notebooks/covid-19-inference.ipynb

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  "metadata": {
    "colab": {
      "name": "Model-based predictions of Covid-19 spread using inference from observed cases",
      "provenance": [],
      "collapsed_sections": [
        "nHHBWKUAaLAE",
        "x1sTKe-l8RL2"
      ],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/oughtinc/ergo/blob/notebooks-readme/notebooks/covid-19-inference.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5cE7NYFm10ZR",
        "colab_type": "text"
      },
      "source": [
        "Notes\n",
        "\n",
        "* Switch to Italy\n",
        "* Graph data and results\n",
        "* Add variable for true initial infections, lockdown start date (11 March)\n",
        "* Add lag time (see Jacob/NYT models)\n",
        "* Add patient recovery"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lqsGCK-lclRH",
        "colab_type": "text"
      },
      "source": [
        "# Setup"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pQ6nYmLBcnpz",
        "colab_type": "text"
      },
      "source": [
        "Install [Ergo](https://github.com/oughtinc/ergo) (our forecasting library) and a few tools we'll use in this colab:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "u5-EaP2LUfBG",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "!pip install --quiet poetry  # Fixes https://github.com/python-poetry/poetry/issues/532\n",
        "!pip install --quiet pendulum seaborn\n",
        "!pip install --quiet torchviz"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vU4gqtY0BUTi",
        "colab_type": "code",
        "outputId": "078d672d-7936-4887-ad54-c4599381d6f9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 90
        }
      },
      "source": [
        "# !pip uninstall --yes --quiet ergo\n",
        "!pip install  --quiet git+https://github.com/oughtinc/ergo.git@william\n",
        "# !pip install --upgrade --no-cache-dir --quiet git+https://github.com/oughtinc/ergo.git\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "  Installing build dependencies ... \u001b[?25l\u001b[?25hdone\n",
            "  Getting requirements to build wheel ... \u001b[?25l\u001b[?25hdone\n",
            "    Preparing wheel metadata ... \u001b[?25l\u001b[?25hdone\n",
            "  Building wheel for ergo (PEP 517) ... \u001b[?25l\u001b[?25hdone\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Nr37FWiJHcqq",
        "colab_type": "code",
        "outputId": "90abeaf6-0a62-40da-cf00-22f1f6e631d8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "import ergo\n",
        "\n",
        "confirmed_infections = ergo.data.covid19.ConfirmedInfections()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "WARNING:root:Diamond Princess not found in regex\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yXEnMn86brxn",
        "colab_type": "code",
        "outputId": "a15b4087-5b1a-470c-ede1-a416ad5ac240",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        }
      },
      "source": [
        "%load_ext google.colab.data_table"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The google.colab.data_table extension is already loaded. To reload it, use:\n",
            "  %reload_ext google.colab.data_table\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uwSj6D6oV-bL",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import re\n",
        "import ergo\n",
        "import pendulum\n",
        "import pandas\n",
        "import seaborn\n",
        "\n",
        "from types import SimpleNamespace\n",
        "from typing import List\n",
        "from pendulum import DateTime\n",
        "from matplotlib import pyplot"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nHHBWKUAaLAE",
        "colab_type": "text"
      },
      "source": [
        "# Questions"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GYW08eB7aVpY",
        "colab_type": "text"
      },
      "source": [
        "Here are Metaculus ids for the questions we'll load, and some short names that will allow us to associate questions with variables in our model:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2eluOE9zaLI-",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "question_ids = [3704, 3712, 3713, 3711, 3722, 3761, 3705, 3706]  # 3740, 3736, \n",
        "question_names = [\n",
        "  # \"WHO Eastern Mediterranean Region on 2020/03/27\",\n",
        "  # \"WHO Region of the Americas on 2020/03/27\",\n",
        "  # \"WHO Western Pacific Region on 2020/03/27\",\n",
        "  # \"WHO South-East Asia Region on 2020/03/27\",\n",
        "  \"South Korea on 2020/03/27\",\n",
        "  # \"United Kingdom on 2020/03/27\",\n",
        "  # \"WHO African Region on 2020/03/27\",\n",
        "  # \"WHO European Region on 2020/03/27\",\n",
        "  # \"Bay Area on 2020/04/01\",\n",
        "  # \"San Francisco on 2020/04/01\"\n",
        "]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vjyK02LqaZxc",
        "colab_type": "text"
      },
      "source": [
        "We load the question data from Metaculus:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Q1TM8scJac-o",
        "colab_type": "code",
        "outputId": "80f05ef6-a451-47d4-ae3b-1517edbbaf7b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "metaculus = ergo.Metaculus(username=\"ought\", password=\"\")\n",
        "questions = [metaculus.get_question(id, name=name) for id, name in zip(question_ids, question_names)]\n",
        "ergo.MetaculusQuestion.to_dataframe(questions)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "application/vnd.google.colaboratory.module+javascript": "\n      import \"https://ssl.gstatic.com/colaboratory/data_table/84ef27dae82052e3/data_table.js\";\n\n      window.createDataTable({\n        data: [[{\n            'v': 0,\n            'f': \"0\",\n        },\n{\n            'v': 3704,\n            'f': \"3704\",\n        },\n\"South Korea on 2020/03/27\",\n\"How many total confirmed cases of novel coronavirus will be reported in the WHO East Mediterranean region by March 27?\",\n\"2020-03-27 09:00:00+00:00\"]],\n        columns: [[\"number\", \"index\"], [\"number\", \"id\"], [\"string\", \"name\"], [\"string\", \"title\"], [\"string\", \"resolve_time\"]],\n        columnOptions: [{\"width\": \"1px\", \"className\": \"index_column\"}],\n        rowsPerPage: 25,\n        helpUrl: \"https://colab.research.google.com/notebooks/data_table.ipynb\",\n        suppressOutputScrolling: true,\n      });\n    ",
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              "    .dataframe tbody tr th:only-of-type {\n",
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              "    .dataframe tbody tr th {\n",
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              "\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>id</th>\n",
              "      <th>name</th>\n",
              "      <th>title</th>\n",
              "      <th>resolve_time</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>3704</td>\n",
              "      <td>South Korea on 2020/03/27</td>\n",
              "      <td>How many total confirmed cases of novel corona...</td>\n",
              "      <td>2020-03-27 09:00:00+00:00</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
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            "text/plain": [
              "     id  ...              resolve_time\n",
              "0  3704  ... 2020-03-27 09:00:00+00:00\n",
              "\n",
              "[1 rows x 4 columns]"
            ]
          },
          "metadata": {
            "tags": []
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          "execution_count": 31
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      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x1sTKe-l8RL2",
        "colab_type": "text"
      },
      "source": [
        "# Data"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3IgdNojqA681",
        "colab_type": "text"
      },
      "source": [
        "Our most important data is the data about confirmed cases (from Hopkins):"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2_pf1up78RT0",
        "colab_type": "code",
        "outputId": "4187542f-20e4-4195-beb3-9694cbe0b751",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "confirmed_infections = ergo.data.covid19.ConfirmedInfections()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "WARNING:root:Diamond Princess not found in regex\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gffrBMP5aq_E",
        "colab_type": "text"
      },
      "source": [
        "# Assumptions"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VDtP45oi8Vc1",
        "colab_type": "text"
      },
      "source": [
        "Assumptions are things that should be inferred from data but currently aren't:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lVU5gNfb_zz3",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "assumptions = SimpleNamespace()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GVxV_g32Ecpm",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "assumptions.lockdown_start = {\n",
        "  \"Italy\": pendulum.datetime(2020,3,11),\n",
        "  \"Spain\": pendulum.datetime(2020,3,15),\n",
        "}"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Iotq1zz_bi5d",
        "colab_type": "text"
      },
      "source": [
        "# Model"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zNzoy6sKwHoV",
        "colab_type": "text"
      },
      "source": [
        "Main model:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VWYcxRL-wH3Q",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import torch\n",
        "import pyro\n",
        "\n",
        "Area = str\n",
        "\n",
        "@ergo.model\n",
        "def model(start: DateTime, end: DateTime, areas: List[Area], training=True):\n",
        "  for area in areas:\n",
        "    doubling_time = ergo.lognormal_from_interval(1., 14., name=f\"doubling_time {area}\")\n",
        "    doubling_time_lockdown = ergo.lognormal_from_interval(1., torch.max(doubling_time, ergo.to_float(1.1)), name=f\"doubling_time_lockdown {area}\")\n",
        "    observation_noise = ergo.halfnormal_from_interval(0.1, name=f\"observation_noise {area}\")\n",
        "    predicted = ergo.to_float(confirmed_infections(area, start))\n",
        "\n",
        "    for i in range(1,(end - start).days):\n",
        "      date = start.add(days=i)\n",
        "      datestr = date.format('YYYY/MM/DD')\n",
        "      confirmed = None\n",
        "      try:\n",
        "        confirmed = ergo.to_float(confirmed_infections(area, date))\n",
        "        ergo.tag(confirmed, f\"actual {area} on {datestr}\")\n",
        "      except KeyError:\n",
        "        pass\n",
        "      doubling_time_today = doubling_time\n",
        "      if area in assumptions.lockdown_start.keys() and date >= assumptions.lockdown_start[area]:\n",
        "        doubling_time_today = doubling_time_lockdown\n",
        "      predicted = predicted * 2**(1. / doubling_time_today)\n",
        "      ergo.tag(predicted, f\"predicted {area} on {datestr}\")\n",
        "      if (not training) or (confirmed is not None):\n",
        "        predict_observed = ergo.normal(predicted, \n",
        "                                      predicted*observation_noise, \n",
        "                                      name=f\"predict_observed {area} on {datestr}\",\n",
        "                                      obs=confirmed)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wUalPuTawICl",
        "colab_type": "text"
      },
      "source": [
        "Run the model:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "10NvnBSt58cI",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "start_date = pendulum.datetime(2020,3,1)\n",
        "end_date = pendulum.datetime(2020,4,1)\n",
        "areas = [\"Italy\", \"Spain\"]\n",
        "model_args = (start_date, end_date, areas)\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6hXRtbxz2y7P",
        "colab_type": "code",
        "outputId": "eacad48c-ee02-4de4-db3f-86b3ea58ae32",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 2434
        }
      },
      "source": [
        "import pandas as pd\n",
        "from pyro.infer import SVI, Trace_ELBO\n",
        "from pyro.infer import Predictive\n",
        "import functools\n",
        "\n",
        "def infer_and_run(model, num_samples=5000, num_iterations=2000, \n",
        "                  debug=False, learning_rate=0.01, \n",
        "                  early_stopping_patience=200) -> pd.DataFrame:\n",
        "  \"\"\"\n",
        "    debug - whether to output debug information\n",
        "    num_iterations - Number of optimizer iterations\n",
        "    learning_rate - Optimizer learning rate\n",
        "    early_stopping_patience - Stop training if loss hasn't improved for this many iterations\n",
        "  \"\"\"\n",
        "  def to_numpy(d):\n",
        "    return {k:v.detach().numpy() for k, v in d.items()}\n",
        "\n",
        "  def debug_output(guide):\n",
        "    quantiles = to_numpy(guide.quantiles([0.05, 0.5, 0.95]))\n",
        "    for k, v in quantiles.items():\n",
        "      print(f\"{k}: {v[1]:.4f} [{v[0]:.4f}, {v[2]:.4f}]\")\n",
        "\n",
        "  guide = pyro.infer.autoguide.AutoNormal(model, \n",
        "                                          init_loc_fn=pyro.infer.autoguide.init_to_median)\n",
        "  pyro.clear_param_store()\n",
        "  guide(training=True)\n",
        "  adam = pyro.optim.Adam({\"lr\": 0.01})\n",
        "  svi = SVI(model, guide, adam, loss=Trace_ELBO())\n",
        "\n",
        "  if debug:\n",
        "    debug_output(guide)\n",
        "    print()\n",
        "\n",
        "  best_loss = None\n",
        "  last_improvement = None\n",
        "\n",
        "  for j in range(num_iterations):\n",
        "      # calculate the loss and take a gradient step\n",
        "      loss = svi.step(training=True)\n",
        "      if best_loss is None or best_loss > loss:\n",
        "        best_loss = loss\n",
        "        last_improvement = j\n",
        "      if j % 100 == 0:\n",
        "        if debug:\n",
        "          print(\"[iteration %04d]\" % (j + 1 ))\n",
        "          print(f\"loss: {loss:.4f}\")\n",
        "          debug_output(guide)\n",
        "          print()\n",
        "        if j > (last_improvement + early_stopping_patience):\n",
        "          print(\"Stopping Early\")\n",
        "          break\n",
        "\n",
        "  print(f\"Final loss: {loss:.4f}\")\n",
        "  predictive = Predictive(model, guide=guide, num_samples=num_samples)\n",
        "  raw_samples = predictive(training=False)\n",
        "  return pandas.DataFrame(to_numpy(raw_samples))\n",
        "\n",
        "\n",
        "\n",
        "samples = infer_and_run(functools.partial(model, *model_args),\n",
        "                        num_iterations=1000, \n",
        "                        num_samples=1000,\n",
        "                        debug=True)\n",
        "samples.describe().transpose()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "ERROR! Session/line number was not unique in database. History logging moved to new session 63\n",
            "doubling_time Italy: 5.3190 [4.5122, 6.2699]\n",
            "doubling_time_lockdown Italy: 2.2932 [1.9454, 2.7031]\n",
            "observation_noise Italy: 0.0391 [0.0332, 0.0461]\n",
            "doubling_time Spain: 4.0816 [3.4625, 4.8113]\n",
            "doubling_time_lockdown Spain: 1.8753 [1.5908, 2.2105]\n",
            "observation_noise Spain: 0.0400 [0.0339, 0.0471]\n",
            "\n",
            "[iteration 0001]\n",
            "loss: 84950.2814\n",
            "doubling_time Italy: 5.2660 [4.4747, 6.1974]\n",
            "doubling_time_lockdown Italy: 2.3162 [1.9681, 2.7258]\n",
            "observation_noise Italy: 0.0395 [0.0335, 0.0466]\n",
            "doubling_time Spain: 4.0410 [3.4224, 4.7713]\n",
            "doubling_time_lockdown Spain: 1.8566 [1.5776, 2.1850]\n",
            "observation_noise Spain: 0.0404 [0.0342, 0.0477]\n",
            "\n",
            "[iteration 0101]\n",
            "loss: 1774.4991\n",
            "doubling_time Italy: 3.7038 [3.3161, 4.1367]\n",
            "doubling_time_lockdown Italy: 4.2917 [3.7622, 4.8958]\n",
            "observation_noise Italy: 0.0646 [0.0551, 0.0756]\n",
            "doubling_time Spain: 2.6136 [2.2543, 3.0303]\n",
            "doubling_time_lockdown Spain: 1.4730 [1.2735, 1.7038]\n",
            "observation_noise Spain: 0.0598 [0.0505, 0.0708]\n",
            "\n",
            "[iteration 0201]\n",
            "loss: 2362.3005\n",
            "doubling_time Italy: 3.3938 [3.1188, 3.6930]\n",
            "doubling_time_lockdown Italy: 4.9256 [4.4309, 5.4755]\n",
            "observation_noise Italy: 0.0716 [0.0613, 0.0836]\n",
            "doubling_time Spain: 2.3670 [2.0685, 2.7087]\n",
            "doubling_time_lockdown Spain: 1.5484 [1.3397, 1.7896]\n",
            "observation_noise Spain: 0.0659 [0.0560, 0.0776]\n",
            "\n",
            "[iteration 0301]\n",
            "loss: 1174.0760\n",
            "doubling_time Italy: 3.2893 [3.0668, 3.5279]\n",
            "doubling_time_lockdown Italy: 5.1564 [4.7155, 5.6384]\n",
            "observation_noise Italy: 0.0760 [0.0652, 0.0886]\n",
            "doubling_time Spain: 2.2899 [2.0138, 2.6038]\n",
            "doubling_time_lockdown Spain: 1.6640 [1.4388, 1.9245]\n",
            "observation_noise Spain: 0.0705 [0.0600, 0.0828]\n",
            "\n",
            "[iteration 0401]\n",
            "loss: 1344.2424\n",
            "doubling_time Italy: 3.2749 [3.0812, 3.4808]\n",
            "doubling_time_lockdown Italy: 5.2573 [4.8504, 5.6983]\n",
            "observation_noise Italy: 0.0791 [0.0678, 0.0923]\n",
            "doubling_time Spain: 2.2407 [1.9855, 2.5287]\n",
            "doubling_time_lockdown Spain: 1.7985 [1.5550, 2.0803]\n",
            "observation_noise Spain: 0.0752 [0.0641, 0.0881]\n",
            "\n",
            "[iteration 0501]\n",
            "loss: 936.6817\n",
            "doubling_time Italy: 3.2610 [3.0861, 3.4457]\n",
            "doubling_time_lockdown Italy: 5.2968 [4.9250, 5.6968]\n",
            "observation_noise Italy: 0.0819 [0.0701, 0.0955]\n",
            "doubling_time Spain: 2.2375 [1.9916, 2.5138]\n",
            "doubling_time_lockdown Spain: 1.9671 [1.6983, 2.2786]\n",
            "observation_noise Spain: 0.0793 [0.0679, 0.0927]\n",
            "\n",
            "[iteration 0601]\n",
            "loss: 632.5699\n",
            "doubling_time Italy: 3.2488 [3.0935, 3.4118]\n",
            "doubling_time_lockdown Italy: 5.2637 [4.9303, 5.6197]\n",
            "observation_noise Italy: 0.0847 [0.0725, 0.0988]\n",
            "doubling_time Spain: 2.2280 [1.9925, 2.4914]\n",
            "doubling_time_lockdown Spain: 2.1501 [1.8571, 2.4893]\n",
            "observation_noise Spain: 0.0831 [0.0713, 0.0969]\n",
            "\n",
            "[iteration 0701]\n",
            "loss: 613.1308\n",
            "doubling_time Italy: 3.2909 [3.1445, 3.4442]\n",
            "doubling_time_lockdown Italy: 5.2994 [4.9850, 5.6335]\n",
            "observation_noise Italy: 0.0865 [0.0740, 0.1011]\n",
            "doubling_time Spain: 2.2213 [1.9948, 2.4735]\n",
            "doubling_time_lockdown Spain: 2.3438 [2.0259, 2.7116]\n",
            "observation_noise Spain: 0.0864 [0.0741, 0.1006]\n",
            "\n",
            "[iteration 0801]\n",
            "loss: 612.4920\n",
            "doubling_time Italy: 3.2495 [3.1133, 3.3916]\n",
            "doubling_time_lockdown Italy: 5.2707 [4.9780, 5.5807]\n",
            "observation_noise Italy: 0.0883 [0.0756, 0.1033]\n",
            "doubling_time Spain: 2.2073 [1.9905, 2.4477]\n",
            "doubling_time_lockdown Spain: 2.5279 [2.1848, 2.9250]\n",
            "observation_noise Spain: 0.0889 [0.0764, 0.1036]\n",
            "\n",
            "[iteration 0901]\n",
            "loss: 827.8549\n",
            "doubling_time Italy: 3.2352 [3.1057, 3.3701]\n",
            "doubling_time_lockdown Italy: 5.2435 [4.9676, 5.5346]\n",
            "observation_noise Italy: 0.0896 [0.0765, 0.1048]\n",
            "doubling_time Spain: 2.1739 [1.9706, 2.3982]\n",
            "doubling_time_lockdown Spain: 2.6844 [2.3255, 3.0987]\n",
            "observation_noise Spain: 0.0915 [0.0786, 0.1064]\n",
            "\n",
            "Final loss: 548.1464\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
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'f': \"29468.15234375\",\n        },\n{\n            'v': 1563.2144775390625,\n            'f': \"1563.2144775390625\",\n        },\n{\n            'v': 22843.552734375,\n            'f': \"22843.552734375\",\n        },\n{\n            'v': 28345.6767578125,\n            'f': \"28345.6767578125\",\n        },\n{\n            'v': 29465.2509765625,\n            'f': \"29465.2509765625\",\n        },\n{\n            'v': 30553.75537109375,\n            'f': \"30553.75537109375\",\n        },\n{\n            'v': 34603.1796875,\n            'f': \"34603.1796875\",\n        }],\n [\"predict_observed Italy on 2020/03/17\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 31506.0,\n            'f': \"31506.0\",\n        },\n{\n            'v': 0.0,\n            'f': \"0.0\",\n        },\n{\n            'v': 31506.0,\n            'f': \"31506.0\",\n        },\n{\n            'v': 31506.0,\n            'f': \"31506.0\",\n        },\n{\n            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'v': 80589.0,\n            'f': \"80589.0\",\n        }],\n [\"predicted Italy on 2020/03/26\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 96859.03125,\n            'f': \"96859.03125\",\n        },\n{\n            'v': 7767.32958984375,\n            'f': \"7767.32958984375\",\n        },\n{\n            'v': 68468.46875,\n            'f': \"68468.46875\",\n        },\n{\n            'v': 91485.95703125,\n            'f': \"91485.95703125\",\n        },\n{\n            'v': 96626.7734375,\n            'f': \"96626.7734375\",\n        },\n{\n            'v': 102100.291015625,\n            'f': \"102100.291015625\",\n        },\n{\n            'v': 121768.375,\n            'f': \"121768.375\",\n        }],\n [\"predict_observed Italy on 2020/03/26\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 80588.8828125,\n            'f': \"80588.8828125\",\n        },\n{\n            'v': 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   },\n{\n            'v': 120.0,\n            'f': \"120.0\",\n        },\n{\n            'v': 120.0,\n            'f': \"120.0\",\n        },\n{\n            'v': 120.0,\n            'f': \"120.0\",\n        },\n{\n            'v': 120.0,\n            'f': \"120.0\",\n        }],\n [\"actual Spain on 2020/03/03\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 165.0,\n            'f': \"165.0\",\n        },\n{\n            'v': 0.0,\n            'f': \"0.0\",\n        },\n{\n            'v': 165.0,\n            'f': \"165.0\",\n        },\n{\n            'v': 165.0,\n            'f': \"165.0\",\n        },\n{\n            'v': 165.0,\n            'f': \"165.0\",\n        },\n{\n            'v': 165.0,\n            'f': \"165.0\",\n        },\n{\n            'v': 165.0,\n            'f': \"165.0\",\n        }],\n [\"predicted Spain on 2020/03/03\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 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'f': \"165.0\",\n        },\n{\n            'v': 165.0,\n            'f': \"165.0\",\n        },\n{\n            'v': 165.0,\n            'f': \"165.0\",\n        },\n{\n            'v': 165.0,\n            'f': \"165.0\",\n        }],\n [\"actual Spain on 2020/03/04\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 222.0,\n            'f': \"222.0\",\n        },\n{\n            'v': 0.0,\n            'f': \"0.0\",\n        },\n{\n            'v': 222.0,\n            'f': \"222.0\",\n        },\n{\n            'v': 222.0,\n            'f': \"222.0\",\n        },\n{\n            'v': 222.0,\n            'f': \"222.0\",\n        },\n{\n            'v': 222.0,\n            'f': \"222.0\",\n        },\n{\n            'v': 222.0,\n            'f': \"222.0\",\n        }],\n [\"predicted Spain on 2020/03/04\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 220.1143341064453,\n            'f': 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},\n{\n            'v': 259.0,\n            'f': \"259.0\",\n        },\n{\n            'v': 259.0,\n            'f': \"259.0\",\n        }],\n [\"actual Spain on 2020/03/06\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 400.0,\n            'f': \"400.0\",\n        },\n{\n            'v': 0.0,\n            'f': \"0.0\",\n        },\n{\n            'v': 400.0,\n            'f': \"400.0\",\n        },\n{\n            'v': 400.0,\n            'f': \"400.0\",\n        },\n{\n            'v': 400.0,\n            'f': \"400.0\",\n        },\n{\n            'v': 400.0,\n            'f': \"400.0\",\n        },\n{\n            'v': 400.0,\n            'f': \"400.0\",\n        }],\n [\"predicted Spain on 2020/03/06\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 419.1479187011719,\n            'f': \"419.1479187011719\",\n        },\n{\n            'v': 40.73905944824219,\n            'f': 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'f': \"400.0\",\n        },\n{\n            'v': 400.0,\n            'f': \"400.0\",\n        }],\n [\"actual Spain on 2020/03/07\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 500.0,\n            'f': \"500.0\",\n        },\n{\n            'v': 0.0,\n            'f': \"0.0\",\n        },\n{\n            'v': 500.0,\n            'f': \"500.0\",\n        },\n{\n            'v': 500.0,\n            'f': \"500.0\",\n        },\n{\n            'v': 500.0,\n            'f': \"500.0\",\n        },\n{\n            'v': 500.0,\n            'f': \"500.0\",\n        },\n{\n            'v': 500.0,\n            'f': \"500.0\",\n        }],\n [\"predicted Spain on 2020/03/07\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 578.7224731445312,\n            'f': \"578.7224731445312\",\n        },\n{\n            'v': 67.74422454833984,\n            'f': \"67.74422454833984\",\n        },\n{\n            'v': 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},\n{\n            'v': 719.3494873046875,\n            'f': \"719.3494873046875\",\n        },\n{\n            'v': 787.2491149902344,\n            'f': \"787.2491149902344\",\n        },\n{\n            'v': 868.815185546875,\n            'f': \"868.815185546875\",\n        },\n{\n            'v': 1430.4859619140625,\n            'f': \"1430.4859619140625\",\n        }],\n [\"predict_observed Spain on 2020/03/08\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 673.0,\n            'f': \"673.0\",\n        },\n{\n            'v': 0.0,\n            'f': \"0.0\",\n        },\n{\n            'v': 673.0,\n            'f': \"673.0\",\n        },\n{\n            'v': 673.0,\n            'f': \"673.0\",\n        },\n{\n            'v': 673.0,\n            'f': \"673.0\",\n        },\n{\n            'v': 673.0,\n            'f': \"673.0\",\n        },\n{\n            'v': 673.0,\n            'f': \"673.0\",\n        }],\n [\"actual Spain on 2020/03/09\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 1073.0,\n            'f': \"1073.0\",\n        },\n{\n            'v': 0.0,\n            'f': \"0.0\",\n        },\n{\n            'v': 1073.0,\n            'f': \"1073.0\",\n        },\n{\n            'v': 1073.0,\n            'f': \"1073.0\",\n        },\n{\n            'v': 1073.0,\n            'f': \"1073.0\",\n        },\n{\n            'v': 1073.0,\n            'f': \"1073.0\",\n        },\n{\n            'v': 1073.0,\n            'f': \"1073.0\",\n        }],\n [\"predicted Spain on 2020/03/09\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 1104.5142822265625,\n            'f': \"1104.5142822265625\",\n        },\n{\n            'v': 173.77415466308594,\n            'f': \"173.77415466308594\",\n        },\n{\n            'v': 698.6041870117188,\n            'f': \"698.6041870117188\",\n        },\n{\n            'v': 977.6360015869141,\n            'f': \"977.6360015869141\",\n        },\n{\n            'v': 1083.790771484375,\n            'f': \"1083.790771484375\",\n        },\n{\n            'v': 1213.0455932617188,\n            'f': \"1213.0455932617188\",\n        },\n{\n            'v': 2144.716796875,\n            'f': \"2144.716796875\",\n        }],\n [\"predict_observed Spain on 2020/03/09\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 1073.0,\n            'f': \"1073.0\",\n        },\n{\n            'v': 0.0,\n            'f': \"0.0\",\n        },\n{\n            'v': 1073.0,\n            'f': \"1073.0\",\n        },\n{\n            'v': 1073.0,\n            'f': \"1073.0\",\n        },\n{\n            'v': 1073.0,\n            'f': \"1073.0\",\n        },\n{\n            'v': 1073.0,\n            'f': \"1073.0\",\n        },\n{\n            'v': 1073.0,\n            'f': \"1073.0\",\n        }],\n [\"actual Spain on 2020/03/10\",\n{\n      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\"1328.6617736816406\",\n        },\n{\n            'v': 1492.0339965820312,\n            'f': \"1492.0339965820312\",\n        },\n{\n            'v': 1693.6624755859375,\n            'f': \"1693.6624755859375\",\n        },\n{\n            'v': 3215.5576171875,\n            'f': \"3215.5576171875\",\n        }],\n [\"predict_observed Spain on 2020/03/10\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 1695.0,\n            'f': \"1695.0\",\n        },\n{\n            'v': 0.0,\n            'f': \"0.0\",\n        },\n{\n            'v': 1695.0,\n            'f': \"1695.0\",\n        },\n{\n            'v': 1695.0,\n            'f': \"1695.0\",\n        },\n{\n            'v': 1695.0,\n            'f': \"1695.0\",\n        },\n{\n            'v': 1695.0,\n            'f': \"1695.0\",\n        },\n{\n            'v': 1695.0,\n            'f': \"1695.0\",\n        }],\n [\"actual Spain on 2020/03/11\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 2277.0,\n            'f': \"2277.0\",\n        },\n{\n            'v': 0.0,\n            'f': \"0.0\",\n        },\n{\n            'v': 2277.0,\n            'f': \"2277.0\",\n        },\n{\n            'v': 2277.0,\n            'f': \"2277.0\",\n        },\n{\n            'v': 2277.0,\n            'f': \"2277.0\",\n        },\n{\n            'v': 2277.0,\n            'f': \"2277.0\",\n        },\n{\n            'v': 2277.0,\n            'f': \"2277.0\",\n        }],\n [\"predicted Spain on 2020/03/11\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 2111.2216796875,\n            'f': \"2111.2216796875\",\n        },\n{\n            'v': 418.975830078125,\n            'f': \"418.975830078125\",\n        },\n{\n            'v': 1186.3673095703125,\n            'f': \"1186.3673095703125\",\n        },\n{\n            'v': 1805.7253112792969,\n            'f': \"1805.7253112792969\",\n        },\n{\n            'v': 2054.0545654296875,\n            'f': \"2054.0545654296875\",\n        },\n{\n            'v': 2364.702880859375,\n            'f': \"2364.702880859375\",\n        },\n{\n            'v': 4821.06103515625,\n            'f': \"4821.06103515625\",\n        }],\n [\"predict_observed Spain on 2020/03/11\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 2277.0,\n            'f': \"2277.0\",\n        },\n{\n            'v': 0.0,\n            'f': \"0.0\",\n        },\n{\n            'v': 2277.0,\n            'f': \"2277.0\",\n        },\n{\n            'v': 2277.0,\n            'f': \"2277.0\",\n        },\n{\n            'v': 2277.0,\n            'f': \"2277.0\",\n        },\n{\n            'v': 2277.0,\n            'f': \"2277.0\",\n        },\n{\n            'v': 2277.0,\n            'f': \"2277.0\",\n        }],\n [\"actual Spain on 2020/03/12\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 2277.0,\n            'f': \"2277.0\",\n        },\n{\n            'v': 0.0,\n            'f': \"0.0\",\n        },\n{\n            'v': 2277.0,\n            'f': \"2277.0\",\n        },\n{\n            'v': 2277.0,\n            'f': \"2277.0\",\n        },\n{\n            'v': 2277.0,\n            'f': \"2277.0\",\n        },\n{\n            'v': 2277.0,\n            'f': \"2277.0\",\n        },\n{\n            'v': 2277.0,\n            'f': \"2277.0\",\n        }],\n [\"predicted Spain on 2020/03/12\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 2920.56298828125,\n            'f': \"2920.56298828125\",\n        },\n{\n            'v': 640.7113647460938,\n            'f': \"640.7113647460938\",\n        },\n{\n            'v': 1546.0130615234375,\n            'f': \"1546.0130615234375\",\n        },\n{\n            'v': 2454.0812377929688,\n            'f': \"2454.0812377929688\",\n        },\n{\n            'v': 2827.777587890625,\n            'f': \"2827.777587890625\",\n        },\n{\n            'v': 3301.6141357421875,\n            'f': \"3301.6141357421875\",\n        },\n{\n            'v': 7228.18017578125,\n            'f': \"7228.18017578125\",\n        }],\n [\"predict_observed Spain on 2020/03/12\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 2277.0,\n            'f': \"2277.0\",\n        },\n{\n            'v': 0.0,\n            'f': \"0.0\",\n        },\n{\n            'v': 2277.0,\n            'f': \"2277.0\",\n        },\n{\n            'v': 2277.0,\n            'f': \"2277.0\",\n        },\n{\n            'v': 2277.0,\n            'f': \"2277.0\",\n        },\n{\n            'v': 2277.0,\n            'f': \"2277.0\",\n        },\n{\n            'v': 2277.0,\n            'f': \"2277.0\",\n        }],\n [\"actual Spain on 2020/03/13\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 5232.0,\n            'f': \"5232.0\",\n        },\n{\n            'v': 0.0,\n            'f': \"0.0\",\n        },\n{\n            'v': 5232.0,\n            'f': \"5232.0\",\n        },\n{\n            'v': 5232.0,\n            'f': \"5232.0\",\n        },\n{\n            'v': 5232.0,\n            'f': \"5232.0\",\n        },\n{\n            'v': 5232.0,\n            'f': \"5232.0\",\n        },\n{\n            'v': 5232.0,\n            'f': \"5232.0\",\n        }],\n [\"predicted Spain on 2020/03/13\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 4041.725341796875,\n            'f': \"4041.725341796875\",\n        },\n{\n            'v': 972.3643798828125,\n            'f': \"972.3643798828125\",\n        },\n{\n            'v': 2014.6849365234375,\n            'f': \"2014.6849365234375\",\n        },\n{\n            'v': 3335.2330322265625,\n            'f': \"3335.2330322265625\",\n        },\n{\n            'v': 3892.947265625,\n       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\"5359.345947265625\",\n        },\n{\n            'v': 6436.1441650390625,\n            'f': \"6436.1441650390625\",\n        },\n{\n            'v': 16248.064453125,\n            'f': \"16248.064453125\",\n        }],\n [\"predict_observed Spain on 2020/03/14\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 6391.0,\n            'f': \"6391.0\",\n        },\n{\n            'v': 0.0,\n            'f': \"0.0\",\n        },\n{\n            'v': 6391.0,\n            'f': \"6391.0\",\n        },\n{\n            'v': 6391.0,\n            'f': \"6391.0\",\n        },\n{\n            'v': 6391.0,\n            'f': \"6391.0\",\n        },\n{\n            'v': 6391.0,\n            'f': \"6391.0\",\n        },\n{\n            'v': 6391.0,\n            'f': \"6391.0\",\n        }],\n [\"actual Spain on 2020/03/15\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 7798.0,\n            'f': \"7798.0\",\n       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'v': 74657.953125,\n            'f': \"74657.953125\",\n        }],\n [\"predict_observed Spain on 2020/03/20\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 20410.0,\n            'f': \"20410.0\",\n        },\n{\n            'v': 0.0,\n            'f': \"0.0\",\n        },\n{\n            'v': 20410.0,\n            'f': \"20410.0\",\n        },\n{\n            'v': 20410.0,\n            'f': \"20410.0\",\n        },\n{\n            'v': 20410.0,\n            'f': \"20410.0\",\n        },\n{\n            'v': 20410.0,\n            'f': \"20410.0\",\n        },\n{\n            'v': 20410.0,\n            'f': \"20410.0\",\n        }],\n [\"actual Spain on 2020/03/21\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 25374.0,\n            'f': \"25374.0\",\n        },\n{\n            'v': 0.0,\n            'f': \"0.0\",\n        },\n{\n            'v': 25374.0,\n            'f': \"25374.0\",\n       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'f': \"39885.0\",\n        },\n{\n            'v': 39885.0,\n            'f': \"39885.0\",\n        },\n{\n            'v': 39885.0,\n            'f': \"39885.0\",\n        }],\n [\"predicted Spain on 2020/03/24\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 65692.34375,\n            'f': \"65692.34375\",\n        },\n{\n            'v': 23721.29296875,\n            'f': \"23721.29296875\",\n        },\n{\n            'v': 26074.6875,\n            'f': \"26074.6875\",\n        },\n{\n            'v': 49721.5546875,\n            'f': \"49721.5546875\",\n        },\n{\n            'v': 61222.85546875,\n            'f': \"61222.85546875\",\n        },\n{\n            'v': 77226.87890625,\n            'f': \"77226.87890625\",\n        },\n{\n            'v': 206344.234375,\n            'f': \"206344.234375\",\n        }],\n [\"predict_observed Spain on 2020/03/24\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 39884.421875,\n            'f': \"39884.421875\",\n        },\n{\n            'v': 0.578414261341095,\n            'f': \"0.578414261341095\",\n        },\n{\n            'v': 39885.0,\n            'f': \"39885.0\",\n        },\n{\n            'v': 39885.0,\n            'f': \"39885.0\",\n        },\n{\n            'v': 39885.0,\n            'f': \"39885.0\",\n        },\n{\n            'v': 39885.0,\n            'f': \"39885.0\",\n        },\n{\n            'v': 39885.0,\n            'f': \"39885.0\",\n        }],\n [\"actual Spain on 2020/03/25\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 49515.66015625,\n            'f': \"49515.66015625\",\n        },\n{\n            'v': 0.6604818105697632,\n            'f': \"0.6604818105697632\",\n        },\n{\n            'v': 49515.0,\n            'f': \"49515.0\",\n        },\n{\n            'v': 49515.0,\n            'f': \"49515.0\",\n        },\n{\n            'v': 49515.0,\n 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'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 57785.16015625,\n            'f': \"57785.16015625\",\n        },\n{\n            'v': 0.8402581810951233,\n            'f': \"0.8402581810951233\",\n        },\n{\n            'v': 57786.0,\n            'f': \"57786.0\",\n        },\n{\n            'v': 57786.0,\n            'f': \"57786.0\",\n        },\n{\n            'v': 57786.0,\n            'f': \"57786.0\",\n        },\n{\n            'v': 57786.0,\n            'f': \"57786.0\",\n        },\n{\n            'v': 57786.0,\n            'f': \"57786.0\",\n        }],\n [\"actual Spain on 2020/03/27\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 65719.7421875,\n            'f': \"65719.7421875\",\n        },\n{\n            'v': 0.7425588965415955,\n            'f': \"0.7425588965415955\",\n        },\n{\n            'v': 65719.0,\n            'f': \"65719.0\",\n        },\n{\n            'v': 65719.0,\n        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2020/03/27\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 65719.7421875,\n            'f': \"65719.7421875\",\n        },\n{\n            'v': 0.7425588965415955,\n            'f': \"0.7425588965415955\",\n        },\n{\n            'v': 65719.0,\n            'f': \"65719.0\",\n        },\n{\n            'v': 65719.0,\n            'f': \"65719.0\",\n        },\n{\n            'v': 65719.0,\n            'f': \"65719.0\",\n        },\n{\n            'v': 65719.0,\n            'f': \"65719.0\",\n        },\n{\n            'v': 65719.0,\n            'f': \"65719.0\",\n        }],\n [\"predicted Spain on 2020/03/28\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 178202.90625,\n            'f': \"178202.90625\",\n        },\n{\n            'v': 77222.6953125,\n            'f': \"77222.6953125\",\n        },\n{\n            'v': 56154.6875,\n            'f': \"56154.6875\",\n        },\n{\n            'v': 126340.05078125,\n            'f': \"126340.05078125\",\n        },\n{\n            'v': 161199.4296875,\n            'f': \"161199.4296875\",\n        },\n{\n            'v': 211736.8828125,\n            'f': \"211736.8828125\",\n        },\n{\n            'v': 605581.5625,\n            'f': \"605581.5625\",\n        }],\n [\"predicted Spain on 2020/03/29\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 228966.140625,\n            'f': \"228966.140625\",\n        },\n{\n            'v': 103846.8125,\n            'f': \"103846.8125\",\n        },\n{\n            'v': 68026.4375,\n            'f': \"68026.4375\",\n        },\n{\n            'v': 158670.39453125,\n            'f': \"158670.39453125\",\n        },\n{\n            'v': 205964.2265625,\n            'f': \"205964.2265625\",\n        },\n{\n            'v': 271373.1484375,\n            'f': \"271373.1484375\",\n        },\n{\n            'v': 810906.4375,\n            'f': \"810906.4375\",\n        }],\n [\"predicted Spain on 2020/03/30\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 294328.6875,\n            'f': \"294328.6875\",\n        },\n{\n            'v': 139674.203125,\n            'f': \"139674.203125\",\n        },\n{\n            'v': 82408.015625,\n            'f': \"82408.015625\",\n        },\n{\n            'v': 199308.4609375,\n            'f': \"199308.4609375\",\n        },\n{\n            'v': 263254.609375,\n            'f': \"263254.609375\",\n        },\n{\n            'v': 350478.8125,\n            'f': \"350478.8125\",\n        },\n{\n            'v': 1103293.75,\n            'f': \"1103293.75\",\n        }],\n [\"predicted Spain on 2020/03/31\",\n{\n            'v': 1000.0,\n            'f': \"1000.0\",\n        },\n{\n            'v': 378529.03125,\n            'f': \"378529.03125\",\n        },\n{\n            'v': 187879.59375,\n            'f': \"187879.59375\",\n        },\n{\n            'v': 99830.0234375,\n            'f': \"99830.0234375\",\n        },\n{\n            'v': 251700.07421875,\n            'f': \"251700.07421875\",\n        },\n{\n            'v': 336425.609375,\n            'f': \"336425.609375\",\n        },\n{\n            'v': 451742.3125,\n            'f': \"451742.3125\",\n        },\n{\n            'v': 1521304.0,\n            'f': \"1521304.0\",\n        }]],\n        columns: [[\"string\", \"index\"], [\"number\", \"count\"], [\"number\", \"mean\"], [\"number\", \"std\"], [\"number\", \"min\"], [\"number\", \"25%\"], [\"number\", \"50%\"], [\"number\", \"75%\"], [\"number\", \"max\"]],\n        columnOptions: [{\"width\": \"1px\", \"className\": \"index_column\"}],\n        rowsPerPage: 25,\n        helpUrl: \"https://colab.research.google.com/notebooks/data_table.ipynb\",\n        suppressOutputScrolling: true,\n      });\n    ",
            "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>count</th>\n",
              "      <th>mean</th>\n",
              "      <th>std</th>\n",
              "      <th>min</th>\n",
              "      <th>25%</th>\n",
              "      <th>50%</th>\n",
              "      <th>75%</th>\n",
              "      <th>max</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>doubling_time Italy</th>\n",
              "      <td>1000.0</td>\n",
              "      <td>3.232849</td>\n",
              "      <td>0.074797</td>\n",
              "      <td>3.005837</td>\n",
              "      <td>3.180853</td>\n",
              "      <td>3.231117</td>\n",
              "      <td>3.281363</td>\n",
              "      <td>3.569232e+00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>doubling_time_lockdown Italy</th>\n",
              "      <td>1000.0</td>\n",
              "      <td>5.255781</td>\n",
              "      <td>0.166990</td>\n",
              "      <td>4.755096</td>\n",
              "      <td>5.142208</td>\n",
              "      <td>5.246454</td>\n",
              "      <td>5.364786</td>\n",
              "      <td>5.850306e+00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>observation_noise Italy</th>\n",
              "      <td>1000.0</td>\n",
              "      <td>0.091576</td>\n",
              "      <td>0.008699</td>\n",
              "      <td>0.068875</td>\n",
              "      <td>0.085420</td>\n",
              "      <td>0.090952</td>\n",
              "      <td>0.097308</td>\n",
              "      <td>1.265293e-01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>predict_observed Italy on 2020/03/28</th>\n",
              "      <td>1000.0</td>\n",
              "      <td>125781.632812</td>\n",
              "      <td>16179.833984</td>\n",
              "      <td>78046.007812</td>\n",
              "      <td>115215.675781</td>\n",
              "      <td>125122.894531</td>\n",
              "      <td>135135.671875</td>\n",
              "      <td>1.880543e+05</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>predict_observed Italy on 2020/03/29</th>\n",
              "      <td>1000.0</td>\n",
              "      <td>144580.375000</td>\n",
              "      <td>18696.285156</td>\n",
              "      <td>81206.281250</td>\n",
              "      <td>131607.417969</td>\n",
              "      <td>143576.250000</td>\n",
              "      <td>156668.558594</td>\n",
              "      <td>2.255855e+05</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",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>predict_observed Spain on 2020/03/27</th>\n",
              "      <td>1000.0</td>\n",
              "      <td>65719.742188</td>\n",
              "      <td>0.742559</td>\n",
              "      <td>65719.000000</td>\n",
              "      <td>65719.000000</td>\n",
              "      <td>65719.000000</td>\n",
              "      <td>65719.000000</td>\n",
              "      <td>6.571900e+04</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>predicted Spain on 2020/03/28</th>\n",
              "      <td>1000.0</td>\n",
              "      <td>178202.906250</td>\n",
              "      <td>77222.695312</td>\n",
              "      <td>56154.687500</td>\n",
              "      <td>126340.050781</td>\n",
              "      <td>161199.429688</td>\n",
              "      <td>211736.882812</td>\n",
              "      <td>6.055816e+05</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>predicted Spain on 2020/03/29</th>\n",
              "      <td>1000.0</td>\n",
              "      <td>228966.140625</td>\n",
              "      <td>103846.812500</td>\n",
              "      <td>68026.437500</td>\n",
              "      <td>158670.394531</td>\n",
              "      <td>205964.226562</td>\n",
              "      <td>271373.148438</td>\n",
              "      <td>8.109064e+05</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>predicted Spain on 2020/03/30</th>\n",
              "      <td>1000.0</td>\n",
              "      <td>294328.687500</td>\n",
              "      <td>139674.203125</td>\n",
              "      <td>82408.015625</td>\n",
              "      <td>199308.460938</td>\n",
              "      <td>263254.609375</td>\n",
              "      <td>350478.812500</td>\n",
              "      <td>1.103294e+06</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>predicted Spain on 2020/03/31</th>\n",
              "      <td>1000.0</td>\n",
              "      <td>378529.031250</td>\n",
              "      <td>187879.593750</td>\n",
              "      <td>99830.023438</td>\n",
              "      <td>251700.074219</td>\n",
              "      <td>336425.609375</td>\n",
              "      <td>451742.312500</td>\n",
              "      <td>1.521304e+06</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>178 rows × 8 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "                                       count  ...           max\n",
              "doubling_time Italy                   1000.0  ...  3.569232e+00\n",
              "doubling_time_lockdown Italy          1000.0  ...  5.850306e+00\n",
              "observation_noise Italy               1000.0  ...  1.265293e-01\n",
              "predict_observed Italy on 2020/03/28  1000.0  ...  1.880543e+05\n",
              "predict_observed Italy on 2020/03/29  1000.0  ...  2.255855e+05\n",
              "...                                      ...  ...           ...\n",
              "predict_observed Spain on 2020/03/27  1000.0  ...  6.571900e+04\n",
              "predicted Spain on 2020/03/28         1000.0  ...  6.055816e+05\n",
              "predicted Spain on 2020/03/29         1000.0  ...  8.109064e+05\n",
              "predicted Spain on 2020/03/30         1000.0  ...  1.103294e+06\n",
              "predicted Spain on 2020/03/31         1000.0  ...  1.521304e+06\n",
              "\n",
              "[178 rows x 8 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 126
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OH6QrQlCquAp",
        "colab_type": "code",
        "outputId": "2c49c3d8-e38b-4f6c-c424-7711b0b2840b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 545
        }
      },
      "source": [
        "from datetime import datetime\n",
        "\n",
        "to_plot = [\n",
        "  # (\"predict_observed\", \"predict_observed {area} on {date}\"),\n",
        "  (\"predicted\", \"predicted {area} on {date}\"),\n",
        "  (\"actual\", \"actual {area} on {date}\"), \n",
        "]\n",
        "\n",
        "high_quantile = 0.95\n",
        "low_quantile = 0.05\n",
        "\n",
        "for area in areas:\n",
        "  for name, template in to_plot:    \n",
        "    indices = [x for x in range((end_date - start_date).days)]\n",
        "    highs = []\n",
        "    lows = []\n",
        "    means = []\n",
        "    for i in indices:\n",
        "      date = start_date.add(days=i)\n",
        "      datestr = date.format('YYYY/MM/DD')\n",
        "      key = template.format(area = area, date=datestr)\n",
        "      try:\n",
        "        means.append(samples[key].mean())\n",
        "        highs.append(samples[key].quantile(high_quantile))\n",
        "        lows.append(samples[key].quantile(low_quantile))\n",
        "      except KeyError:\n",
        "        means.append(float(\"NaN\"))\n",
        "        highs.append(float(\"NaN\"))\n",
        "        lows.append(float(\"NaN\"))\n",
        "    pyplot.fill_between(indices, lows, highs, label=name, alpha=0.5)\n",
        "    pyplot.plot(indices, means, label=name)\n",
        "  pyplot.title(area)\n",
        "  pyplot.legend()\n",
        "  pyplot.yscale(\"log\")\n",
        "  pyplot.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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pV1hPqEdLqDscGecuhJ3RWlOwfxteqU8S35hFk3s4n419nMNBCzhU0cqeIyV0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\nAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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MFlSFGIdcLs2p6mYOllpo7x7aYqnd6eLDC00cq2ik2zm8uuo+LgdxraeZ1nSI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\nQwihhyK5hxBCD/0CXTEBOf4jr+AAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}