='theta_0')\n",
+    "df_unpooled"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 53,
+   "id": "c7b83279-f6ae-4c16-9006-b900720d9ccc",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.clf()\n",
+    "plt.scatter(df_unpooled['theta'], df_unpooled['pos'])\n",
+    "plt.errorbar(df_unpooled['theta'], df_unpooled['pos'], yerr = df_unpooled['pos_err'], ls = 'None')\n",
+    "plt.xlabel(r'$\\theta_0$')\n",
+    "plt.ylabel('x position')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2b8008a3-d3cc-49d6-a44f-3ceea19d4682",
+   "metadata": {},
+   "source": [
+    "## Make the static dataframe for the totally non-hierarchical case\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 55,
+   "id": "34c9c342-a5e7-4935-929c-96e83800f8f6",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>length</th>\n",
+       "      <th>theta</th>\n",
+       "      <th>a_g</th>\n",
+       "      <th>time</th>\n",
+       "      <th>pos</th>\n",
+       "      <th>pos_err</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>2.871105</td>\n",
+       "      <td>0.031861</td>\n",
+       "      <td>11.133572</td>\n",
+       "      <td>0.75</td>\n",
+       "      <td>0.007528</td>\n",
+       "      <td>0.000858</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>5.448619</td>\n",
+       "      <td>0.022775</td>\n",
+       "      <td>4.867815</td>\n",
+       "      <td>0.75</td>\n",
+       "      <td>0.103401</td>\n",
+       "      <td>0.009418</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>3.187087</td>\n",
+       "      <td>0.037103</td>\n",
+       "      <td>10.685782</td>\n",
+       "      <td>0.75</td>\n",
+       "      <td>0.026184</td>\n",
+       "      <td>0.002320</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>6.879361</td>\n",
+       "      <td>0.017425</td>\n",
+       "      <td>8.745679</td>\n",
+       "      <td>0.75</td>\n",
+       "      <td>0.092032</td>\n",
+       "      <td>0.007950</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>5.770837</td>\n",
+       "      <td>0.033164</td>\n",
+       "      <td>12.653497</td>\n",
+       "      <td>0.75</td>\n",
+       "      <td>0.089182</td>\n",
+       "      <td>0.008499</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>...</th>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>95</th>\n",
+       "      <td>5.406246</td>\n",
+       "      <td>0.030629</td>\n",
+       "      <td>8.581573</td>\n",
+       "      <td>0.75</td>\n",
+       "      <td>0.087823</td>\n",
+       "      <td>0.009699</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>96</th>\n",
+       "      <td>4.688578</td>\n",
+       "      <td>0.028146</td>\n",
+       "      <td>8.411600</td>\n",
+       "      <td>0.75</td>\n",
+       "      <td>0.057896</td>\n",
+       "      <td>0.007078</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>97</th>\n",
+       "      <td>5.265508</td>\n",
+       "      <td>0.034329</td>\n",
+       "      <td>8.050434</td>\n",
+       "      <td>0.75</td>\n",
+       "      <td>0.106009</td>\n",
+       "      <td>0.010842</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>98</th>\n",
+       "      <td>5.535740</td>\n",
+       "      <td>0.020886</td>\n",
+       "      <td>7.327576</td>\n",
+       "      <td>0.75</td>\n",
+       "      <td>0.064109</td>\n",
+       "      <td>0.007517</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>99</th>\n",
+       "      <td>6.590619</td>\n",
+       "      <td>0.049454</td>\n",
+       "      <td>10.927742</td>\n",
+       "      <td>0.75</td>\n",
+       "      <td>0.175149</td>\n",
+       "      <td>0.018532</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "<p>100 rows × 6 columns</p>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "      length     theta        a_g  time       pos   pos_err\n",
+       "0   2.871105  0.031861  11.133572  0.75  0.007528  0.000858\n",
+       "1   5.448619  0.022775   4.867815  0.75  0.103401  0.009418\n",
+       "2   3.187087  0.037103  10.685782  0.75  0.026184  0.002320\n",
+       "3   6.879361  0.017425   8.745679  0.75  0.092032  0.007950\n",
+       "4   5.770837  0.033164  12.653497  0.75  0.089182  0.008499\n",
+       "..       ...       ...        ...   ...       ...       ...\n",
+       "95  5.406246  0.030629   8.581573  0.75  0.087823  0.009699\n",
+       "96  4.688578  0.028146   8.411600  0.75  0.057896  0.007078\n",
+       "97  5.265508  0.034329   8.050434  0.75  0.106009  0.010842\n",
+       "98  5.535740  0.020886   7.327576  0.75  0.064109  0.007517\n",
+       "99  6.590619  0.049454  10.927742  0.75  0.175149  0.018532\n",
+       "\n",
+       "[100 rows x 6 columns]"
+      ]
+     },
+     "execution_count": 55,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
     "# this needs to have the extra 1 so that SBI is happy\n",
     "xs = np.zeros((total_length,1))\n",
     "\n",
     "# use same rs as above, which is:    \n",
-    "#rs = np.random.RandomState(666)# \n",
+    "#rs = np.random.RandomState(667)# \n",
     "\n",
     "\n",
     "lengths_draw = abs(rs.normal(loc=5, scale=2, size = pendulums_per_planet))\n",
     "thetas_draw = abs(rs.normal(loc=jnp.pi/100, scale=jnp.pi/500, size = pendulums_per_planet))\n",
+    "ags_draw = abs(rs.normal(loc=10, scale=3, size = pendulums_per_planet))\n",
     "\n",
     "params_in = [lengths_draw,\n",
-    "             thetas_draw]\n",
+    "             thetas_draw,\n",
+    "             ags_draw]\n",
     "\n",
-    "a_gs, xs_out = save_thetas_and_xs_non_hierarchical(params_in)\n",
-    "\n"
+    "xs_out = save_thetas_and_xs_non_hierarchical(params_in, noises, time)\n",
+    "\n",
+    "# now make it into a dataframe\n",
+    "data_params = {\n",
+    "    'length': lengths_draw,\n",
+    "    'theta': thetas_draw,\n",
+    "    'a_g': ags_draw,\n",
+    "    'time': np.repeat(time, len(lengths_draw)),\n",
+    "    'pos': xs_out,\n",
+    "    \n",
+    "}\n",
+    "\n",
+    "## create the DataFrame\n",
+    "df_non_hierarchical = pd.DataFrame(data_params)\n",
+    "df_non_hierarchical['pos_err'] = analysis.calc_error_prop(df_non_hierarchical['length'],\n",
+    "                         df_non_hierarchical['theta'],\n",
+    "                         df_non_hierarchical['a_g'],\n",
+    "                         0.1*df_non_hierarchical['theta'],\n",
+    "                         df_non_hierarchical['time'],\n",
+    "                         wrt='theta_0')\n",
+    "df_non_hierarchical"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f13bcfcb-8281-4def-aa3c-6739fffe27e3",
+   "id": "1fe3aa78-973c-47fc-8c30-5341ae8979d1",
    "metadata": {},
    "outputs": [],
-   "source": []
+   "source": [
+    "plt.clf()\n",
+    "plt.scatter(df_unpooled['theta'], df_unpooled['pos'], label = 'unpooled')\n",
+    "plt.errorbar(df_unpooled['theta'], df_unpooled['pos'], yerr = df_unpooled['pos_err'], ls = 'None')\n",
+    "plt.xlabel(r'$\\theta_0$')\n",
+    "plt.ylabel('x position')\n",
+    "plt.show()"
+   ]
   }
  ],
  "metadata": {