diff --git a/Projects/GalacticCenter/GalacticCenter.ipynb b/Projects/GalacticCenter/GalacticCenter.ipynb new file mode 100644 index 0000000..c79a06c --- /dev/null +++ b/Projects/GalacticCenter/GalacticCenter.ipynb @@ -0,0 +1,33 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "id": "7d6b1fe9", + "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": "3.8.8" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/Projects/MeasurementUncertainty/MeasurementUncertainty.ipynb b/Projects/MeasurementUncertainty/MeasurementUncertainty.ipynb new file mode 100644 index 0000000..25548d3 --- /dev/null +++ b/Projects/MeasurementUncertainty/MeasurementUncertainty.ipynb @@ -0,0 +1,237 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "af6ff963", + "metadata": {}, + "source": [ + "# Measurement Uncertainty and Error Propagation" + ] + }, + { + "cell_type": "markdown", + "id": "69eea134", + "metadata": {}, + "source": [ + "\"All measurements, however careful and scientific, are subject to some uncertainties.\" \n", + "-J.R Taylor in *An Introduction to Error Analysis*" + ] + }, + { + "cell_type": "markdown", + "id": "686a6f01", + "metadata": {}, + "source": [ + "## Inevitability of Uncertainty" + ] + }, + { + "cell_type": "markdown", + "id": "16c11299", + "metadata": {}, + "source": [ + "Every time we conduct a measurement, the number we obtain comes with an associated uncertainty. This uncertainty quantifies the precision of the experiment as well as our degree of ignorance of the targeted number.\n", + "\n", + "For example, every time we use a tape measure, graduated in eigths of an inch, we may be able to tell that say, the length of a window, is between 54 1/8'' and 54 2/8'' --or between 54.175 in and 54.25 in. But we are unable to precisely tell if the length is 54.18 in or 54.24 in. Moreover, if the tape measure *appears* to exactly fall at the 54 1/8'' mark, we are not able to tell accurately if the length of the window is 54.175 or 54.1750001," + ] + }, + { + "cell_type": "markdown", + "id": "de87126a", + "metadata": {}, + "source": [ + "## Types of error" + ] + }, + { + "cell_type": "markdown", + "id": "fe92da1e", + "metadata": {}, + "source": [ + "**Measurement uncertainty** is often (but not always) used interchangeably with **experimental error**" + ] + }, + { + "cell_type": "markdown", + "id": "6c1af631", + "metadata": {}, + "source": [ + "$$(\\rm{ measured}\\,A)=A_\\rm{ best}\\pm\\delta A$$" + ] + }, + { + "cell_type": "markdown", + "id": "67977c29", + "metadata": {}, + "source": [ + "## Displaying Uncertainty in a Graph: Error bars" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "effc4fe5", + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import pandas as pd\n", + "%matplotlib inline\n", + "\n", + "kepler_url=\"https://exoplanetarchive.ipac.caltech.edu/cgi-bin/nstedAPI/nph-nstedAPI?table=cumulative&where=koi_disposition+like+'CONFIRMED'&format=csv\"\n", + "df=pd.read_csv(kepler_url) " + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "id": "7f0c0748", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Index(['kepid', 'kepoi_name', 'kepler_name', 'koi_disposition',\n", + " 'koi_pdisposition', 'koi_score', 'koi_fpflag_nt', 'koi_fpflag_ss',\n", + " 'koi_fpflag_co', 'koi_fpflag_ec', 'koi_period', 'koi_period_err1',\n", + " 'koi_period_err2', 'koi_time0bk', 'koi_time0bk_err1',\n", + " 'koi_time0bk_err2', 'koi_impact', 'koi_impact_err1', 'koi_impact_err2',\n", + " 'koi_duration', 'koi_duration_err1', 'koi_duration_err2', 'koi_depth',\n", + " 'koi_depth_err1', 'koi_depth_err2', 'koi_prad', 'koi_prad_err1',\n", + " 'koi_prad_err2', 'koi_teq', 'koi_teq_err1', 'koi_teq_err2', 'koi_insol',\n", + " 'koi_insol_err1', 'koi_insol_err2', 'koi_model_snr', 'koi_tce_plnt_num',\n", + " 'koi_tce_delivname', 'koi_steff', 'koi_steff_err1', 'koi_steff_err2',\n", + " 'koi_slogg', 'koi_slogg_err1', 'koi_slogg_err2', 'koi_srad',\n", + " 'koi_srad_err1', 'koi_srad_err2', 'ra_str', 'dec_str', 'koi_kepmag',\n", + " 'koi_kepmag_err'],\n", + " dtype='object')\n" + ] + } + ], + "source": [ + "print(df.columns)" + ] + }, + { + "cell_type": "markdown", + "id": "57f6ed45", + "metadata": {}, + "source": [ + "Now let us make an error bar graph plotting the planet radius \\\\( R_{\\rm p}\\\\) (labeled 'koi_radius' in the dataframe) vs the planet period (labeled 'koi_period'). We include the uncertainties in both period and radius. Note that the uncertainty **above** the \"best measurement\" does not necessarily equal to the uncertainty **below** the measurement. Also, note that, although the uncertainties in the period are included" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "id": "21b7be25", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(1,figsize=(10,8))\n", + "ax=fig.add_subplot(111)\n", + "\n", + "ax.errorbar(df['koi_period'],df['koi_prad'],yerr=[-df['koi_prad_err2'].values,df['koi_prad_err1'].values],\n", + " xerr=[-df['koi_period_err2'].values,df['koi_period_err1'].values],fmt='s',lw=0.5,ms=3.0)\n", + "ax.set_xscale('log')\n", + "ax.set_yscale('log')\n", + "ax.set_xlabel(r'$P_{\\rm p}[{\\rm d}]$',size=26)\n", + "ax.set_ylabel(r'$R_{\\rm p}[R_{\\oplus}]$',size=26)\n", + "ax.tick_params(axis='both',width=2,length=4,labelsize=18)\n", + "ax.tick_params(axis='both',which='both',width=2)" + ] + }, + { + "cell_type": "markdown", + "id": "5071e7b0", + "metadata": {}, + "source": [ + "Now, nobody went toward each planetary system and used a ruler to measure each planet's radius. So how were all these radii measured? More importantly for our current purposes: how are those radius uncertainties calculated if no ruler was used?" + ] + }, + { + "cell_type": "markdown", + "id": "6f1dd11e", + "metadata": {}, + "source": [ + "## Error propagation" + ] + }, + { + "cell_type": "markdown", + "id": "e5a6bff3", + "metadata": {}, + "source": [ + "Multiple textbooks cover the concept of *error propagation*" + ] + }, + { + "cell_type": "markdown", + "id": "63d1ec31", + "metadata": {}, + "source": [ + "## Measurements as Random Variables" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "499cc3f7", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy.random as rnd\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c23d6e81", + "metadata": {}, + "outputs": [], + "source": [ + "np.random.seed(19680801)\n", + "\n", + "# example data\n", + "mu = 100 # mean of distribution\n", + "sigma = 15 # standard deviation of distribution\n", + "x = mu + sigma * np.random.randn(437)" + ] + } + ], + "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": "3.8.8" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}