{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Curve fitting\n", "\n", "> Marcos Duarte \n", "> [Laboratory of Biomechanics and Motor Control](https://bmclab.pesquisa.ufabc.edu.br/) \n", "> Federal University of ABC, Brazil" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Curve fitting is the process of fitting a model, expressed in terms of a mathematical function, that depends on adjustable parameters to a series of data points and once adjusted, that curve has the best fit to the data points. \n", "\n", "The model can be an arbitrary class of functions such as polynomials and the fit would determine the polynomial coefficients to simplily summarize the data or the model parameters can represent a underlying theory that the data are supposed to satisfy such as fitting an exponential function to data of a decay process to determine its decay rate or a parabola to the position data of an object falling to determine the gravity acceleration.\n", "\n", "The general approach to the fitting procedure involves the definition of a merit function that measures the agreement between data and model. The model parameters are then adjusted to yield the best-fit parameters as a problem of minimization. A fitting procedure should provide (i) parameters, (ii) error estimates on the parameters, and (iii) a statistical measure of goodness-of-fit. When the third item suggests that the model is an unlikely match to the data, then items (i) and (ii) are probably worthless. \n", "(Numerical Recipes 2007, Bevington and Robinson 2002)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Least squares\n", "\n", "Consider $ n $ data points $(x_i, y_i),\\: i=1, \\dots , n$, where $x_i$ is the independent variable (or predictor) and $y_i$ is the dependent variable (or response) to be fitted by a model function $y$ with $m$ adjustable parameters $\\beta_i,\\: i=1, \\dots , m$. The problem is to find the parameter values for the model which best fits the data. A classical solution is to find the best fit by minimizing the sum of the squared differences between data points and the model function (the sum of squared residuals as the merit function), which is known as the least-squares fit:\n", "\n", "$$ \\sum_{i=1}^{n} \\left[ y_i - y(x | \\beta_1 \\dots \\beta_{m}) \\right]^2 \\;\\;\\;\\;\\;\\; \\mathrm{minimize\\; over:} \\;\\;\\; \\beta_1 \\dots \\beta_{m} $$ \n", "\n", "**Chi-Square** \n", "If we consider that each response $y_i$ has a measurement error or uncertainty described by a standard deviation, $ \\sigma_i $, the problem now is to minimize the following function:\n", "\n", "$$ \\sum_{i=1}^{n} \\left[ \\frac{ y_i - y(x | \\beta_1 \\dots \\beta_{m}) }{\\sigma_i} \\right]^2 = \\chi^2 $$\n", "\n", "Considering that the residuals are normally distributed, the sum of squared residuals divided by their variance, $\\sigma_i^2$, by definition will have a [chi-squared distribution](http://en.wikipedia.org/wiki/Chi-squared_distribution), $ \\chi^2 $. Once the best-fit parameters are found, the terms in the sum above are not all statistically independent and the probability distribution of $\\chi^2$ will be the chi-squared distribution for $n-m$ degrees of freedom.\n", "\n", "The uncertainty $\\sigma_i$ can be seen as the inverse of the weights in a weighted sum (because less certainty we have about this measure). Larger $\\sigma_i$, smaller the weight of $y_i$ in the sum. If $y_i$ has no uncertainty, $\\sigma_i$ should be equal to one. \n", "\n", "A rough estimate of the goodness of fit is the reduced chi-square statistic, $\\chi^2_{red}$: the $\\chi^2$ value divided by the number of degrees of freedom ($n-m$). \n", "A good fitting should have $\\chi^2_{red}$ equals to one." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Linear fit\n", "\n", "Let's derive the analytical expression for the least-square fit when the model function is a straight line (a.k.a. linear regression) and the dependent variable $y_i$ has uncertainty:\n", "\n", "$$ y(x) = y(x | a,b) = a + bx $$ \n", "\n", "We want to find $a, b$ such that minimizes the $\\chi^2$ function defined above (a.k.a. $\\chi^2$ fitting):\n", "\n", "$$ \\chi^2(a,b) = \\sum_{i=1}^{n} \\left[ \\frac{ y_i - (a + bx_i) }{\\sigma_i} \\right]^2 $$\n", "\n", "Using the property that at the minimum of $\\chi^2$ its derivative is zero:\n", "\n", "$$ \\frac{\\partial \\chi^2}{\\partial a} = -2 \\sum_{i=1}^{n} \\frac{ y_i - a - bx_i }{\\sigma_i^2} = 0 $$\n", "\n", "$$ \\frac{\\partial \\chi^2}{\\partial b} = -2 \\sum_{i=1}^{n} \\frac{ x_i(y_i - a - bx_i) }{\\sigma_i^2} = 0 $$\n", "\n", "To solve these two equations, let's define the sums as:\n", "\n", "$$ S = \\sum_{i=1}^{n} \\frac{1}{\\sigma_i^2} \\;\\;\\; S_x = \\sum_{i=1}^{n} \\frac{x_i}{\\sigma_i^2} \\;\\;\\; S_y = \\sum_{i=1}^{n} \\frac{y_i}{\\sigma_i^2} \\;\\;\\; S_{xx} = \\sum_{i=1}^{n} \\frac{x_i^2}{\\sigma_i^2} \\;\\;\\; S_{xy} = \\sum_{i=1}^{n} \\frac{x_i y_i}{\\sigma_i^2} $$\n", "\n", "Using these definitions, the former two equations become:\n", "\n", "$$ S_y \\:\\: = aS + bS_x $$\n", "\n", "$$ S_{xy} = aS_x + bS_{xx} $$\n", "\n", "And solving these two equations for the two unknowns:\n", "\n", "$$ a = \\frac{S_{xx}S_y - S_x S_{xy}}{\\Delta} $$\n", "\n", "$$ b = \\frac{S S_{xy} - S_x S_y}{\\Delta} $$ \n", "\n", "Where:\n", "\n", "$$ \\Delta = S S_{xx} - S_x^2 $$\n", "\n", "With the parameters above, the straight line will be the best fit in the sense that the sum of the squared residuals are minimum. \n", "\n", "**Estimating the uncertainty of the parameters**\n", "\n", "The uncertainty of each parameter is given by:\n", "\n", "$$ \\sigma_a^2 = \\frac{Sxx}{\\Delta} $$\n", "\n", "$$ \\sigma_b^2 = \\frac{S}{\\Delta} $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Correlation coefficient\n", "\n", "The Pearson product-moment correlation coefficient, or simply the correlation coefficient, is a measure of the linear correlation between two variables $x$ and $y$, with values varying from +1 to −1, where 1 is total positive correlation, 0 is no correlation, and −1 is total negative correlation. \n", "The correlation coefficient between populations of two random variables is the covariance of the two variables divided by the product of their standard deviations:\n", "\n", "$$ \\rho_{x, y} = \\frac{cov(x, y)}{\\sigma_x\\sigma_y} = \\frac{E[(x-\\mu_x)(y-\\mu_y)]}{\\sqrt{E[(x-\\mu_x)^2]}\\sqrt{E[(y-\\mu_y)^2]}} $$ \n", "\n", "Where $ E[\\cdot] $ is the expectation operator.\n", "\n", "For samples of two random variables, the covariance and standard deviation are given by:\n", "\n", "$$ cov(x, y) = \\frac{1}{n-1}\\sum_{i=1}^{n}(x_i-\\bar{x})(y_i-\\bar{y}) $$\n", "\n", "$$ \\sigma_x = \\sqrt{\\frac{1}{n-1}\\sum_{i=1}^{n}(x_i-\\bar{x})^2} $$\n", "\n", "So, the correlation coefficient for the samples is:\n", "\n", "$$ r_{x, y} = \\frac{\\sum_{i=1}^{n}(x_i-\\bar{x})(y_i-\\bar{y})}{\\sqrt{\\sum_{i=1}^{n}(x_i-\\bar{x})^2}\\sqrt{\\sum_{i=1}^{n}(y_i-\\bar{y})^2}} $$\n", "\n", "The square of the sample correlation coefficient, denoted $r^2$ or $R^2$, is called the coefficient of determination and it can be shown it is related to the linear fit formalism by:\n", "\n", "$$ R^2(y, \\widehat{y}) = \\frac{\\sum_{i=1}^{n}(\\widehat{y}_i-\\bar{y})^2}{\\sum_{i=1}^{n}(y_i-\\bar{y})^2}$$\n", "\n", "Where $\\widehat{y}_i$ are the fitted values from the linear fit.\n", "\n", "Examining the division above, it consists of the variance of the fitted values around the mean value of $y$ divided by the variance of $y_i$. Because of that, it is said that the coefficient of determination is the proportion of variance in $y$ explained by a linear function of $x$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Computing the curve fitting\n", "\n", "Python and its ecosystem for scientific computing have plenty of functions ready available for curve fitting. Instead of writting our own code to implement the formula above, let's use the functions available which will cover many more cases (general polynomials, nonlinear functions, etc.).\n", "\n", "First, if we only want to fit polynomials, we can use the Numpy polyfit function: \n", "\n", " polyfit(x, y, deg, rcond=None, full=False, w=None, cov=False) \n", " Least squares polynomial fit. \n", " \n", " Fit a polynomial ``p(x) = p[0] * x**deg + ... + p[deg]`` of degree `deg` \n", " to points `(x, y)`. Returns a vector of coefficients `p` that minimises \n", " the squared error. \n", " \n", "Let's demonstrate how polyfit works:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# Import the necessary libraries\n", "import numpy as np\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import scipy.stats as stats" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generate some data:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "n = 50\n", "x = np.arange(1, n+1)\n", "y = x + 10*np.random.randn(n) + 10\n", "yerr = np.abs(10*np.random.randn(n)) + 5" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, let's plot the data and perform the curve fitting without considering the uncertainty:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "p, cov = np.polyfit(x, y, 1, cov=True) # coefficients and covariance matrix\n", "yfit = np.polyval(p, x) # evaluate the polynomial at x\n", "\n", "perr = np.sqrt(np.diag(cov)) # standard-deviation estimates for each coefficient\n", "R2 = np.corrcoef(x, y)[0, 1]**2 # coefficient of determination between x and y\n", "resid = y - yfit\n", "chi2red = np.sum((resid/yerr)**2)/(y.size - 2)\n", "\n", "plt.figure(figsize=(10, 5))\n", "plt.plot(x, y, 'bo')\n", "plt.plot(x, yfit, linewidth=3, color=[1, 0, 0, .5])\n", "plt.xlabel('x', fontsize=16)\n", "plt.ylabel('y', fontsize=16)\n", "plt.title('$y = %.2f \\pm %.2f + (%.2f \\pm %.2f)x \\; [R^2=%.2f,\\, \\chi^2_{red}=%.1f]$'\n", " %(p[1], perr[1], p[0], perr[0], R2, chi2red), fontsize=20, color=[0, 0, 0])\n", "plt.xlim((0, n+1))\n", "plt.ylim((-50, 100))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The curve fitting by a line considering the uncertainty:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "p, cov = np.polyfit(x, y, 1, w=1/yerr, cov=True) # coefficients and covariance matrix\n", "yfit = np.polyval(p, x) # evaluate the polynomial at x\n", "\n", "perr = np.sqrt(np.diag(cov)) # standard-deviation estimates for each coefficient\n", "R2 = np.corrcoef(x, y)[0, 1]**2 # coefficient of determination between x and y\n", "resid = y - yfit\n", "chi2red = np.sum((resid/yerr)**2)/(y.size - 2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And the plot:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10, 5))\n", "plt.errorbar(x, y, yerr=yerr, fmt = 'bo', ecolor='b', capsize=0)\n", "plt.plot(x, yfit, linewidth=3, color=[1, 0, 0, .5])\n", "plt.xlabel('x', fontsize=16)\n", "plt.ylabel('y', fontsize=16)\n", "plt.title('$y = %.2f \\pm %.2f + (%.2f \\pm %.2f)x \\; [R^2=%.2f,\\, \\chi^2_{red}=%.1f]$'\n", " %(p[1], perr[1], p[0], perr[0], R2, chi2red), fontsize=20, color=[0, 0, 0])\n", "plt.xlim((0, n+1))\n", "plt.ylim((-50, 100))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "According to our assumptions, the residuals should be normally distributed. Let's create a function to plot the residuals and a probability plot that will be useful to check if the residuals are normally distributed:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "def plot_resid(x, resid):\n", " \"\"\" plot residuals and probability plot of residuals for a normal distribution.\"\"\"\n", "\n", " import matplotlib.pyplot as plt\n", " import scipy.stats as stats\n", " fig, ax = plt.subplots(1, 2, figsize=(13, 5))\n", " ax[0].plot(x, resid, 'ro')\n", " ax[0].plot([0, x[-1]], [0, 0], 'k')\n", " ax[0].set_xlabel('x', fontsize=12)\n", " ax[0].set_ylabel('Residuals', fontsize=12)\n", " stats.probplot(resid, dist=\"norm\", plot=plt)\n", " ax[1].set_xlabel('Quantiles', fontsize=12)\n", " ax[1].set_ylabel('Ordered values', fontsize=12)\n", " ax[1].set_title('Probability Plot of the residuals')\n", "\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_resid(x, resid)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We could apply a statistical test to verify if the data above is normallly distributed, but for now, by visual inspection, the residuals indeed seem to be normallly distributed." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The effect of uncertainty on the curve fitting\n", "\n", "To demonstrate the effect of uncertainty on the curve fitting, let's plot the same (x, y) values but with different errors:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "# data\n", "x = np.array([1, 2, 3, 4, 5])\n", "y = np.array([1, 2, 3, 6, 4])\n", "yerr = np.array([[0, 0, 0, 0, 0],\n", " [1, 1, 1, 1, 1],\n", " [1, 1, 1, .5, 2],\n", " [1, 1, 1, 2, .5]])" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "# function for the linear fit to automate the process\n", "def linearfit(x, y, yerr=None):\n", " w = None if (yerr is None or np.sum(yerr)==0) else 1/yerr\n", " p, cov = np.polyfit(x, y, 1, w=w, cov=True) # coefficients and covariance matrix\n", " yfit = np.polyval(p, x) # evaluate the polynomial at x\n", "\n", " perr = np.sqrt(np.diag(cov)) # standard-deviation estimates for each coefficient\n", " R2 = np.corrcoef(x, y)[0, 1]**2 # coefficient of determination between x and y\n", " resid = y - yfit\n", " chi2red = np.sum((resid/yerr)**2)/(y.size - 2) if w is not None else np.nan\n", "\n", " return yfit, p, R2, chi2red, perr, resid" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot\n", "fig, ax = plt.subplots(2, 2, figsize=(10, 6), sharex=True, sharey=True)\n", "axs = ax.flatten()\n", "for i, ax in enumerate(axs):\n", " yf, p, R2, chi2red, perr, resid = linearfit(x, y, yerr=yerr[i, :])\n", " ax.errorbar(x, y, yerr=yerr[i, :], fmt = 'bo', ecolor='b', capsize=0, elinewidth=2)\n", " ax.plot(x, yf, linewidth=3, color=[1, 0, 0, .5])\n", " ax.set_title('$y = %.2f + %.2f x \\, [R^2=%.2f,\\chi^2_{red}=%.1f]$'\n", " %(p[1], p[0], R2, chi2red), fontsize=18)\n", " ax.grid()\n", "\n", "ax.set_xlim(0.5, 5.5)\n", "fig.subplots_adjust(bottom=0.1, left=.05, right=.95, hspace=.2, wspace=.05)\n", "plt.suptitle('The effect of uncertainty on the curve fitting (same data, different errors)',\n", " fontsize=16, y=1.02)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From figure above, if the errors (weights) are all equal, the fitting is the same as if we don't input any error (first line). \n", "When the errors are different across data, the uncertainty has a strong impact on the curve fitting (second line)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Curve fitting as a model\n", "\n", "We have to be carefull in interpreting the results of a curve fitting to determine whether the fitted model truely captures the relation between the independent variable (predictor) and the dependent variable (response).\n", "\n", "An illustrative example to demonstrate that the result of a curve fitting is not necessarily an indicator of the phenomenon being modelled is the [Anscombe's quartet](http://en.wikipedia.org/wiki/Anscombe%27s_quartet) data. These four sets of data have very similar basic statistical properties and linear fitting parameters, but are very different when visualized. Let's work with these data:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The Anscombe's quartet data ha)ve the same basic statistical properties:\n", "Mean of x : [7.50090909 7.50090909 7.5 7.50090909]\n", "Variance of x: [3.75206281 3.75239008 3.74783636 3.74840826]\n", "Mean of y : [7.50090909 7.50090909 7.5 7.50090909]\n", "Variance of y: [3.75206281 3.75239008 3.74783636 3.74840826]\n" ] } ], "source": [ "# Anscombe's quartet data\n", "x = np.array([[10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5],\n", " [10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5],\n", " [10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5],\n", " [8, 8, 8, 8, 8, 8, 8, 19, 8, 8, 8]])\n", "y = np.array([[8.04, 6.95, 7.58, 8.81, 8.33, 9.96, 7.24, 4.26, 10.84, 4.82, 5.68],\n", " [9.14, 8.14, 8.74, 8.77, 9.26, 8.10, 6.13, 3.10, 9.13, 7.26, 4.74],\n", " [7.46, 6.77, 12.74, 7.11, 7.81, 8.84, 6.08, 5.39, 8.15, 6.42, 5.73],\n", " [6.58, 5.76, 7.71, 8.84, 8.47, 7.04, 5.25, 12.50, 5.56, 7.91, 6.89]])\n", "# basic descriptive statistics\n", "print(\"The Anscombe's quartet data ha)ve the same basic statistical properties:\")\n", "print('Mean of x :', np.mean(y, axis=1))\n", "print('Variance of x:', np.var(y, axis=1))\n", "print('Mean of y :', np.mean(y, axis=1))\n", "print('Variance of y:', np.var(y, axis=1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or we can use Pandas to describe the data:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
X1X2X3X4Y1Y2Y3Y4
count11.00000011.00000011.00000011.00000011.00000011.00000011.00000011.000000
mean9.0000009.0000009.0000009.0000007.5009097.5009097.5000007.500909
std3.3166253.3166253.3166253.3166252.0315682.0316572.0304242.030579
min4.0000004.0000004.0000008.0000004.2600003.1000005.3900005.250000
25%6.5000006.5000006.5000008.0000006.3150006.6950006.2500006.170000
50%9.0000009.0000009.0000008.0000007.5800008.1400007.1100007.040000
75%11.50000011.50000011.5000008.0000008.5700008.9500007.9800008.190000
max14.00000014.00000014.00000019.00000010.8400009.26000012.74000012.500000
\n", "
" ], "text/plain": [ " X1 X2 X3 X4 Y1 Y2 \\\n", "count 11.000000 11.000000 11.000000 11.000000 11.000000 11.000000 \n", "mean 9.000000 9.000000 9.000000 9.000000 7.500909 7.500909 \n", "std 3.316625 3.316625 3.316625 3.316625 2.031568 2.031657 \n", "min 4.000000 4.000000 4.000000 8.000000 4.260000 3.100000 \n", "25% 6.500000 6.500000 6.500000 8.000000 6.315000 6.695000 \n", "50% 9.000000 9.000000 9.000000 8.000000 7.580000 8.140000 \n", "75% 11.500000 11.500000 11.500000 8.000000 8.570000 8.950000 \n", "max 14.000000 14.000000 14.000000 19.000000 10.840000 9.260000 \n", "\n", " Y3 Y4 \n", "count 11.000000 11.000000 \n", "mean 7.500000 7.500909 \n", "std 2.030424 2.030579 \n", "min 5.390000 5.250000 \n", "25% 6.250000 6.170000 \n", "50% 7.110000 7.040000 \n", "75% 7.980000 8.190000 \n", "max 12.740000 12.500000 " ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "df = pd.DataFrame(np.vstack((x, y)).T, columns=['X1', 'X2', 'X3', 'X4', 'Y1', 'Y2', 'Y3', 'Y4'])\n", "df.describe()" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot\n", "fig, ax = plt.subplots(2, 2, figsize=(10, 6), sharex=True, sharey=True)\n", "axs = ax.flatten()\n", "resid = np.empty_like(y)\n", "for i, ax in enumerate(axs):\n", " yf, p, R2, chi2red, perr, resid[i, :] = linearfit(x[i, :], y[i, :], yerr=None)\n", " ax.plot(x[i, :], y[i, :], color=[0, .2, 1, .8], marker='o', linestyle='', markersize=8)\n", " ax.plot(x[i, :], yf, linewidth=3, color=[1, 0, 0, .8])\n", " ax.set_title('$y = %.2f + %.2f x \\, [R^2=%.2f]$' %(p[1], p[0], R2), fontsize=18)\n", " ax.grid()\n", "\n", "ax.set_xlim(0, 20)\n", "fig.subplots_adjust(bottom=0.1, left=.05, right=.95, hspace=.2, wspace=.05)\n", "plt.suptitle(\"Linear fit of the Anscombe's quartet data\",\n", " fontsize=18, y=1.02)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And we can check whether the residuals of the linear fit are normally distributed:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(10, 6))\n", "for i in range(4):\n", " ax = plt.subplot(2, 2, i+1)\n", " stats.probplot(resid[i, :], dist=\"norm\", plot=plt)\n", "\n", "plt.suptitle('Probability plot of the residuals for a normal distribution',\n", " fontsize=18, y=1.05)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Even the residuals don't look bad! \n", "Exactly the same model fits very different data. \n", "We should be very carefull in interpreting the result of a curve fitting as a description of a phenomenon." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Confidence and prediction intervals for the linear fit\n", "\n", "Analog to the case for a random variable (see [Confidence and prediction intervals](http://nbviewer.ipython.org/github/demotu/BMC/blob/master/notebooks/ConfidencePredictionIntervals.ipynb)), we can estimate confidence and prediction intervals for the linear fit (for the deduction of these intervals see for example Montgomery (2013)). \n", "\n", "**Confidence interval** \n", "\n", "A 95% confidence interval for the linear fit gives the 95% probability that this interval around the linear fit, $\\hat{\\mu}_{y|x0}$, contains the mean response of new values, $\\mu_{y|x0}$, at a specified value, $x_0$, and it is given by:\n", "\n", "$$ \\left| \\: \\hat{\\mu}_{y|x0} - \\mu_{y|x0} \\: \\right| \\; \\leq \\; T_{n-2}^{.975} \\; \\hat{\\sigma} \\; \\sqrt{\\frac{1}{n}+\\frac{(x_0-\\bar{x})^2}{\\sum_{i=1}^n{(x_i-\\bar{x})^2}}}$$\n", "\n", "Where: \n", "\n", "$ \\hat{\\mu}_{y|x0} = a + bx_0$ is computed from the lineat fit. \n", "\n", "$T_{n-2}^{.975}$ is the $97.5^{th}$ percentile of the Student's t-distribution with n−2 degrees of freedom. \n", "\n", "$\\hat{\\sigma}$ is the standard deviation of the error term in the linear fit (residuals) given by:\n", "\n", "$$ \\hat{\\sigma} = \\sqrt{\\sum_{i=1}^n{\\frac{(y_i-\\hat{y})^2}{n-2}}} $$\n", "\n", "**Prediction interval** \n", "\n", "A 95% prediction interval for the linear fit gives the 95% probability that this interval around the linear fit, $\\hat{y}_0$, contains a new observation, $y_0$, at a specified value, $x_0$, and it is given by:\n", "\n", "$$ \\left| \\: \\hat{y}_0 - y_0 \\: \\right| \\; \\leq \\; T_{n-2}^{.975} \\; \\hat{\\sigma} \\; \\sqrt{1 + \\frac{1}{n}+\\frac{(x_0-\\bar{x})^2}{\\sum_{i=1}^n{(x_i-\\bar{x})^2}}}$$\n", "\n", "Where $ \\hat{y}_0 = a + bx_0$ is computed from the lineat fit.\n", "\n", "**Implementation in Python**\n", "\n", "Here is an implementation of the linear fit with the confidence and prediction intervals:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "def linearfit(x, y, yerr):\n", " \"\"\"Linear fit of x and y with uncertainty and plots results.\"\"\"\n", "\n", " import numpy as np\n", " import scipy.stats as stats\n", "\n", " x, y = np.asarray(x), np.asarray(y)\n", " n = y.size\n", " p, cov = np.polyfit(x, y, 1, w=1/yerr, cov=True) # coefficients and covariance matrix\n", " yfit = np.polyval(p, x) # evaluate the polynomial at x\n", " perr = np.sqrt(np.diag(cov)) # standard-deviation estimates for each coefficient\n", " R2 = np.corrcoef(x, y)[0, 1]**2 # coefficient of determination between x and y\n", " resid = y - yfit\n", " chi2red = np.sum((resid/yerr)**2)/(n - 2) # Chi-square reduced\n", " s_err = np.sqrt(np.sum(resid**2)/(n - 2)) # standard deviation of the error (residuals)\n", "\n", " # Confidence interval for the linear fit:\n", " t = stats.t.ppf(0.975, n - 2)\n", " ci = t * s_err * np.sqrt( 1/n + (x - np.mean(x))**2/np.sum((x-np.mean(x))**2))\n", " # Prediction interval for the linear fit:\n", " pi = t * s_err * np.sqrt(1 + 1/n + (x - np.mean(x))**2/np.sum((x-np.mean(x))**2))\n", "\n", " # Plot\n", " plt.figure(figsize=(10, 5))\n", " plt.fill_between(x, yfit+pi, yfit-pi, color=[1, 0, 0, 0.1], edgecolor=None)\n", " plt.fill_between(x, yfit+ci, yfit-ci, color=[1, 0, 0, 0.15], edgecolor=None)\n", " plt.errorbar(x, y, yerr=yerr, fmt = 'bo', ecolor='b', capsize=0)\n", " plt.plot(x, yfit, linewidth=3, color=[1, 0, 0, .8])\n", " plt.xlabel('x', fontsize=16)\n", " plt.ylabel('y', fontsize=16)\n", " plt.title('$y = %.2f \\pm %.2f + (%.2f \\pm %.2f)x \\; [R^2=%.2f,\\, \\chi^2_{red}=%.1f]$'\n", " %(p[1], perr[1], p[0], perr[0], R2, chi2red), fontsize=20, color=[0, 0, 0])\n", " plt.xlim((0, n+1))\n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And an example:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 20\n", "x = np.arange(1, n+1)\n", "y = x + 5*np.random.randn(n)\n", "yerr = np.abs(4*np.random.randn(n)) + 2\n", "linearfit(x, y, yerr)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Non-linear curve fitting\n", "\n", "A more general curve fitting function is the `scipy.optimize.curve_fit`:\n", "\n", " scipy.optimize.curve_fit(f, xdata, ydata, p0=None, sigma=None, **kw)[source]\n", " Use non-linear least squares to fit a function, f, to data.\n", " \n", "For the `curve_fit` funcion, we need to define a model (e.g., a mathematical expression) for the fit:\n", "\n", " f : callable\n", " The model function, f(x, ...). It must take the independent variable as the first argument and the parameters to fit as separate remaining arguments.\n", " \n", "Let's create a gaussian curve as model:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "# Import the necessary libraries\n", "import numpy as np\n", "from scipy.optimize import curve_fit\n", "from IPython.display import display, Math\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define the function for curve fitting:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle y = a * exp\\left(-\\frac{(x-b)^2}{2c^2}\\right) + d$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def func(x, a, b, c, d):\n", " # Gauss function\n", " return a*np.exp(-(x-b)**2/(2*c**2)) + d\n", "\n", "display(Math( r'y = a * exp\\left(-\\frac{(x-b)^2}{2c^2}\\right) + d' ))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generate numeric data to be fitted:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "x = np.linspace(0, 8, 101)\n", "noise = np.random.randn(len(x)) + 1\n", "y = func(x, 10, 4, 1, np.mean(noise)) + noise\n", "yerr = np.abs(np.random.randn(len(x))) + 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Perform the curve fitting:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Fitted parameters:\n" ] }, { "data": { "text/latex": [ "$\\displaystyle a=-4.94 \\pm 0.99$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle b=0.89 \\pm 0.24$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle c=0.84 \\pm 0.28$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle d=6.23 \\pm 0.43$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\chi^2_{red}=4.72$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "p, cov = curve_fit(func, x, y, sigma=yerr)\n", "yfit = func(x, p[0], p[1], p[2], p[3])\n", "perr = np.sqrt(np.diag(cov)) # standard-deviation estimates for each coefficient\n", "resid = y - yfit\n", "chi2red = np.sum((resid/yerr)**2)/(y.size - 4)\n", "\n", "print('Fitted parameters:')\n", "display(Math( r'a=%.2f \\pm %.2f' %(p[0], perr[0]) ))\n", "display(Math( r'b=%.2f \\pm %.2f' %(p[1], perr[1]) ))\n", "display(Math( r'c=%.2f \\pm %.2f' %(p[2], perr[2]) ))\n", "display(Math( r'd=%.2f \\pm %.2f' %(p[3], perr[3]) ))\n", "display(Math( r'\\chi^2_{red}=%.2f' %(chi2red) ))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot data and fitted curve:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10, 5))\n", "plt.errorbar(x, y, yerr=yerr, fmt = 'bo', ecolor='b', capsize=0)\n", "plt.plot(x, yfit, linewidth=3, color=[1, 0, 0, .5])\n", "plt.xlabel('x', fontsize=16)\n", "plt.ylabel('y', fontsize=16)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Evidently this is not correct.\n", "\n", "We need to enter an initial guess for the parameters (`p0`):" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Fitted parameters:\n" ] }, { "data": { "text/latex": [ "$\\displaystyle a=10.16 \\pm 0.26$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle b=3.98 \\pm 0.03$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle c=0.96 \\pm 0.03$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle d=1.97 \\pm 0.14$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\chi^2_{red}=0.34$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "p, cov = curve_fit(func, x, y, p0=[1, 4, 1, 1], sigma=yerr)\n", "yfit = func(x, p[0], p[1], p[2], p[3])\n", "perr = np.sqrt(np.diag(cov)) # standard-deviation estimates for each coefficient\n", "resid = y - yfit\n", "chi2red = np.sum((resid/yerr)**2)/(y.size - 3)\n", "\n", "print('Fitted parameters:')\n", "display(Math( r'a=%.2f \\pm %.2f' %(p[0], perr[0]) ))\n", "display(Math( r'b=%.2f \\pm %.2f' %(p[1], perr[1]) ))\n", "display(Math( r'c=%.2f \\pm %.2f' %(p[2], perr[2]) ))\n", "display(Math( r'd=%.2f \\pm %.2f' %(p[3], perr[3]) ))\n", "display(Math( r'\\chi^2_{red}=%.2f' %(chi2red) ))\n", "\n", "plt.figure(figsize=(10, 5))\n", "plt.errorbar(x, y, yerr=yerr, fmt = 'bo', ecolor='b', capsize=0)\n", "plt.plot(x, yfit, linewidth=3, color=[1, 0, 0, .5])\n", "plt.xlabel('x', fontsize=16)\n", "plt.ylabel('y', fontsize=16)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once again, according to our assumptions, the residuals should be normally distributed:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_resid(x, resid)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "- [Bevington and Robinson (2002) Data Reduction and Error Analysis for the Physical Science. McGraw-Hill Science/Engineering/Math; 3rd edition](https://www.mcgraw-hill.co.uk/html/0071199268.html).\n", "- [Press et al. (2007) Numerical Recipes 3rd Edition: The Art of Scientific Computing. Cambridge University Press](http://www.nr.com/). \n", "- [Montgomery (2013) Applied Statistics and Probability for Engineers. John Wiley & Sons](http://books.google.com.br/books?id=_f4KrEcNAfEC).\n", "- [NIST/SEMATECH e-Handbook of Statistical Methods](http://www.itl.nist.gov/div898/handbook/pri/section2/pri24.htm)" ] } ], "metadata": { "hide_input": false, "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.11.4" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false }, "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 }, "widgets": { "application/vnd.jupyter.widget-state+json": { "state": {}, "version_major": 2, "version_minor": 0 } } }, "nbformat": 4, "nbformat_minor": 4 }