Skip to content

Instantly share code, notes, and snippets.

@smsharma
Last active March 4, 2018 01:00
Show Gist options
  • Save smsharma/ec908c47882888ee1f4dc4bb7a1bd6e1 to your computer and use it in GitHub Desktop.
Save smsharma/ec908c47882888ee1f4dc4bb7a1bd6e1 to your computer and use it in GitHub Desktop.
Display the source blob
Display the rendered blob
Raw
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Several ways of doing a fit to supernova data"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"import emcee\n",
"import corner\n",
"\n",
"from scipy.optimize import curve_fit as cf\n",
"from scipy.optimize import minimize\n",
"\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from matplotlib import rcParams\n",
"\n",
"# Set plotting options\n",
"rcParams['xtick.labelsize'] = 20\n",
"rcParams['ytick.labelsize'] = 20\n",
"rcParams['axes.labelsize'] = 20\n",
"rcParams['axes.titlesize'] = 20\n",
"rcParams['font.family'] = 'serif'\n",
"rcParams['font.serif'] = 'CMU Serif'\n",
"rcParams['figure.figsize'] = (6,5)\n",
"rcParams['legend.fontsize'] = 16\n",
"rcParams['lines.linewidth'] = 1.5\n",
"rcParams['text.usetex'] = True\n",
"rcParams['figure.figsize'] = (6,5)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>name</th>\n",
" <th>z</th>\n",
" <th>dist_mod</th>\n",
" <th>dist_mod_err</th>\n",
" <th>prob</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>1993ah</td>\n",
" <td>0.028488</td>\n",
" <td>35.346583</td>\n",
" <td>0.223906</td>\n",
" <td>0.128419</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>1993ag</td>\n",
" <td>0.050043</td>\n",
" <td>36.682368</td>\n",
" <td>0.166829</td>\n",
" <td>0.128419</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>1993o</td>\n",
" <td>0.052926</td>\n",
" <td>36.817691</td>\n",
" <td>0.155756</td>\n",
" <td>0.128419</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>1993b</td>\n",
" <td>0.070086</td>\n",
" <td>37.446737</td>\n",
" <td>0.158467</td>\n",
" <td>0.128419</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>1992bs</td>\n",
" <td>0.062668</td>\n",
" <td>37.483409</td>\n",
" <td>0.156099</td>\n",
" <td>0.128419</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" name z dist_mod dist_mod_err prob\n",
"0 1993ah 0.028488 35.346583 0.223906 0.128419\n",
"1 1993ag 0.050043 36.682368 0.166829 0.128419\n",
"2 1993o 0.052926 36.817691 0.155756 0.128419\n",
"3 1993b 0.070086 37.446737 0.158467 0.128419\n",
"4 1992bs 0.062668 37.483409 0.156099 0.128419"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sn_data = pd.read_csv(\"sn_data.txt\", sep='\\t', names=['name','z','dist_mod','dist_mod_err','prob'])\n",
"sn_data.head()"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Extract data points at redshifts z < 0.3\n",
"x = sn_data['z'][sn_data['z'] < 0.3]\n",
"y = sn_data['dist_mod'][sn_data['z'] < 0.3]\n",
"yerr = sn_data['dist_mod_err'][sn_data['z'] < 0.3]"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def distmod(z, H0, q0):\n",
" \"\"\" Distance modulus\n",
" H0: Hubble parameter\n",
" q0: deceleration parameter\n",
" \"\"\"\n",
" return 43.23 - 5*np.log10(H0/68.) + 5*np.log10(z) + 1.086*(1-q0)*z"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## With `Scipy`, curve fit"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[69.92907516 -0.30862454]\n"
]
}
],
"source": [
"from scipy.optimize import curve_fit as cf\n",
"params, _ = cf(distmod, x, y, sigma=yerr)\n",
"print params"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## With `Scipy`, maximization of a likelihood"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def lnlike(theta, x, y, yerr):\n",
" \"\"\" Likelihood function to maximize\n",
" \"\"\"\n",
" H0, q0 = theta\n",
" model = distmod(x, H0, q0)\n",
" inv_sigma2 = 1.0/(yerr**2)\n",
" return -0.5*(np.sum((y-model)**2*inv_sigma2 - np.log(inv_sigma2)))"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[69.92907561 -0.30862467]\n"
]
}
],
"source": [
"nll = lambda *args: -lnlike(*args) # Scipy minimizes, so need minus\n",
"result = minimize(nll, [68,0], args=(x, y, yerr))\n",
"print result['x']"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Bayesian posterior scan with `emcee`"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def lnprior(theta):\n",
" \"\"\" Prior on our parameter\n",
" \"\"\"\n",
" H0, q0 = theta\n",
" if -1000 < H0 < 1000 and -5. < q0 < 5.:\n",
" return 0.0\n",
" return -np.inf\n",
"\n",
"def lnprob(theta, x, y, yerr):\n",
" \"\"\" Likelihood, combined with prior\n",
" \"\"\"\n",
" lp = lnprior(theta)\n",
" if not np.isfinite(lp):\n",
" return -np.inf\n",
" return lp + lnlike(theta, x, y, yerr)\n",
"\n",
"ndim, nwalkers = 2, 100\n",
"pos = [[68,0] + 1e-4*np.random.randn(ndim) for i in range(nwalkers)]"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Initialize emcee samples\n",
"sampler = emcee.EnsembleSampler(nwalkers, ndim, lnprob, args=(x, y, yerr))"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Run MCMC posterior scan\n",
"sampler.run_mcmc(pos, 300);"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAgYAAAIkCAYAAABlW+OdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nMTAMwzAMI4QpBoZhGIZhhPj/kw+Mioae0CUAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10f1be990>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Get and plot posterior samples\n",
"samples = sampler.chain[:, 100:, :].reshape((-1, ndim))\n",
"fig = corner.corner(samples, labels=[\"$H_0$\", \"$q_0$\"], show_titles=True)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.12"
}
},
"nbformat": 4,
"nbformat_minor": 1
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment