{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Various notes on fitting emission lines" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pylab as pl\n", "import orb.fit\n", "import orb.fft\n", "import orb.utils.fit\n", "import orb.sim" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bayesian Information Criterion\n", "\n", "https://en.wikipedia.org/wiki/Bayesian_information_criterion\n", "\n", "This is a good way to compare 2 different models on the same fit. The lowest BIC is the best model. In the least square fit framework, as long as the noise is normally distributed (which is the case with SITELLE spectra) we can write:\n", "\n", "$\\chi^2 = \\sum_{i=1}^{n}{(x_i - \\hat{x_i})^2}$\n", "\n", "$\\text{BIC} = n \\ln{\\left(\\frac{\\chi^2}{n}\\right)} + k \\ln{(n)}$\n", "\n", "Where, $n$ is the number of samples (length of the spectrum) and $k$ is the number of parameters. The $\\chi^2$ is the sum of the square of the residual. This is automatically computed with ORCS.\n", "\n", "In this example we compare a two-components model with a one-component model on a low SNR spectrum." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "=== Fit results ===\n", "lines: ['H3', '[NII]6548', '[NII]6584', '[SII]6717', '[SII]6731'], fmodel: sincgauss\n", "iterations: 105, fit time: 5.84e-01 s\n", "number of free parameters: 7, BIC: -1.80505e+03, chi2: 4.29e+00\n", "Velocity (km/s): [79(11) 79(11) 79(11) 79(11) 79(11)] \n", "Flux: [9.39(67) 0.84(13) 2.53(40) 0.72(40) 0.28(40)]\n", "Broadening (km/s): [190(10) 190(10) 190(10) 190(10) 190(10)]\n", "SNR (km/s): [20.70613363 6.67199224 6.67199224 1.80709523 0.69757399]\n", "\n", "=== Fit results ===\n", "lines: ['H3', '[NII]6548', '[NII]6584', '[SII]6717', '[SII]6731', 'H3', '[NII]6548', '[NII]6584', '[SII]6717', '[SII]6731'], fmodel: sincgauss\n", "iterations: 155, fit time: 1.08e+00 s\n", "number of free parameters: 13, BIC: -1.81256e+03, chi2: 3.86e+00\n", "Velocity (km/s): [4(17) 4(17) 4(17) 4(17) 4(17) 305(38) 305(38) 305(38) 305(38) 305(38)] \n", "Flux: [5.93(85) 0.61(12) 1.84(35) 0.62(30) -0.09(31) 3.56(95) 0.24(12) 0.71(36)\n", " 0.12(32) 0.50(34)]\n", "Broadening (km/s): [110(13) 110(13) 110(13) 110(13) 110(13) 127(30) 127(30) 127(30) 127(30)\n", " 127(30)]\n", "SNR (km/s): [12.21788687 6.57829917 6.57829917 2.11201869 -0.2985682 8.46690204\n", " 2.24659491 2.24659491 0.36821189 1.57306382]\n", "\n", "=== BIC COMPARISON ===\n", "if positive and > 2, two component fit is better\n", "0 to 2 \t\tNot worth more than a bare mention\n", "2 to 6 \t\tPositive\n", "6 to 10 \tStrong\n", ">10 \t\tVery strong \n", "DELTA BIC = 7.51597034035467\n" ] }, { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "### synthetic spectrum\n", "\n", "lines = ['Halpha', '[NII]6548', '[NII]6584', '[SII]6717', '[SII]6731']\n", "amp = np.array([1, 0.1, 0.3, 0.1, 0.1]) # amplitude of the lines\n", "sigma = 100 # line broadening in km/s\n", "vel_diff = 275 # velocity diffrence between both components in km/s\n", "amp2_ratio = 0.5 # ratio between the second component and the first one\n", "\n", "step_nb = 850 # resolution ~ 5000\n", "filter_name = 'SN3'\n", "ss = orb.sim.Spectrum(step_nb, filter_name)\n", "ss.add_component(lines, amp, sigma=sigma)\n", "ss.add_component(lines, amp2_ratio * amp, sigma=sigma, vel=vel_diff)\n", "spectrum = ss.get_spectrum()\n", "# add noise\n", "spectrum.data += np.random.standard_normal(size=spectrum.data.size) * 0.1 # SNR 10\n", "\n", "\n", "### 1 component fit\n", "fit1 = spectrum.fit(lines, fmodel='sincgauss', pos_def='1', pos_cov=0, sigma_def='1', sigma_cov=sigma, \n", " amp_def=['1','2','2','3','4'], amp_guess=[1,1,2.985,1,1])\n", "print(fit1)\n", "spectrum.plot()\n", "fit1.get_spectrum().plot()\n", "pl.xlim(14800, 15300)\n", "\n", "### 2 components fit\n", "fit2 = spectrum.fit(lines + lines, fmodel='sincgauss', \n", " pos_def=['1','1','1','1','1', '2','2','2','2','2'], pos_cov=[0, vel_diff], \n", " sigma_def=['1','1','1','1','1', '2','2','2','2','2'], sigma_cov=[sigma, sigma], \n", " amp_def=['1','2','2','3','4', '5','6','6','7','8'], amp_guess=[1,1,2.985,1,1,1,1,2.985,1,1])\n", "print(fit2)\n", "pl.figure()\n", "spectrum.plot()\n", "fit2.get_spectrum().plot()\n", "pl.xlim(14800, 15300)\n", "\n", "\n", "print('=== BIC COMPARISON ===')\n", "print('if positive and > 2, two component fit is better')\n", "print(\"\"\"0 to 2 \\t\\tNot worth more than a bare mention\n", "2 to 6 \\t\\tPositive\n", "6 to 10 \\tStrong\n", ">10 \\t\\tVery strong \"\"\")\n", "\n", "print('DELTA BIC =', fit1['BIC'] - fit2['BIC'])" ] }, { "cell_type": "code", "execution_count": null, "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": "3.7.9" } }, "nbformat": 4, "nbformat_minor": 5 }