{ "cells": [ { "cell_type": "markdown", "metadata": { "papermill": { "duration": 0.013228, "end_time": "2020-03-28T20:07:07.958634", "exception": false, "start_time": "2020-03-28T20:07:07.945406", "status": "completed" }, "tags": [] }, "source": [ "# COVID-19 Growth Rate Prediction\n", "> Predictions of COVID-19 Growth Rates Using Bayesian Modeling\n", "\n", "- comments: true\n", "- author: Thomas Wiecki & Hamel Husain\n", "- categories: [growth, MCMC]\n", "- image: images/covid-bayesian.png\n", "- permalink: /growth-bayes/" ] }, { "cell_type": "markdown", "metadata": { "papermill": { "duration": 0.009684, "end_time": "2020-03-28T20:07:07.978892", "exception": false, "start_time": "2020-03-28T20:07:07.969208", "status": "completed" }, "tags": [] }, "source": [ "> Note: This dashboard contains the results of a predictive model. The author has tried to make it as accurate as possible. But the COVID-19 situation is changing quickly, and these models inevitably include some level of speculation." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "papermill": { "duration": 0.018499, "end_time": "2020-03-28T20:07:08.007221", "exception": false, "start_time": "2020-03-28T20:07:07.988722", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "#hide\n", "from pathlib import Path\n", "\n", "loadpy = Path('load_covid_data.py')\n", "if not loadpy.exists():\n", " ! wget https://raw.githubusercontent.com/github/covid19-dashboard/master/_notebooks/load_covid_data.py" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "papermill": { "duration": 4.135398, "end_time": "2020-03-28T20:07:12.152011", "exception": false, "start_time": "2020-03-28T20:07:08.016613", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "WARNING (theano.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n" ] } ], "source": [ "#hide\n", "%matplotlib inline\n", "import numpy as np\n", "from IPython.display import display, Markdown\n", "import matplotlib.pyplot as plt\n", "import matplotlib\n", "import pandas as pd\n", "import seaborn as sns\n", "import arviz as az\n", "import pymc3 as pm\n", "import altair as alt\n", "\n", "import load_covid_data\n", "\n", "sns.set_context('talk')\n", "plt.style.use('seaborn-whitegrid')\n", "\n", "## Set this to true to see legacy charts\n", "debug=False" ] }, { "cell_type": "markdown", "metadata": { "papermill": { "duration": 0.009888, "end_time": "2020-03-28T20:07:12.172418", "exception": false, "start_time": "2020-03-28T20:07:12.162530", "status": "completed" }, "tags": [] }, "source": [ "## Data" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "papermill": { "duration": 1.835421, "end_time": "2020-03-28T20:07:14.017985", "exception": false, "start_time": "2020-03-28T20:07:12.182564", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "#hide\n", "\n", "df = load_covid_data.load_data(drop_states=True, filter_n_days_100=2)\n", "# We only have data for China after they already had a significant number of cases.\n", "# They also are not well modeled by the exponential, so we drop them here for simplicity.\n", "df = df.loc[lambda x: x.country != 'China (total)']\n", "\n", "countries = df.country.unique()\n", "n_countries = len(countries)\n", "df = df.loc[lambda x: (x.days_since_100 >= 0)]\n", "\n", "annotate_kwargs = dict(\n", " s='Based on COVID Data Repository by Johns Hopkins CSSE ({})\\nBy Thomas Wiecki'.format(df.index.max().strftime('%B %d, %Y')), \n", " xy=(0.05, 0.01), xycoords='figure fraction', fontsize=10)" ] }, { "cell_type": "markdown", "metadata": { "papermill": { "duration": 0.010134, "end_time": "2020-03-28T20:07:14.038380", "exception": false, "start_time": "2020-03-28T20:07:14.028246", "status": "completed" }, "tags": [] }, "source": [ "These are the countries included in the model:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "papermill": { "duration": 0.021951, "end_time": "2020-03-28T20:07:14.070296", "exception": false, "start_time": "2020-03-28T20:07:14.048345", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "text/plain": [ "'Albania, Algeria, Andorra, Argentina, Armenia, Australia (total), Austria, Bahrain, Belgium, Bosnia and Herzegovina, Brazil, Brunei, Bulgaria, Burkina Faso, Canada (total), Chile, Colombia, Costa Rica, Croatia, Cyprus, Czechia, Denmark, Denmark (total), Diamond Princess, Dominican Republic, Ecuador, Egypt, Estonia, Finland, France, France (total), Germany, Greece, Hong Kong, Hungary, Iceland, India, Indonesia, Iran, Iraq, Ireland, Israel, Italy, Japan, Jordan, Korea, South, Kuwait, Latvia, Lebanon, Lithuania, Luxembourg, Malaysia, Malta, Mexico, Moldova, Morocco, Netherlands, New Zealand, North Macedonia, Norway, Pakistan, Panama, Peru, Philippines, Poland, Portugal, Qatar, Romania, Russia, San Marino, Saudi Arabia, Serbia, Singapore, Slovakia, Slovenia, South Africa, Spain, Sri Lanka, Sweden, Switzerland, Taiwan*, Thailand, Tunisia, Turkey, US, Ukraine, United Arab Emirates, United Kingdom, United Kingdom (total), Uruguay, Vietnam'" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#hide_input\n", "', '.join(sorted(df.country.unique().tolist()))" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "papermill": { "duration": 86.205638, "end_time": "2020-03-28T20:08:40.286666", "exception": false, "start_time": "2020-03-28T20:07:14.081028", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "#hide\n", "\n", "#####################################\n", "##### This Cell Runs The Model ######\n", "#####################################\n", "\n", "with pm.Model() as model:\n", " ############\n", " # Intercept\n", " # Group mean\n", " a_grp = pm.Normal('a_grp', 100, 50)\n", " # Group variance\n", " a_grp_sigma = pm.HalfNormal('a_grp_sigma', 50)\n", " # Individual intercepts\n", " a_ind = pm.Normal('a_ind', \n", " mu=a_grp, sigma=a_grp_sigma, \n", " shape=n_countries)\n", " ########\n", " # Slope\n", " # Group mean\n", " b_grp = pm.Normal('b_grp', 1.33, .5)\n", " # Group variance\n", " b_grp_sigma = pm.HalfNormal('b_grp_sigma', .5)\n", " # Individual slopes\n", " b_ind = pm.Normal('b_ind', \n", " mu=b_grp, sigma=b_grp_sigma, \n", " shape=n_countries)\n", " \n", " # Error\n", " sigma = pm.HalfNormal('sigma', 500., shape=n_countries)\n", " \n", " # Create likelihood for each country\n", " for i, country in enumerate(countries):\n", " df_country = df.loc[lambda x: (x.country == country)]\n", " \n", " # By using pm.Data we can change these values after sampling.\n", " # This allows us to extend x into the future so we can get\n", " # forecasts by sampling from the posterior predictive\n", " x = pm.Data(country + \"x_data\", \n", " df_country.days_since_100.values)\n", " confirmed = pm.Data(country + \"y_data\", \n", " df_country.confirmed.astype('float64').values)\n", " \n", " # Likelihood\n", " pm.NegativeBinomial(\n", " country, \n", " (a_ind[i] * b_ind[i] ** x), # Exponential regression\n", " sigma[i], \n", " observed=confirmed)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "papermill": { "duration": 1289.41235, "end_time": "2020-03-28T20:30:09.709559", "exception": false, "start_time": "2020-03-28T20:08:40.297209", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Initializing NUTS using jitter+adapt_diag...\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Sequential sampling (1 chains in 1 job)\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "NUTS: [sigma, b_ind, b_grp_sigma, b_grp, a_ind, a_grp_sigma, a_grp]\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ 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"text": [ "\r", " 98%|█████████▊| 78/80 [01:22<00:01, 1.00it/s]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", " 99%|█████████▉| 79/80 [01:23<00:00, 1.03it/s]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "100%|██████████| 80/80 [01:24<00:00, 1.05it/s]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "100%|██████████| 80/80 [01:24<00:00, 1.06s/it]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "#hide\n", "with model:\n", " # Sample posterior\n", " trace = pm.sample(tune=1500, chains=1, cores=2, target_accept=.9)\n", " \n", " # Update data so that we get predictions into the future\n", " for country in countries:\n", " df_country = df.loc[lambda x: (x.country == country)]\n", " x_data = np.arange(0, 30)\n", " y_data = np.array([np.nan] * len(x_data))\n", " pm.set_data({country + \"x_data\": x_data})\n", " pm.set_data({country + \"y_data\": y_data})\n", " \n", " # Sample posterior predictive\n", " post_pred = pm.sample_posterior_predictive(trace, samples=80)" ] }, { "cell_type": "markdown", "metadata": { "papermill": { "duration": 0.598317, "end_time": "2020-03-28T20:30:10.891461", "exception": false, "start_time": "2020-03-28T20:30:10.293144", "status": "completed" }, "tags": [] }, "source": [ "## Predicted Cases By Country\n", "\n", "Select a country from the drop down list below to toggle the visualization. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "papermill": { "duration": 1.118124, "end_time": "2020-03-28T20:30:12.598233", "exception": false, "start_time": "2020-03-28T20:30:11.480109", "status": "completed" }, "scrolled": true, "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/opt/hostedtoolcache/Python/3.6.10/x64/lib/python3.6/site-packages/ipykernel_launcher.py:55: SettingWithCopyWarning: \n", "A value is trying to be set on a copy of a slice from a DataFrame.\n", "Try using .loc[row_indexer,col_indexer] = value instead\n", "\n", "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n" ] } ], "source": [ "#hide\n", "\n", "##############################################\n", "#### Pre processing of Data For Altair Viz ###\n", "##############################################\n", "\n", "# Flatten predictions & target for each country into a pandas DataFrame\n", "prediction_dfs_list = []\n", "\n", "for country in post_pred:\n", " arr = post_pred[country]\n", " preds = arr.flatten().tolist() # get predictions in a flattened array\n", " pred_idx = np.indices(arr.shape)[0].flatten().tolist() # prediction for model (there are many per country, thes are the grey lines)\n", " days_since = np.indices(arr.shape)[1].flatten().tolist() # days since 100 cases\n", " pred_df = pd.DataFrame({'country': country, \n", " 'predictions': preds, \n", " 'pred_idx': pred_idx,\n", " 'days_since_100': days_since}\n", " )\n", " prediction_dfs_list.append(pred_df)\n", "\n", "predictionsDF = pd.concat(prediction_dfs_list)\n", "\n", "\n", "# Compute the maximum value to plot on the y-axis as 15x the last confirmed case\n", "ylims = pd.DataFrame(df.groupby('country').last().confirmed * 15).reset_index()\n", "ylims.columns = ['country', 'ylim']\n", "\n", "\n", "# Filter out any predictions exceed the y-axis limit\n", "predictionsDF_filtered = (predictionsDF.merge(ylims, on='country', how='left')\n", " .loc[lambda x: x.predictions <= x.ylim])\n", "\n", "\n", "# Compute a 33% daily growth rate (dashed line) as a reference for visualizations\n", "first_case_count = df.groupby('country').first().confirmed.reset_index()\n", "date_anchor = predictionsDF_filtered[['country', 'days_since_100']].drop_duplicates()\n", "max_pred = predictionsDF_filtered.groupby('country').max()[['predictions']].reset_index()\n", "benchmark = (date_anchor\n", " .merge(first_case_count, on='country', how='left')\n", " .merge(max_pred, on='country', how='left')\n", " )\n", "benchmark['benchmark'] = benchmark.apply(lambda x: x.confirmed * (1.3**(x.days_since_100)),\n", " axis=1)\n", "benchmarkDF_filtered = benchmark.loc[lambda x: x.benchmark <= x.predictions]\n", "\n", "\n", "# Compute the last known total confirmed case, which is the black dot at the end of the red line in the viz\n", "lastpointDF = df.groupby('country').last().reset_index()\n", "\n", "\n", "# DataFrame of Chart Titles by country. This a enables a hack to allow Altiar to switch values\n", "titleDF = lastpointDF[['country']]\n", "titleDF['title'] = titleDF.apply(lambda x: x.country + ': Actual vs. Predicted Growth',\n", " axis=1)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "papermill": { "duration": 5.893886, "end_time": "2020-03-28T20:30:19.100925", "exception": false, "start_time": "2020-03-28T20:30:13.207039", "status": "completed" }, "scrolled": false, "tags": [] }, "outputs": [ { "data": { "text/html": [ "\n", "
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