{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Polynomial fitting with confidence/prediction intervals\n", "\n", "> Marcos Duarte \n", "> Laboratory of Biomechanics and Motor Control ([http://demotu.org/](http://demotu.org/)) \n", "> Federal University of ABC, Brazil" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2017-12-30T07:20:57.580664Z", "start_time": "2017-12-30T07:20:57.571928Z" } }, "outputs": [], "source": [ "import numpy as np\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import sys\n", "sys.path.insert(1, r'./../functions')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's implement the polynomial fit by least squares and calculate the confidence and prediction intervals assuming normal distribution of the residuals. \n", "The code of the `polyfit.py` function is at the end of this notebook (or download the function from the GitHub repo)." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2017-12-30T07:21:04.658840Z", "start_time": "2017-12-30T07:21:04.461819Z" } }, "outputs": [], "source": [ "from polyfit import polyfit" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2017-12-30T07:22:09.356316Z", "start_time": "2017-12-30T07:22:09.350357Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Help on function polyfit in module polyfit:\n", "\n", "polyfit(x, y, degree, yerr=None, plot=True, xlabel='x', ylabel='y', title=True, legend=True, plotCI=True, plotPI=True, axis=None)\n", " Least squares polynomial regression of order degree for x vs. y [1]_\n", " \n", " Parameters\n", " ----------\n", " x : numpy array_like, shape (N,)\n", " Independent variable, x-coordinates of the N points (x[i], y[i]).\n", " y : numpy array_like, shape (N,)\n", " Dependent variable, y-coordinates of the N points (x[i], y[i]).\n", " degree : integer\n", " Degree of the polynomial to be fitted to the data.\n", " yerr : numpy array_like, shape (N,), optional (default = None)\n", " Error (uncertainty) in y. If no error is entered, unitary equal errors\n", " for all y values are assumed.\n", " plot : bool, optional (default = True)\n", " Show plot (True) of not (False). \n", " xlabel : string, optional (default = 'x')\n", " Label for the x (horizontal) axis.\n", " ylabel : string, optional (default = 'y')\n", " Label for the y (vertical) axis.\n", " title : bool, optional (default = True)\n", " Show title (True) of not (False) in the plot.\n", " legend : bool, optional (default = True)\n", " Show legend (True) of not (False) in the plot.\n", " plotCI : bool, optional (default = True)\n", " Plot the shaded area for the confidence interval (True) of not (False).\n", " plotPI : bool, optional (default = True)\n", " Plot the shaded area for the prediction interval (True) of not (False).\n", " axis : matplotlib object, optional (default = None)\n", " Matplotlib axis object where to plot.\n", " \n", " Returns\n", " ------- \n", " p : numpy array, shape (deg + 1,)\n", " Coefficients of the least squares polynomial fit.\n", " perr : numpy array, shape (deg + 1,)\n", " Standard-deviation of the coefficients.\n", " R2 : float\n", " Coefficient of determination.\n", " chi2red : float\n", " Reduced chi-squared\n", " yfit : numpy array, shape (N + 1,)\n", " Values of the fitted polynomial evaluated at x.\n", " ci : numpy array, shape (N + 1,)\n", " Values of the 95% confidence interval evaluated at x.\n", " pi : numpy array, shape (N + 1,)\n", " Values of the 68% prediction interval evaluated at x.\n", " \n", " References\n", " ----------\n", " .. [1] https://docs.scipy.org/doc/numpy/reference/generated/numpy.polyfit.html\n", " \n", " \n", " Examples\n", " --------\n", " >>> import numpy as np\n", " >>> import matplotlib.pyplot as plt\n", " >>> N = 50\n", " >>> x = np.linspace(-2, 4, N)\n", " >>> y = np.polyval([3, 1, 2], x) + np.random.randn(N)*8\n", " >>> # simple use:\n", " >>> polyfit(x, y, 2);\n", " >>> # compare two models:\n", " >>> fig, ax = plt.subplots(1, 2, figsize=(14, 5))\n", " >>> p1, perr1, R21, chi2red1, yfit1, ci1, pi1 = polyfit(x, y, 1, axis=ax[0])\n", " >>> p2, perr2, R22, chi2red2, yfit2, ci2, pi2 = polyfit(x, y, 2, axis=ax[1])\n", " >>> plt.tight_layout()\n", " >>> Enter error (uncertainty) in y:\n", " >>> yerr = np.ones(N)*8\n", " >>> polyfit(x, y, 2, yerr);\n", "\n" ] } ], "source": [ "help(polyfit)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Some data to play:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "ExecuteTime": { "end_time": "2017-12-30T07:24:23.464833Z", "start_time": "2017-12-30T07:24:23.456844Z" } }, "outputs": [], "source": [ "N = 50\n", "x = np.linspace(-2, 4, N)\n", "y = np.polyval([3, 1, 2], x) + np.random.randn(N)*8" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "ExecuteTime": { "end_time": "2017-12-30T07:25:24.810638Z", "start_time": "2017-12-30T07:25:24.535715Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "p, perr, R2, chi2red, yfit, ci, pi = polyfit(x, y, 2)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "ExecuteTime": { "end_time": "2017-12-30T07:25:33.853800Z", "start_time": "2017-12-30T07:25:33.848380Z" } }, "outputs": [ { "data": { "text/plain": [ "array([ 2.25111764, 2.94582783, 2.03470099])" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The $\\chi^2_{red}$ value is much higher than one, suggesting a poor fitting (although the $R^2$ value is good). We can see that the data variability not accounted by the model is very high. One way of considering this variability is to treat it as error (uncertainty) in the measurement of the y variable. The square root of the $\\chi^2_{red}$ value is a good average estimate of this error in y (see for example page 79 of [https://www.astro.rug.nl/software/kapteyn/_downloads/statmain.pdf](https://www.astro.rug.nl/software/kapteyn/_downloads/statmain.pdf)). \n", "Let's generate an array for the error in y:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "ExecuteTime": { "end_time": "2017-12-30T07:26:03.775357Z", "start_time": "2017-12-30T07:26:03.769490Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Average uncertainty in y: 8.88453379119\n" ] } ], "source": [ "yerr = np.ones(N)*np.sqrt(chi2red)\n", "print('Average uncertainty in y:', yerr[0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And let's run the fitting again:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "ExecuteTime": { "end_time": "2017-12-30T07:26:10.638163Z", "start_time": "2017-12-30T07:26:10.351175Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "p, perr, R2, chi2red, yfit, ci, pi = polyfit(x, y, deg, yerr=yerr)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's see the results of linear and quadratic fits:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "ExecuteTime": { "end_time": "2017-12-30T07:26:32.289627Z", "start_time": "2017-12-30T07:26:31.800910Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 2, figsize=(12, 5))\n", "p, perr, R2, chi2red, yfit, ci, pi = polyfit(x, y, degree=1, axis=ax[0])\n", "p, perr, R2, chi2red, yfit, ci, pi = polyfit(x, y, degree=2, axis=ax[1], ylabel='')\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## P.S.: Calculation of moving standard-deviation\n", "\n", "Let's calculate the moving standard-deviation just to compare with the 68% (1 SD) prediction interval for the fitted polynomial given in the plot above." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "ExecuteTime": { "end_time": "2017-12-30T07:27:06.460551Z", "start_time": "2017-12-30T07:27:06.281680Z" } }, "outputs": [], "source": [ "import pandas as pd\n", "\n", "ys = pd.Series(y)\n", "# use a moving window of one-tenth of the size of the data.\n", "ys_std = ys.rolling(window=int(np.round(N/10)), min_periods=4, center=True).std()" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "ExecuteTime": { "end_time": "2017-12-30T07:27:08.724429Z", "start_time": "2017-12-30T07:27:08.480267Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10, 5))\n", "plt.fill_between(x, yfit+ys_std, yfit-ys_std, color=[1, 0, 0, 0.1], edgecolor='',\n", " label='Moving standard-deviation')\n", "plt.plot(x, y, 'o', color=[0, 0.1, .9, 1], markersize=8) \n", "plt.plot(x, yfit, 'r', linewidth=3, color=[1, 0, 0, .8], label='Polynomial (degree {}) fit'.format(deg))\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Function `polyfit.py`" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "ExecuteTime": { "end_time": "2017-12-30T07:27:28.430893Z", "start_time": "2017-12-30T07:27:28.425306Z" } }, "outputs": [], "source": [ "# %load ./../functions/polyfit.py\n", "\"\"\"Least squares polynomial regression with confidence/prediction intervals.\n", "\"\"\"\n", "\n", "__author__ = 'Marcos Duarte, https://github.com/demotu/BMC'\n", "__version__ = 'polyfit.py v.1.0.1 2017/04/16'\n", "__license__ = \"MIT\"\n", "\n", "import numpy as np\n", "import scipy.stats as stats\n", "import matplotlib.pyplot as plt\n", "\n", "def polyfit(x, y, degree, yerr=None, plot=True, xlabel='x', ylabel='y',\n", " title=True, legend=True, plotCI=True, plotPI=True, axis=None):\n", " \"\"\"Least squares polynomial regression of order degree for x vs. y [1]_\n", " \n", " Parameters\n", " ----------\n", " x : numpy array_like, shape (N,)\n", " Independent variable, x-coordinates of the N points (x[i], y[i]).\n", " y : numpy array_like, shape (N,)\n", " Dependent variable, y-coordinates of the N points (x[i], y[i]).\n", " degree : integer\n", " Degree of the polynomial to be fitted to the data.\n", " yerr : numpy array_like, shape (N,), optional (default = None)\n", " Error (uncertainty) in y. If no error is entered, unitary equal errors\n", " for all y values are assumed.\n", " plot : bool, optional (default = True)\n", " Show plot (True) of not (False). \n", " xlabel : string, optional (default = 'x')\n", " Label for the x (horizontal) axis.\n", " ylabel : string, optional (default = 'y')\n", " Label for the y (vertical) axis.\n", " title : bool, optional (default = True)\n", " Show title (True) of not (False) in the plot.\n", " legend : bool, optional (default = True)\n", " Show legend (True) of not (False) in the plot.\n", " plotCI : bool, optional (default = True)\n", " Plot the shaded area for the confidence interval (True) of not (False).\n", " plotPI : bool, optional (default = True)\n", " Plot the shaded area for the prediction interval (True) of not (False).\n", " axis : matplotlib object, optional (default = None)\n", " Matplotlib axis object where to plot.\n", "\n", " Returns\n", " ------- \n", " p : numpy array, shape (deg + 1,)\n", " Coefficients of the least squares polynomial fit.\n", " perr : numpy array, shape (deg + 1,)\n", " Standard-deviation of the coefficients.\n", " R2 : float\n", " Coefficient of determination.\n", " chi2red : float\n", " Reduced chi-squared\n", " yfit : numpy array, shape (N + 1,)\n", " Values of the fitted polynomial evaluated at x.\n", " ci : numpy array, shape (N + 1,)\n", " Values of the 95% confidence interval evaluated at x.\n", " pi : numpy array, shape (N + 1,)\n", " Values of the 68% prediction interval evaluated at x.\n", "\n", " References\n", " ----------\n", " .. [1] https://docs.scipy.org/doc/numpy/reference/generated/numpy.polyfit.html\n", " \n", "\n", " Examples\n", " --------\n", " >>> import numpy as np\n", " >>> import matplotlib.pyplot as plt\n", " >>> N = 50\n", " >>> x = np.linspace(-2, 4, N)\n", " >>> y = np.polyval([3, 1, 2], x) + np.random.randn(N)*8\n", " >>> # simple use:\n", " >>> polyfit(x, y, 2);\n", " >>> # compare two models:\n", " >>> fig, ax = plt.subplots(1, 2, figsize=(14, 5))\n", " >>> p1, perr1, R21, chi2red1, yfit1, ci1, pi1 = polyfit(x, y, 1, axis=ax[0])\n", " >>> p2, perr2, R22, chi2red2, yfit2, ci2, pi2 = polyfit(x, y, 2, axis=ax[1])\n", " >>> plt.tight_layout()\n", " >>> Enter error (uncertainty) in y:\n", " >>> yerr = np.ones(N)*8\n", " >>> polyfit(x, y, 2, yerr);\n", " \"\"\"\n", " \n", " x, y = np.asarray(x), np.asarray(y)\n", " N = y.size\n", " if yerr is None:\n", " yerr = np.ones(N)\n", " errorbar = False\n", " else:\n", " errorbar = True\n", " # coefficients and covariance matrix of the least squares polynomial fit\n", " p, cov = np.polyfit(x, y, degree, w=1/yerr, cov=True)\n", " # evaluate the polynomial at x\n", " yfit = np.polyval(p, x) \n", " # standard-deviation of the coefficients\n", " perr = np.sqrt(np.diag(cov)) \n", " # residuals\n", " res = y - yfit \n", " # reduced chi-squared, see for example page 79 of\n", " # https://www.astro.rug.nl/software/kapteyn/_downloads/statmain.pdf\n", " chi2red = np.sum(res**2/yerr**2)/(N - degree - 1) \n", " # standard deviation of the error (residuals)\n", " s_err = np.sqrt(np.sum(res**2)/(N - degree - 1)) \n", " # sum of squared residuals\n", " SSres = np.sum(res**2) \n", " # sum of squared totals\n", " SStot = np.sum((y - np.mean(y))**2) \n", " # coefficient of determination\n", " R2 = 1 - SSres/SStot \n", " # adjusted coefficient of determination\n", " R2adj = 1 - (SSres/(N - degree - 1)) / (SStot/(N - 1))\n", " # 95% (2 SD) confidence interval for the fit\n", " t95 = stats.t.ppf(0.95 + (1-0.95)/2, N - degree - 1)\n", " ci = t95 * s_err * np.sqrt( 1/N + (x - np.mean(x))**2/np.sum((x-np.mean(x))**2))\n", " # 68% (1 SD) prediction interval for the fit\n", " t68 = stats.t.ppf(0.683 + (1-0.683)/2, N - degree - 1)\n", " pi = t68 * s_err * np.sqrt(1 + 1/N + (x - np.mean(x))**2/np.sum((x-np.mean(x))**2))\n", " # plot\n", " if plot:\n", " # generate values if number of input values is too small or too large\n", " if N < 50 or N > 500:\n", " x2 = np.linspace(np.min(x), np.max(x), 100)\n", " yfit2 = np.polyval(p, x2)\n", " ci2 = np.interp(x2, x, ci)\n", " pi2 = np.interp(x2, x, pi)\n", " else:\n", " x2, yfit2, ci2, pi2 = x, yfit, ci, pi\n", "\n", " if axis is None:\n", " fig, axis = plt.subplots(1, 1, figsize=(10, 5))\n", " else:\n", " fig = 0\n", " if plotPI:\n", " axis.fill_between(x2, yfit2+pi2, yfit2-pi2, color=[1, 0, 0, 0.1],\n", " edgecolor='', label='68% prediction interval')\n", " if plotCI:\n", " axis.fill_between(x2, yfit2+ci2, yfit2-ci2, color=[1, 0, 0, 0.3],\n", " edgecolor='', label='95% confidence interval')\n", " if errorbar:\n", " axis.errorbar(x, y, yerr=yerr, fmt='o', capsize=0,\n", " color=[0, 0.1, .9, 1], markersize=8)\n", " else:\n", " axis.plot(x, y, 'o', color=[0, 0.1, .9, 1], markersize=8)\n", " axis.plot(x2, yfit2, 'r', linewidth=3, color=[1, 0, 0, .8],\n", " label='Polynomial (degree {}) fit'.format(degree))\n", " axis.set_xlabel(xlabel, fontsize=16)\n", " axis.set_ylabel(ylabel, fontsize=16)\n", " if legend:\n", " axis.legend()\n", " if title:\n", " xs = ['', 'x'] + ['x^{:d}'.format(ideg) for ideg in range(2, degree+1)]\n", " title = ['({:.2f} \\pm {:.2f}) {}'.format(i, j, k) for i, j, k in zip(p, perr, xs)]\n", " R2str = '\\, (R^2 = ' + '{:.2f}'.format(R2) + \\\n", " ', \\chi^2_{red} = ' + '{:.1f}'.format(chi2red) + ')'\n", " title = '$ y = ' + '+'.join(title) + R2str + '$'\n", " axis.set_title(title, fontsize=12, color=[0, 0, 0]) \n", " if fig:\n", " plt.show()\n", " \n", " return p, perr, R2, chi2red, yfit, ci, pi" ] } ], "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": "3.6.4" }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }