figure_2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Figure 2f\n",
    "This notebook reproduces the GP regression plots provided in Figure 2. The code is kind of verbose, but I wanted to be sort of explicit about what I'm doing to generate these figures."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import pyro\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import os\n",
    "\n",
    "# import GP regression code\n",
    "from importlib import reload\n",
    "import dli_gpr\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Input data\n",
    "Read input text files (provided in data directory of this repository)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_dir = \"data\"\n",
    "\n",
    "# data files\n",
    "pe1_r_fname = os.path.join(data_dir, \"v3_MetaclusterPE1_R_gprinput.txt\")\n",
    "pe1_nr_fname = os.path.join(data_dir, \"v3_MetaclusterPE1_NR_gprinput.txt\")\n",
    "pe2_r_fname = os.path.join(data_dir, \"v3_MetaclusterPE2_R_gprinput.txt\")\n",
    "pe2_nr_fname = os.path.join(data_dir, \"v3_MetaclusterPE2_NR_gprinput.txt\")\n",
    "te_r_fname = os.path.join(data_dir, \"v3_MetaclusterTE_R_gprinput.txt\")\n",
    "te_nr_fname = os.path.join(data_dir, \"v3_MetaclusterTE_NR_gprinput.txt\")\n",
    "\n",
    "# read these with pandas (tsv)\n",
    "pe1_r_df = pd.read_csv(pe1_r_fname, sep=\"\\t\")\n",
    "pe1_nr_df = pd.read_csv(pe1_nr_fname, sep=\"\\t\")\n",
    "pe2_r_df = pd.read_csv(pe2_r_fname, sep=\"\\t\")\n",
    "pe2_nr_df = pd.read_csv(pe2_nr_fname, sep=\"\\t\")\n",
    "te_r_df = pd.read_csv(te_r_fname, sep=\"\\t\")\n",
    "te_nr_df = pd.read_csv(te_nr_fname, sep=\"\\t\")\n",
    "\n",
    "# get rid of NaNs\n",
    "pe1_r_df.dropna(inplace=True)\n",
    "pe1_nr_df.dropna(inplace=True)\n",
    "pe2_r_df.dropna(inplace=True)\n",
    "pe2_nr_df.dropna(inplace=True)\n",
    "te_r_df.dropna(inplace=True)\n",
    "te_nr_df.dropna(inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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>time</th>\n",
       "      <th>proportion(y)</th>\n",
       "      <th>numcellsincluster(x)</th>\n",
       "      <th>totalcellsinsample(n)</th>\n",
       "      <th>patientID</th>\n",
       "      <th>sampleID</th>\n",
       "      <th>tumorburden</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-30</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>1</td>\n",
       "      <td>329</td>\n",
       "      <td>DFCI-5310</td>\n",
       "      <td>1</td>\n",
       "      <td>94.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>180</td>\n",
       "      <td>0.2031</td>\n",
       "      <td>21</td>\n",
       "      <td>1310</td>\n",
       "      <td>DFCI-5310</td>\n",
       "      <td>2</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-42</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>127</td>\n",
       "      <td>2834</td>\n",
       "      <td>DFCI-5309</td>\n",
       "      <td>5</td>\n",
       "      <td>11.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>90</td>\n",
       "      <td>0.0005</td>\n",
       "      <td>88</td>\n",
       "      <td>2030</td>\n",
       "      <td>DFCI-5309</td>\n",
       "      <td>6</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>0.0437</td>\n",
       "      <td>7</td>\n",
       "      <td>3184</td>\n",
       "      <td>DFCI-5311</td>\n",
       "      <td>9</td>\n",
       "      <td>44.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>90</td>\n",
       "      <td>0.0125</td>\n",
       "      <td>32</td>\n",
       "      <td>3762</td>\n",
       "      <td>DFCI-5311</td>\n",
       "      <td>11</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>270</td>\n",
       "      <td>0.0926</td>\n",
       "      <td>24</td>\n",
       "      <td>8662</td>\n",
       "      <td>DFCI-5311</td>\n",
       "      <td>12</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0</td>\n",
       "      <td>0.0022</td>\n",
       "      <td>116</td>\n",
       "      <td>1358</td>\n",
       "      <td>DFCI-5312</td>\n",
       "      <td>21</td>\n",
       "      <td>38.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>270</td>\n",
       "      <td>0.0769</td>\n",
       "      <td>1</td>\n",
       "      <td>13</td>\n",
       "      <td>DFCI-5312</td>\n",
       "      <td>22</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>-5</td>\n",
       "      <td>0.0264</td>\n",
       "      <td>10</td>\n",
       "      <td>1174</td>\n",
       "      <td>DFCI-5317</td>\n",
       "      <td>23</td>\n",
       "      <td>80.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>345</td>\n",
       "      <td>0.1210</td>\n",
       "      <td>5</td>\n",
       "      <td>4390</td>\n",
       "      <td>DFCI-5317</td>\n",
       "      <td>24</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>-30</td>\n",
       "      <td>0.0160</td>\n",
       "      <td>5</td>\n",
       "      <td>1566</td>\n",
       "      <td>DFCI-5314</td>\n",
       "      <td>25</td>\n",
       "      <td>94.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1095</td>\n",
       "      <td>0.0944</td>\n",
       "      <td>38</td>\n",
       "      <td>1853</td>\n",
       "      <td>DFCI-5314</td>\n",
       "      <td>26</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>-416</td>\n",
       "      <td>0.0111</td>\n",
       "      <td>4</td>\n",
       "      <td>995</td>\n",
       "      <td>DFCI-5311</td>\n",
       "      <td>29</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>-90</td>\n",
       "      <td>0.0071</td>\n",
       "      <td>52</td>\n",
       "      <td>1544</td>\n",
       "      <td>DFCI-5311</td>\n",
       "      <td>30</td>\n",
       "      <td>16.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>-152</td>\n",
       "      <td>0.0076</td>\n",
       "      <td>65</td>\n",
       "      <td>1447</td>\n",
       "      <td>DFCI-5314</td>\n",
       "      <td>31</td>\n",
       "      <td>78.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>29</td>\n",
       "      <td>0.0312</td>\n",
       "      <td>4</td>\n",
       "      <td>1216</td>\n",
       "      <td>DFCI-5314</td>\n",
       "      <td>32</td>\n",
       "      <td>98.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>-416</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>4</td>\n",
       "      <td>731</td>\n",
       "      <td>DFCI-5317</td>\n",
       "      <td>38</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>-50</td>\n",
       "      <td>0.0324</td>\n",
       "      <td>4</td>\n",
       "      <td>1051</td>\n",
       "      <td>DFCI-5317</td>\n",
       "      <td>39</td>\n",
       "      <td>80.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>-416</td>\n",
       "      <td>0.0119</td>\n",
       "      <td>68</td>\n",
       "      <td>1430</td>\n",
       "      <td>DFCI-5309</td>\n",
       "      <td>40</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    time  proportion(y)  numcellsincluster(x)  totalcellsinsample(n)  \\\n",
       "0    -30         0.0000                     1                    329   \n",
       "1    180         0.2031                    21                   1310   \n",
       "2    -42         0.0000                   127                   2834   \n",
       "3     90         0.0005                    88                   2030   \n",
       "4      0         0.0437                     7                   3184   \n",
       "6     90         0.0125                    32                   3762   \n",
       "7    270         0.0926                    24                   8662   \n",
       "8      0         0.0022                   116                   1358   \n",
       "9    270         0.0769                     1                     13   \n",
       "10    -5         0.0264                    10                   1174   \n",
       "11   345         0.1210                     5                   4390   \n",
       "12   -30         0.0160                     5                   1566   \n",
       "13  1095         0.0944                    38                   1853   \n",
       "14  -416         0.0111                     4                    995   \n",
       "15   -90         0.0071                    52                   1544   \n",
       "16  -152         0.0076                    65                   1447   \n",
       "17    29         0.0312                     4                   1216   \n",
       "18  -416         0.0000                     4                    731   \n",
       "19   -50         0.0324                     4                   1051   \n",
       "20  -416         0.0119                    68                   1430   \n",
       "\n",
       "    patientID  sampleID  tumorburden  \n",
       "0   DFCI-5310         1         94.0  \n",
       "1   DFCI-5310         2          0.0  \n",
       "2   DFCI-5309         5         11.0  \n",
       "3   DFCI-5309         6          0.0  \n",
       "4   DFCI-5311         9         44.0  \n",
       "6   DFCI-5311        11          0.0  \n",
       "7   DFCI-5311        12          0.0  \n",
       "8   DFCI-5312        21         38.0  \n",
       "9   DFCI-5312        22          0.0  \n",
       "10  DFCI-5317        23         80.0  \n",
       "11  DFCI-5317        24          0.0  \n",
       "12  DFCI-5314        25         94.0  \n",
       "13  DFCI-5314        26          0.0  \n",
       "14  DFCI-5311        29          0.0  \n",
       "15  DFCI-5311        30         16.0  \n",
       "16  DFCI-5314        31         78.0  \n",
       "17  DFCI-5314        32         98.0  \n",
       "18  DFCI-5317        38          0.0  \n",
       "19  DFCI-5317        39         80.0  \n",
       "20  DFCI-5309        40          0.0  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# check to make sure looks ok\n",
    "pe1_r_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Prepare GPR input for tumor burden\n",
    "This is a regular GPR model. We use the same bandwidth for all models, use SE of the data to initialize the variance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x12c65c850>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# time input\n",
    "time_r = pe2_r_df[\"time\"].values\n",
    "tb_r = pe2_r_df[\"tumorburden\"].values/100.\n",
    "time_nr = pe2_nr_df[\"time\"].values\n",
    "tb_nr = pe2_nr_df[\"tumorburden\"].values/100.\n",
    "\n",
    "# plot stuff to make sure it looks ok\n",
    "plt.scatter(time_r, tb_r, c=\"cornflowerblue\", label=\"R\")\n",
    "plt.scatter(time_nr, tb_nr, c=\"orange\", label=\"NR\")\n",
    "plt.title(\"Tumor burden\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "reload(dli_gpr)\n",
    "# convert everything to torch tensors\n",
    "torch_time_r = torch.FloatTensor(time_r)\n",
    "torch_time_nr = torch.FloatTensor(time_nr)\n",
    "torch_tb_r = torch.FloatTensor(tb_r)\n",
    "torch_tb_nr = torch.FloatTensor(tb_nr)\n",
    "\n",
    "# initialize models\n",
    "tb_r_model = dli_gpr.gpr(torch_time_r, torch_tb_r)\n",
    "tb_nr_model = dli_gpr.gpr(torch_time_nr, torch_tb_nr)\n",
    "\n",
    "# have to initialize kernel\n",
    "tb_r_model.initialize_variables()\n",
    "tb_nr_model.initialize_variables()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 5000/5000 [00:05<00:00, 994.26it/s] \n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1025.82it/s]\n"
     ]
    }
   ],
   "source": [
    "# optimize sigma by max likelihood\n",
    "pyro.clear_param_store()\n",
    "tb_r_losses = tb_r_model.optimize(n_steps=5000)\n",
    "\n",
    "pyro.clear_param_store()\n",
    "tb_nr_losses = tb_nr_model.optimize(n_steps=5000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x12ccdf610>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# make sure looks like it is actually converging\n",
    "plt.plot(tb_nr_losses)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# get predictions for new points...\n",
    "# new input time points\n",
    "new_y = torch.FloatTensor(np.linspace(-600, 1200, 100))\n",
    "\n",
    "# compute conditional distribution of response variable\n",
    "tb_r_mean, tb_r_cov = tb_r_model.conditional_distribution(new_y)\n",
    "tb_nr_mean, tb_nr_cov = tb_nr_model.conditional_distribution(new_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# prepare values for plotting\n",
    "\n",
    "# time points as numpy array\n",
    "new_times = new_y.numpy()\n",
    "\n",
    "# means\n",
    "tb_r_mean = tb_r_mean.numpy()\n",
    "tb_nr_mean = tb_nr_mean.numpy()\n",
    "\n",
    "# variance\n",
    "tb_r_var = torch.diag(tb_r_cov).numpy()\n",
    "tb_nr_var = torch.diag(tb_nr_cov).numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Tumor burden\\nNR')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# make plots\n",
    "fig, ax = plt.subplots(1,2, figsize=(7,3), tight_layout=True)\n",
    "\n",
    "# plot tumor burden for R\n",
    "ax[0].plot(new_times, tb_r_mean, \"k-\", alpha=0.5)\n",
    "ax[0].scatter(time_r, tb_r, c=\"silver\", marker=\"x\")\n",
    "ax[0].fill_between(new_times, tb_r_mean + tb_r_var, tb_r_mean - tb_r_var, color=\"silver\", alpha=0.3)\n",
    "ax[0].set_title(\"Tumor burden\\nR\")\n",
    "\n",
    "# plot tumor burden for NR\n",
    "ax[1].plot(new_times, tb_nr_mean, \"k-\", alpha=0.5)\n",
    "ax[1].scatter(time_nr, tb_nr, c=\"silver\", marker=\"x\")\n",
    "ax[1].fill_between(new_times, tb_nr_mean + tb_nr_var, tb_nr_mean - tb_nr_var, color=\"silver\", alpha=0.3)\n",
    "ax[1].set_title(\"Tumor burden\\nNR\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Metacluster models\n",
    "This is the hierarchical model for heteroskedascic noise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# prepare input (numpy arrays)\n",
    "te_r = te_r_df[\"proportion(y)\"].values\n",
    "pe1_r = pe1_r_df[\"proportion(y)\"].values\n",
    "pe2_r = pe2_r_df[\"proportion(y)\"].values\n",
    "te_nr = te_nr_df[\"proportion(y)\"].values\n",
    "pe1_nr = pe1_nr_df[\"proportion(y)\"].values\n",
    "pe2_nr = pe2_nr_df[\"proportion(y)\"].values\n",
    "\n",
    "# convert to torch tensors\n",
    "torch_te_r = torch.FloatTensor(te_r)\n",
    "torch_pe1_r = torch.FloatTensor(pe1_r)\n",
    "torch_pe2_r = torch.FloatTensor(pe2_r)\n",
    "torch_te_nr = torch.FloatTensor(te_nr)\n",
    "torch_pe1_nr = torch.FloatTensor(pe1_nr)\n",
    "torch_pe2_nr = torch.FloatTensor(pe2_nr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# get relative weights for each\n",
    "sizes_r = te_r_df[\"totalcellsinsample(n)\"].values\n",
    "sizes_nr = te_nr_df[\"totalcellsinsample(n)\"].values\n",
    "\n",
    "# convert to torch\n",
    "torch_sizes_r = torch.FloatTensor(sizes_r)\n",
    "torch_sizes_nr = torch.FloatTensor(sizes_nr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# initialize models\n",
    "reload(dli_gpr)\n",
    "te_r_model = dli_gpr.dli_gpr(torch_time_r, torch_te_r, torch_sizes_r)\n",
    "pe1_r_model = dli_gpr.dli_gpr(torch_time_r, torch_pe1_r, torch_sizes_r)\n",
    "pe2_r_model = dli_gpr.dli_gpr(torch_time_r, torch_pe2_r, torch_sizes_r)\n",
    "te_nr_model = dli_gpr.dli_gpr(torch_time_nr, torch_te_nr, torch_sizes_nr)\n",
    "pe1_nr_model = dli_gpr.dli_gpr(torch_time_nr, torch_pe1_nr, torch_sizes_nr)\n",
    "pe2_nr_model = dli_gpr.dli_gpr(torch_time_nr, torch_pe2_nr, torch_sizes_nr)\n",
    "\n",
    "# initialize variables\n",
    "te_r_model.initialize_variables()\n",
    "pe1_r_model.initialize_variables()\n",
    "pe2_r_model.initialize_variables()\n",
    "te_nr_model.initialize_variables()\n",
    "pe1_nr_model.initialize_variables()\n",
    "pe2_nr_model.initialize_variables()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 2000/2000 [00:03<00:00, 528.11it/s]\n",
      "100%|██████████| 2000/2000 [00:03<00:00, 506.36it/s]\n",
      "100%|██████████| 2000/2000 [00:03<00:00, 544.84it/s]\n",
      "100%|██████████| 2000/2000 [00:03<00:00, 551.17it/s]\n",
      "100%|██████████| 2000/2000 [00:03<00:00, 559.40it/s]\n",
      "100%|██████████| 2000/2000 [00:04<00:00, 485.99it/s]\n"
     ]
    }
   ],
   "source": [
    "for model in [te_r_model, pe1_r_model, pe2_r_model, te_nr_model, pe1_nr_model, pe2_nr_model]:\n",
    "    pyro.clear_param_store()\n",
    "    model.optimize(n_steps=2000);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# compute conditional distribution of response variable\n",
    "te_r_mean, te_r_cov = te_r_model.conditional_distribution(new_y)\n",
    "pe1_r_mean, pe1_r_cov = pe1_r_model.conditional_distribution(new_y)\n",
    "pe2_r_mean, pe2_r_cov = pe2_r_model.conditional_distribution(new_y)\n",
    "\n",
    "te_nr_mean, te_nr_cov = te_nr_model.conditional_distribution(new_y)\n",
    "pe1_nr_mean, pe1_nr_cov = pe1_nr_model.conditional_distribution(new_y)\n",
    "pe2_nr_mean, pe2_nr_cov = pe2_nr_model.conditional_distribution(new_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# convert back to numpy array for plotting\n",
    "te_r_mean, te_r_var = te_r_mean.numpy(), np.diag(te_r_cov.numpy())\n",
    "pe1_r_mean, pe1_r_var = pe1_r_mean.numpy(), np.diag(pe1_r_cov.numpy())\n",
    "pe2_r_mean, pe2_r_var = pe2_r_mean.numpy(), np.diag(pe2_r_cov.numpy())\n",
    "\n",
    "te_nr_mean, te_nr_var = te_nr_mean.numpy(), np.diag(te_nr_cov.numpy())\n",
    "pe1_nr_mean, pe1_nr_var = pe1_nr_mean.numpy(), np.diag(pe1_nr_cov.numpy())\n",
    "pe2_nr_mean, pe2_nr_var = pe2_nr_mean.numpy(), np.diag(pe2_nr_cov.numpy())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# get metacell cluster sizes for plotting\n",
    "plotting_sizes_r = sizes_r/50\n",
    "plotting_sizes_nr = sizes_nr/50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x360 with 12 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# make plots\n",
    "fig, ax = plt.subplots(2,3, figsize=(12,5), tight_layout=True)\n",
    "\n",
    "# plot metacluster TE for R\n",
    "ax[0,0].plot(new_times, te_r_mean, \"cornflowerblue\", alpha=0.5)\n",
    "ax[0,0].scatter(time_r, te_r, c=\"cornflowerblue\", marker=\".\", sizes=plotting_sizes_r)\n",
    "ax[0,0].fill_between(new_times, te_r_mean + te_r_var, te_r_mean - te_r_var, color=\"cornflowerblue\", alpha=0.3)\n",
    "ax[0,0].set_title(\"TE R\")\n",
    "\n",
    "# plot metacluster TE for NR\n",
    "ax[1,0].plot(new_times, te_nr_mean, c=\"orange\", alpha=0.5)\n",
    "ax[1,0].scatter(time_nr, te_nr, c=\"orange\", marker=\".\", sizes=plotting_sizes_nr)\n",
    "ax[1,0].fill_between(new_times, te_nr_mean + te_nr_var, te_nr_mean - te_nr_var, color=\"orange\", alpha=0.3)\n",
    "ax[1,0].set_title(\"TE NR\")\n",
    "\n",
    "# plot metacluster PE1 for R\n",
    "ax[0,1].plot(new_times, pe1_r_mean, \"cornflowerblue\", alpha=0.5)\n",
    "ax[0,1].scatter(time_r, pe1_r, c=\"cornflowerblue\", marker=\".\", sizes=plotting_sizes_r)\n",
    "ax[0,1].fill_between(new_times, pe1_r_mean + pe1_r_var, pe1_r_mean - pe1_r_var, color=\"cornflowerblue\", alpha=0.3)\n",
    "ax[0,1].set_title(\"PE1 R\")\n",
    "\n",
    "# plot metacluster PE1 for NR\n",
    "ax[1,1].plot(new_times, pe1_nr_mean, \"orange\", alpha=0.5)\n",
    "ax[1,1].scatter(time_nr, pe1_nr, c=\"orange\", marker=\".\", sizes=plotting_sizes_nr)\n",
    "ax[1,1].fill_between(new_times, pe1_nr_mean + pe1_nr_var, pe1_nr_mean - pe1_nr_var, color=\"orange\", alpha=0.3)\n",
    "ax[1,1].set_title(\"PE1 NR\")\n",
    "\n",
    "# plot metacluster PE1 for R\n",
    "ax[0,2].plot(new_times, pe2_r_mean, \"cornflowerblue\", alpha=0.5)\n",
    "ax[0,2].scatter(time_r, pe2_r, c=\"cornflowerblue\", marker=\".\", sizes=plotting_sizes_r)\n",
    "ax[0,2].fill_between(new_times, pe2_r_mean + pe2_r_var, pe2_r_mean - pe2_r_var, color=\"cornflowerblue\", alpha=0.3)\n",
    "ax[0,2].set_title(\"PE2 R\")\n",
    "\n",
    "# plot metacluster PE1 for NR\n",
    "ax[1,2].plot(new_times, pe2_nr_mean, \"orange\", alpha=0.5)\n",
    "ax[1,2].scatter(time_nr, pe2_nr, c=\"orange\", marker=\".\", sizes=plotting_sizes_nr)\n",
    "ax[1,2].fill_between(new_times, pe2_nr_mean + pe2_nr_var, pe2_nr_mean - pe2_nr_var, color=\"orange\", alpha=0.3)\n",
    "ax[1,2].set_title(\"PE2 NR\")\n",
    "\n",
    "# add duplicated axis to plot tumor burden for R\n",
    "for ix in range(3):\n",
    "    ax2 = ax[0,ix].twinx()\n",
    "    ax2.plot(new_times, tb_r_mean, \"k-\", alpha=0.5)\n",
    "    ax2.scatter(time_r, tb_r, c=\"k\", marker=\"x\", alpha=0.5)\n",
    "    ax2.fill_between(new_times, tb_r_mean + tb_r_var, tb_r_mean - tb_r_var, color=\"silver\", alpha=0.3)\n",
    "    if ix == 0:\n",
    "        ax[0,ix].set_ylim(-0.2, 0.8)\n",
    "    elif ix == 1:\n",
    "        ax[0,ix].set_ylim(-0.1, 0.5)\n",
    "    elif ix == 2:\n",
    "        ax[0,ix].set_ylim(-0.1, 0.75)\n",
    "    ax2.set_ylim(-0.2,1.2)\n",
    "    if ix==2:\n",
    "        ax2.set_ylabel(\"tumor burden\\nR\")\n",
    "    if ix==0:\n",
    "        ax[0,ix].set_ylabel(\"metacluster\\nproportion\")\n",
    "        \n",
    "# add duplicated axis to plot tumor burden for NR\n",
    "for ix in range(3):\n",
    "    ax2 = ax[1,ix].twinx()\n",
    "    ax2.plot(new_times, tb_nr_mean, \"k-\", alpha=0.5)\n",
    "    ax2.scatter(time_nr, tb_nr, c=\"k\", marker=\"x\", alpha=0.5)\n",
    "    ax2.fill_between(new_times, tb_nr_mean + tb_nr_var, tb_nr_mean - tb_nr_var, color=\"silver\", alpha=0.3)\n",
    "    # limit y axis\n",
    "    ax[1,ix].set_ylim(-0.2, 0.8)\n",
    "    ax2.set_ylim(-0.2,1.2)\n",
    "    if ix==2:\n",
    "        ax2.set_ylabel(\"tumor burden\\nR\")\n",
    "    if ix==0:\n",
    "        ax[1,ix].set_ylabel(\"metacluster\\nproportion\")\n",
    "        \n",
    "# save figure\n",
    "#plt.savefig(\"figure2_v2.pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cross correlation analysis\n",
    "The simplest thing to do is to a Gaussian process model to tumor burdens under different shifts, then compute the correlation between the estimated mean tumor burden and metacluster proportions. This is done separately for each cluster below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 306,
   "metadata": {},
   "outputs": [],
   "source": [
    "# shifts (the bandwidth is 285)\n",
    "shifts = np.arange(-300, 800, 25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 307,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 5000/5000 [00:04<00:00, 1015.86it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1005.66it/s]\n",
      "100%|██████████| 5000/5000 [00:05<00:00, 943.51it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 998.43it/s] \n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1005.38it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1036.58it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1019.84it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1034.45it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1024.41it/s]\n",
      "100%|██████████| 5000/5000 [00:05<00:00, 987.31it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 965.97it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 945.37it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 916.26it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 961.45it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 937.52it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 925.02it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 925.16it/s]\n",
      "100%|██████████| 5000/5000 [00:05<00:00, 973.87it/s]\n",
      "100%|██████████| 5000/5000 [00:05<00:00, 958.83it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 980.10it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 956.70it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 963.65it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 963.92it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 923.39it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 983.42it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 990.47it/s] \n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1044.55it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1029.46it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1036.92it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1026.55it/s]\n",
      "100%|██████████| 5000/5000 [00:05<00:00, 997.03it/s] \n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1039.67it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1006.56it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1007.39it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1007.51it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1008.77it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1009.77it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1019.43it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1010.22it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1000.37it/s]\n",
      "100%|██████████| 5000/5000 [00:05<00:00, 994.91it/s] \n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1009.15it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1022.28it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1009.19it/s]\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import pearsonr\n",
    "\n",
    "# cluster-specific parameters\n",
    "tumor_time = torch_time_r\n",
    "tumor_burden = torch_tb_r\n",
    "metacluster_time = torch_time_r\n",
    "metacluster_proportions = torch_te_r\n",
    "\n",
    "# for storing r, p\n",
    "te_r, te_p = np.zeros(len(shifts)), np.zeros(len(shifts))\n",
    "\n",
    "for ix, shift in enumerate(shifts):\n",
    "    # time input\n",
    "    shifted_time = tumor_time + shift\n",
    "    \n",
    "    # model initialization\n",
    "    model = dli_gpr.gpr(shifted_time, tumor_burden)\n",
    "    model.initialize_variables()\n",
    "    \n",
    "    # fit model\n",
    "    pyro.clear_param_store()\n",
    "    model.optimize(n_steps=5000)\n",
    "    \n",
    "    # get estimates\n",
    "    est_mean, est_cov = model.conditional_distribution(metacluster_time)\n",
    "    \n",
    "    # get R, p\n",
    "    r, p = pearsonr(est_mean.numpy(), metacluster_proportions.numpy())\n",
    "    \n",
    "    # store r and p\n",
    "    te_r[ix] = r\n",
    "    te_p[ix] = p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 308,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 5000/5000 [00:05<00:00, 902.72it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 959.43it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 984.97it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 987.01it/s] \n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1028.05it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1008.70it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1022.97it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1008.71it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1024.72it/s]\n",
      "100%|██████████| 5000/5000 [00:05<00:00, 959.19it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 977.60it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 991.18it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 962.39it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 979.14it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 879.67it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 967.06it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 929.24it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 956.66it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 975.49it/s] \n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1013.95it/s]\n",
      "100%|██████████| 5000/5000 [00:05<00:00, 978.40it/s] \n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1031.31it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1030.93it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1026.42it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1022.95it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1034.24it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1035.71it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1039.03it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1030.88it/s]\n",
      "100%|██████████| 5000/5000 [00:05<00:00, 963.06it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 978.69it/s] \n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1033.06it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1008.78it/s]\n",
      "100%|██████████| 5000/5000 [00:05<00:00, 964.44it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 996.14it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 967.35it/s] \n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1015.74it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1029.76it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1024.37it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1031.57it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1024.87it/s]\n",
      "100%|██████████| 5000/5000 [00:05<00:00, 950.82it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 960.66it/s] \n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1061.13it/s]\n"
     ]
    }
   ],
   "source": [
    "# cluster-specific parameters (PE1)\n",
    "tumor_time = torch_time_r\n",
    "tumor_burden = torch_tb_r\n",
    "metacluster_time = torch_time_r\n",
    "metacluster_proportions = torch_pe1_r\n",
    "\n",
    "# for storing r, p\n",
    "pe1_r, pe1_p = np.zeros(len(shifts)), np.zeros(len(shifts))\n",
    "\n",
    "for ix, shift in enumerate(shifts):\n",
    "    # time input\n",
    "    shifted_time = tumor_time + shift\n",
    "    \n",
    "    # model initialization\n",
    "    model = dli_gpr.gpr(shifted_time, tumor_burden)\n",
    "    model.initialize_variables()\n",
    "    \n",
    "    # fit model\n",
    "    pyro.clear_param_store()\n",
    "    model.optimize(n_steps=5000)\n",
    "    \n",
    "    # get estimates\n",
    "    est_mean, est_cov = model.conditional_distribution(metacluster_time)\n",
    "    \n",
    "    # get R, p\n",
    "    r, p = pearsonr(est_mean.numpy(), metacluster_proportions.numpy())\n",
    "    \n",
    "    # store r and p\n",
    "    pe1_r[ix] = r\n",
    "    pe1_p[ix] = p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 309,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 5000/5000 [00:04<00:00, 1043.33it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1056.07it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1061.59it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1063.49it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1053.03it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1063.08it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1067.28it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1059.79it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1064.29it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1059.17it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1057.57it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1064.53it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1065.74it/s]\n",
      "100%|██████████| 5000/5000 [00:05<00:00, 984.69it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 925.15it/s]\n",
      "100%|██████████| 5000/5000 [00:05<00:00, 972.39it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 971.27it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 993.62it/s] \n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1035.32it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1016.07it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1003.20it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1023.08it/s]\n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1009.13it/s]\n",
      "100%|██████████| 5000/5000 [00:05<00:00, 935.72it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 930.35it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 969.49it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 978.04it/s] \n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1003.09it/s]\n",
      "100%|██████████| 5000/5000 [00:05<00:00, 986.66it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 951.48it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 932.29it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 922.63it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 943.95it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 913.16it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 982.97it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 957.19it/s] \n",
      "100%|██████████| 5000/5000 [00:06<00:00, 796.31it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 979.21it/s] \n",
      "100%|██████████| 5000/5000 [00:05<00:00, 926.44it/s]\n",
      "100%|██████████| 5000/5000 [00:05<00:00, 957.40it/s] \n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1025.07it/s]\n",
      "100%|██████████| 5000/5000 [00:05<00:00, 930.37it/s] \n",
      "100%|██████████| 5000/5000 [00:04<00:00, 1027.67it/s]\n",
      "100%|██████████| 5000/5000 [00:05<00:00, 970.95it/s] \n"
     ]
    }
   ],
   "source": [
    "# cluster-specific parameters (PE2)\n",
    "tumor_time = torch_time_r\n",
    "tumor_burden = torch_tb_r\n",
    "metacluster_time = torch_time_r\n",
    "metacluster_proportions = torch_pe2_r\n",
    "\n",
    "# for storing r, p\n",
    "pe2_r, pe2_p = np.zeros(len(shifts)), np.zeros(len(shifts))\n",
    "\n",
    "for ix, shift in enumerate(shifts):\n",
    "    # time input\n",
    "    shifted_time = tumor_time + shift\n",
    "    \n",
    "    # model initialization\n",
    "    model = dli_gpr.gpr(shifted_time, tumor_burden)\n",
    "    model.initialize_variables()\n",
    "    \n",
    "    # fit model\n",
    "    pyro.clear_param_store()\n",
    "    model.optimize(n_steps=5000)\n",
    "    \n",
    "    # get estimates\n",
    "    est_mean, est_cov = model.conditional_distribution(metacluster_time)\n",
    "    \n",
    "    # get R, p\n",
    "    r, p = pearsonr(est_mean.numpy(), metacluster_proportions.numpy())\n",
    "    \n",
    "    # store r and p\n",
    "    pe2_r[ix] = r\n",
    "    pe2_p[ix] = p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 311,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 648x216 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1,3, figsize=(9,3), tight_layout=True)\n",
    "\n",
    "# plot as vertical lines\n",
    "axs[0].vlines(shifts, np.zeros(len(shifts)), te_r, color=\"silver\")\n",
    "\n",
    "# get argmax and plot that\n",
    "ix = np.argmax(te_r)\n",
    "axs[0].vlines(shifts[ix], 0, te_r[ix], color=\"r\")\n",
    "axs[0].set_ylim(-0.75, 0.75)\n",
    "axs[0].set_xlabel(\"shift\")\n",
    "axs[0].set_ylabel(\"correlation\")\n",
    "axs[0].set_title(\"TE R\\nmax = %d days\\np = %.3f\" % (int(shifts[ix]), te_p[ix]))\n",
    "\n",
    "# plot as vertical lines\n",
    "axs[1].vlines(shifts, np.zeros(len(shifts)), pe1_r, color=\"silver\")\n",
    "\n",
    "# get argmax and plot that\n",
    "ix = np.argmax(pe1_r)\n",
    "axs[1].vlines(shifts[ix], 0, pe1_r[ix], color=\"r\")\n",
    "axs[1].set_ylim(-0.75, 0.75)\n",
    "axs[1].set_xlabel(\"shift\")\n",
    "axs[1].set_title(\"PE1 R\\nmax = %d days\\np = %.3f\" % (int(shifts[ix]), pe1_p[ix]))\n",
    "\n",
    "# plot as vertical lines\n",
    "axs[2].vlines(shifts, np.zeros(len(shifts)), pe2_r, color=\"silver\")\n",
    "\n",
    "# get argmax and plot that\n",
    "ix = np.argmax(pe2_r)\n",
    "axs[2].vlines(shifts[ix], 0, pe2_r[ix], color=\"r\")\n",
    "axs[2].set_ylim(-0.75, 0.75)\n",
    "axs[2].set_xlabel(\"shift\")\n",
    "axs[2].set_title(\"PE2 R\\nmax = %d days\\np = %.3f\" % (int(shifts[ix]), pe2_p[ix]))\n",
    "\n",
    "#plt.savefig(\"correlations_v2.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}