{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "#Chapter 2: Estimation and errors: Describing data" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab inline\n", "import numpy as np\n", "import pylab as plt\n", "import figrc\n", "\n", "theme = figrc.Theme_Gray() + figrc.Theme_Ezrc(16, 1, 22)\n", "theme.apply()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Background information\n", "\n", "## Exploring the stellar parameter dataset from the lecture\n", "\n", "Look at the file `star.dat` in the data directory. This contains the astrophysical parameters (columns) for\n", "stars (one star per row). \n", "\n", "We will now explore the different properties from this dataset and highlight some correlations and eventually emphasize the physics." ] }, { "cell_type": "code", "execution_count": 225, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "dtype([('g', '" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.hist(np.log10(data['mass']), bins=60)\n", "plt.xlabel(r'log$_{10}$(M/M$_\\odot$)')\n", "plt.ylabel(r'dN/dlogM');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* A boxplot showing the dispersion of the data in the `teff` column when binned according to `logg` values\n", "\n", "**In python there is never one single method to do so.**\n", "\n", "Below, I do the plot from basic libraries and then with Pandas. \n", "Note that `pandas` and `seaborn` could offer good alternatives but requires some learning." ] }, { "cell_type": "code", "execution_count": 71, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from itertools import groupby\n", "\n", "#extract column information and sort by logg\n", "logg = np.round(data['logg'])\n", "ind = np.argsort(logg)\n", "teff = data['teff'][ind]\n", "logg = np.round(data['logg'])[ind]\n", "\n", "# group data by logg values\n", "d = []\n", "pos = []\n", "for v, g in groupby(zip(teff, logg), lambda x: x[1]):\n", " pos.append(v)\n", " d.append(np.array(list(g))[:, 0])\n", "\n", "# plot\n", "plt.boxplot(d, positions=pos, widths=0.9)\n", "plt.ylim(3900, 8100)\n", "plt.xlabel('logg')\n", "plt.ylabel('teff');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using the `pandas` package, could be a bit more efficient for this particular plot. Below I give an example of similar figure using `pandas`" ] }, { "cell_type": "code", "execution_count": 138, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from pandas import DataFrame\n", "\n", "df = DataFrame(data)\n", "df.boxplot('teff', by=np.round(df['logg']), widths=0.9);\n", "plt.suptitle('')\n", "plt.title('')\n", "plt.ylim(3900, 8100)\n", "plt.xlabel('logg')\n", "plt.ylabel('teff');\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Some 2d distributions\n", "\n", "Again many possibilities to make similar plots. I only show one method, feel free to explore other ways." ] }, { "cell_type": "code", "execution_count": 104, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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CKXbroKUS8Wz4aHS0C2+8ocOcOUbMmWPEtm2NXDhmSoqJyxmxa5cC27c3IinJ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\nwPbt2/td33XUvr7Ud9z5dKd9p06dwr59+5Cfn8//7+2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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(np.log10(data['teff']), data['mg'])\n", "plt.ylim(plt.ylim()[::-1])\n", "plt.xlim(plt.xlim()[::-1])\n", "plt.xlabel('log$_{10}$Teff')\n", "plt.ylabel('M$_G$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Density distributions can be represented by many means. Below I show an histrogram and a gaussian kernel density estimator." ] }, { "cell_type": "code", "execution_count": 106, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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nYrGYYrHYhOO3tbUpEmkYM3ZDyjEymx5rNQ0+uDiB8HUpsufWwafGH87XBxd/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\ni6SRzxakb4dcv379pMcFZiu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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.hist2d(np.log10(data['teff']), data['mg'], bins=40)\n", "plt.ylim(plt.ylim()[::-1])\n", "plt.xlim(plt.xlim()[::-1])\n", "plt.xlabel('log$_{10}$Teff')\n", "plt.ylabel('M$_G$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Unfortunately, there is not a one-liner KDE plot with the standard libraries.\n", "\n", "Note that `seaborn` offers a one-liner option. (`sns.kdeplot(x, y, cmap=cmap, shade=True, cut=5, ax=ax)`)" ] }, { "cell_type": "code", "execution_count": 115, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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oTuZLHrNjqsptaN6TesuWLWI/9yf38joMM5XdL+uFF16wHTt22NTUlI2OjlpP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\n7XhJADAjq1atuuqSzBMTE3I1Rj9pee+9906HKC4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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.stats import gaussian_kde\n", "kernel = gaussian_kde(np.vstack([np.log10(data['teff']), data['mg']]))\n", "mins = kernel.dataset.min(1)\n", "maxs = kernel.dataset.max(1)\n", "X, Y = np.meshgrid(np.linspace(mins[0], maxs[0],100), np.linspace(mins[1], maxs[1],100))\n", "vals = kernel(np.vstack([X.ravel(),Y.ravel()])).reshape(X.shape)\n", "plt.pcolor(X, Y, vals)\n", "plt.xlim(maxs[0], mins[0])\n", "plt.ylim(maxs[1], mins[1])\n", "plt.xlabel('log$_{10}$Teff')\n", "plt.ylabel('M$_G$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Exercices\n", "\n", "## Exercice 1: more exploration on stellar parameters (20 points)\n", "\n", "\n", "Again, the dataset represents properties of individual stars. _We_ know from stellar physics that there are relations between stellar properties, such as _luminosity_, _gravity_, and _mass_. These relations are relatively simple equations:\n", "\n", "* magnitudes and luminosities are related with\n", "\n", "$$ M = -2.5 \\log_{10} (lum) $$\n", "\n", "* luminosity and magnitudes depend on distance as:\n", "$$ G - 5 \\log_{10}(dist) = M_G + A_G - 5 $$\n", "\n", "* Luminosity is related to the temperature by thermodynamics ($\\sigma \\approx 5.670373 . 10^{-8} W . m^{-2}. K^{-4}$ is the Stefan–Boltzmann constant):\n", "$$ L = 4 \\pi R^2 \\sigma T_{eff} ^ 4 $$\n", "\n", "\n", "* and gravity comes from the mass and usual newtonian equation ($\\mathcal{G} \\approx 6.673 . 10^{-11} N.(m/kg) ^ 2$, gravitational constant)\n", "\n", "$$ g = \\frac{\\mathcal{G} M}{R^2} $$\n", "\n", "**Now you're on your own... **\n", "\n", "1. Visualize for each of the 4 relations if the stars from the dataset obey stellar physics.\n", "\n", "2. Reality is never perfect, either because our understanding of stellar physics is imperfect, or uncertain measurements. For each relation, characterize the dispersion of the dataset with respect to our expectations from the physics.\n", "\n", "**tip**: the table at the top of this document describes the columns of the dataset." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Excercise 2: Variable transformations (15 points)\n", "\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider the uniform distribution, $p(x)$. \n", "\n", "* Show empirically that $m = (x_{max} + x_{min} )/2$ (\"midpoint\") is a more efficient estimator than the mean, $\\mu$.\n", " Do this by drawing a sample of size $n$ from the distribution, calculating the estimators,\n", " and then plotting them against a large range of values $n$, in order to see which converges more rapidly.\n", "\n", "* How the variation of the standard deviation of $\\mu$ with $n$ compares with theory? (i.e., overplot it). \n", "* How the standard deviation in m varies with n? Explain your result.\n", "\n", "**Recall that \"efficiency\" refers to the variance of the estimator. **\n", "\n", "**Hint**: generate many samples for a given $n$, calculate for each the mean and midpoint, then compute the\n", "mean and standard deviation of the estimators (given $n$). \n", "\n", "** Important: Careful to the stddev definition in your coding language **, it may not be always the same" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercice 3: Monty Hall or Three doors problem. (30 points)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You are in a game show and presented with three closed doors.\n", "Behind one of them (chosen at random without your knowledge) is a prize car, behind each of the\n", "others is a goat. Your goal is to reveal (and thus win) the car. \n", "\n", "You first select a door at random.\n", "\n", "The game show host (who knows where the car is) then opens one of the other doors to reveal a\n", "goat (He will never open a door to reveal the car). He then gives you the opportunity to change\n", "your choice of door to the other closed one. \n", "\n", "Do you? More specifically, what is the probability of winning the car if you do and if you do not change?" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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le0SpJ7N7ksjAQ3pWkEmmzEXVpiNEtpZW+NFEqdOehsIgKJKMQi0tXuLyCJGW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\n9L2rSenZSQyZZPuBXUMiE/FSQ/v1e5n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"text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import Image\n", "Image('http://imgs.xkcd.com/comics/monty_hall.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1. Work out the probabiliy of winning the car if you switch always, randomly, and never? Explain your results either mathematically or intuitively.\n", "\n", "2. Write a piece of code that simulates the game to allow you to verify your findings. \n", "simulate many games and plot the distribution of wins depending on 3 strategies:\n", " 1. you never switch \n", " 2. you always switch\n", " 3. you randomly switch\n", " \n", "3. generalize your code to an arbitrary number of doors." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Exercise 4: Lifetime of an element (15 points)\n", "\n", "if $t$ is the lifetime of an element, which follows an exponential decay law with a charactistic time $\\tau$:\n", "$$f(t) = A \\exp(-t/\\tau)$$\n", "\n", "1. find $A$ such that $f(t)$ has properties of a probability density function.\n", "2. what is the mean and standard deviation of this lifetime\n", "3. if $\\tau = 5 min$, what is the probability that the lifetime is greater than or equal to $10 min$. \n", "4. Estimate the probability of a lifetime of at least $10 min$ given that it has been observed for already $5$ minutes: $P(T > 10 min | T > 5 min)$ (same $\\tau=5$ min).\n", "5. generalize the previous question: estimate $P(T > a + b | T > a)$." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercice 5: speed of light and error propagation (20 points)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below is the result of 5 experiments to measure the speed of light with some associated uncertainties.\n", "\n", "|measurements | uncertainties |\n", "| ------|---------------------|\n", "| [km/s]| [km/s] |\n", "|299 794|3 |\n", "|299 791|5 |\n", "|299 770|2 |\n", "|299 789|3 |\n", "|299 790|4 |\n", "\n", "\n", "1. Calculate the best estimate of the speed of light, as well as your uncertainty in that estimate from the measurements only.\n", "\n", "2. Take weighted average using uncertainties as weights, and quote the variance of this (all in the lecture notes)\n", "\n", "**tip**: be critic about your data, and detail your assumptions." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "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": "3.4.3" } }, "nbformat": 4, "nbformat_minor": 0 }