{ "cells": [ { "cell_type": "markdown", "id": "frozen-raising", "metadata": {}, "source": [ "# How to draw error bands\n", "\n", "We show two ways to compute 1-sigma bands around a fitted curve.\n", "\n", "Whether the curve describes a probability density (from a maximum-likelihood fit) or an expectation (from a least-squares fit) does not matter, the procedure is the same. We demonstrate this on an unbinned extended maximum-likelihood fit of a Gaussian." ] }, { "cell_type": "code", "execution_count": 1, "id": "white-dress", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from numba_stats import norm\n", "from iminuit import Minuit\n", "from iminuit.cost import ExtendedUnbinnedNLL\n", "import matplotlib.pyplot as plt\n", "\n", "# generate toy sample\n", "rng = np.random.default_rng(1)\n", "x = rng.normal(size=100)\n", "\n", "# bin it\n", "w, xe = np.histogram(x, bins=100, range=(-5, 5))\n", "\n", "# compute bin-wise density estimates\n", "werr = w ** 0.5\n", "cx = 0.5 * (xe[1:] + xe[:-1])\n", "dx = np.diff(xe)\n", "d = w / dx\n", "derr = werr / dx \n", "\n", "\n", "# define model and cost function\n", "def model(x, par):\n", " return par[0], par[0] * norm.pdf(x, par[1], par[2])\n", "\n", "cost = ExtendedUnbinnedNLL(x, model)\n", "\n", "# fit the model\n", "m = Minuit(cost, (1, 0, 1))\n", "m.migrad()\n", "m.hesse()\n", "\n", "# plot everything\n", "plt.errorbar(cx, d, derr, fmt=\"o\", label=\"data\", zorder=0)\n", "\n", "plt.plot(cx, model(cx, m.values)[1], lw=3,\n", " label=\"fit\")\n", "plt.legend(frameon=False,\n", " title=f\"$n = {m.values[0]:.2f} +/- {m.errors[0]:.2f}$\\n\"\n", " f\"$\\mu = {m.values[1]:.2f} +/- {m.errors[1]:.2f}$\\n\"\n", " f\"$\\sigma = {m.values[2]:.2f} +/- {m.errors[2]:.2f}$\");" ] }, { "cell_type": "markdown", "id": "realistic-trail", "metadata": {}, "source": [ "We want to understand how uncertain the Gaussian curve is. Thus we want to draw a 1-sigma error band around the curve, which approximates the 68 % confidence interval." ] }, { "cell_type": "markdown", "id": "polyphonic-patient", "metadata": {}, "source": [ "## With error propagation\n", "\n", "The uncertainty is quantified in form of the covariance matrix of the fitted parameters. We can use [error propagation](https://en.wikipedia.org/wiki/Propagation_of_uncertainty) to obtain the uncertainty of the curve,\n", "\n", "$$\n", "C' = J \\, C \\, J^T,\n", "$$\n", "\n", "where $C$ is the covariance matrix of the input vector, $C'$ is the covariance matrix of the output vector and $J$ is the matrix of first derivatives of the mapping function between input and output. The mapping in this case is the curve, $\\vec y = f(\\vec{x}; \\vec{p})$, regarded as a function of $\\vec{p}$ and not of $\\vec{x}$, which is fixed. The function maps from $\\vec{p}$ to $\\vec{y}$ and the Jacobi matrix is made from elements\n", "\n", "$$\n", "J_{ik} = \\frac{\\partial y_i}{\\partial p_k}.\n", "$$\n", "\n", "To compute the derivatives one can sometimes use [Sympy](https://www.sympy.org/en/index.html) or an auto-differentiation tool like [JAX](https://jax.readthedocs.io/en/latest/) if the function permits it, but in general they need to be computed numerically. The library [Jacobi](https://github.com/hDembinski/jacobi) provides a fast and robust calculator for numerical derivatives and a function for error propagation." ] }, { "cell_type": "code", "execution_count": 2, "id": "technological-justice", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from jacobi import propagate\n", "\n", "# run error propagation\n", "y, ycov = propagate(lambda p: model(cx, p)[1], m.values, m.covariance)\n", "\n", "# plot everything\n", "plt.errorbar(cx, d, derr, fmt=\"o\", label=\"data\", zorder=0)\n", "\n", "plt.plot(cx, y, lw=3, label=\"fit\")\n", "\n", "# draw 1 sigma error band\n", "yerr_prop = np.diag(ycov) ** 0.5\n", "plt.fill_between(cx, y - yerr_prop, y + yerr_prop, facecolor=\"C1\", alpha=0.5)\n", "\n", "plt.legend(frameon=False,\n", " title=f\"$n = {m.values[0]:.2f} +/- {m.errors[0]:.2f}$\\n\"\n", " f\"$\\mu = {m.values[1]:.2f} +/- {m.errors[1]:.2f}$\\n\"\n", " f\"$\\sigma = {m.values[2]:.2f} +/- {m.errors[2]:.2f}$\");" ] }, { "cell_type": "markdown", "id": "final-sensitivity", "metadata": {}, "source": [ "Error propagation is relatively fast." ] }, { "cell_type": "code", "execution_count": 3, "id": "continent-astrology", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.96 ms ± 0 ns per loop (mean ± std. dev. of 1 run, 1,000 loops each)\n" ] } ], "source": [ "%%timeit -r 1 -n 1000\n", "propagate(lambda p: model(cx, p)[1], m.values, m.covariance)" ] }, { "cell_type": "markdown", "id": "advance-flight", "metadata": {}, "source": [ "## With the bootstrap\n", "\n", "Another generic way to compute uncertainties is bootstrapping. We know that the parameters asymptotically follow a multivariate normal distribution, so we can simulate new experiments with varied parameter values." ] }, { "cell_type": "code", "execution_count": 4, "id": "duplicate-community", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rng = np.random.default_rng(1)\n", "\n", "par_b = rng.multivariate_normal(m.values, m.covariance, size=1000)\n", "\n", "# standard deviation of bootstrapped curves\n", "y_b = [model(cx, p)[1] for p in par_b]\n", "yerr_boot = np.std(y_b, axis=0)\n", "\n", "# plot everything\n", "plt.errorbar(cx, d, derr, fmt=\"o\", label=\"data\", zorder=0)\n", "\n", "plt.plot(cx, y, lw=3, label=\"fit\")\n", "\n", "# draw 1 sigma error band\n", "plt.fill_between(cx, y - yerr_boot, y + yerr_boot, facecolor=\"C1\", alpha=0.5)\n", "\n", "plt.legend(frameon=False,\n", " title=f\"$n = {m.values[0]:.2f} +/- {m.errors[0]:.2f}$\\n\"\n", " f\"$\\mu = {m.values[1]:.2f} +/- {m.errors[1]:.2f}$\\n\"\n", " f\"$\\sigma = {m.values[2]:.2f} +/- {m.errors[2]:.2f}$\");" ] }, { "cell_type": "markdown", "id": "greater-surge", "metadata": {}, "source": [ "The result is visually indistinguishable from before, as it should be. If you worry about deviations between the two methods, read on." ] }, { "cell_type": "markdown", "id": "excess-parking", "metadata": {}, "source": [ "In this example, computing the band from 1000 samples is slower than error propagation." ] }, { "cell_type": "code", "execution_count": 5, "id": "grave-month", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3.72 ms ± 0 ns per loop (mean ± std. dev. of 1 run, 100 loops each)\n" ] } ], "source": [ "%%timeit -r 1 -n 100\n", "par_b = rng.multivariate_normal(m.values, m.covariance, size=1000)\n", "y_b = [model(cx, p)[1] for p in par_b]\n", "np.std(y_b, axis=0)" ] }, { "cell_type": "markdown", "id": "cordless-elder", "metadata": {}, "source": [ "However, the calculation time scales linearly with the number of samples. One can simply draw fewer samples if the additional uncertainty is acceptable. If we draw only 50 samples, bootstrapping wins over numerical error propagation." ] }, { "cell_type": "code", "execution_count": 6, "id": "lucky-happening", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "258 µs ± 0 ns per loop (mean ± std. dev. of 1 run, 1,000 loops each)\n" ] } ], "source": [ "%%timeit -r 1 -n 1000\n", "rng = np.random.default_rng(1)\n", "par_b = rng.multivariate_normal(m.values, m.covariance, size=50)\n", "y_b = [model(cx, p)[1] for p in par_b]\n", "np.std(y_b, axis=0)" ] }, { "cell_type": "markdown", "id": "moral-keeping", "metadata": {}, "source": [ "Let's see how the result looks, whether it deviates noticably." ] }, { "cell_type": "code", "execution_count": 7, "id": "brilliant-football", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# compute bootstrapped curves with 50 samples\n", "par_b = rng.multivariate_normal(m.values, m.covariance, size=50)\n", "y_b = [model(cx, p)[1] for p in par_b]\n", "yerr_boot_50 = np.std(y_b, axis=0)\n", "\n", "# plot everything\n", "plt.errorbar(cx, d, derr, fmt=\"o\", label=\"data\", zorder=0)\n", "\n", "plt.plot(cx, y, lw=3, label=\"fit\")\n", "\n", "# draw 1 sigma error band\n", "plt.fill_between(cx, y - yerr_boot_50, y + yerr_boot_50, facecolor=\"C1\", alpha=0.5)\n", "\n", "plt.legend(frameon=False,\n", " title=f\"$n = {m.values[0]:.2f} +/- {m.errors[0]:.2f}$\\n\"\n", " f\"$\\mu = {m.values[1]:.2f} +/- {m.errors[1]:.2f}$\\n\"\n", " f\"$\\sigma = {m.values[2]:.2f} +/- {m.errors[2]:.2f}$\");" ] }, { "cell_type": "markdown", "id": "adequate-automation", "metadata": {}, "source": [ "No, the result is still visually indistinguishable. This suggests that 50 samples can be enough for plotting.\n", "\n", "Numerically, the three error bands differ at the 10 % level in the central region (expected relative error is $50^{-1/2} \\approx 0.14$). The eye cannot pickup these differences, but they are there. The curves differ more in the tails, which is not visible in linear scale, but noticable in log-scale." ] }, { "cell_type": "code", "execution_count": 8, "id": "hindu-moderator", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 2, figsize=(12, 5))\n", "\n", "plt.sca(ax[0])\n", "plt.plot(cx, y - yerr_prop, \"-C0\", label=\"prop\")\n", "plt.plot(cx, y + yerr_prop, \"-C0\", label=\"prop\")\n", "plt.plot(cx, y - yerr_boot, \"--C1\", label=\"boot[1000]\")\n", "plt.plot(cx, y + yerr_boot, \"--C1\", label=\"boot[1000]\")\n", "plt.plot(cx, y - yerr_boot_50, \":C2\", label=\"boot[50]\")\n", "plt.plot(cx, y + yerr_boot_50, \":C2\", label=\"boot[50]\")\n", "plt.legend()\n", "plt.semilogy();\n", "\n", "plt.sca(ax[1])\n", "plt.plot(cx, yerr_boot / yerr_prop, label=\"boot[1000] / prop\")\n", "plt.plot(cx, yerr_boot_50 / yerr_prop, label=\"boot[50] / prop\")\n", "plt.legend()\n", "plt.axhline(1, ls=\"--\", color=\"0.5\", zorder=0)\n", "for delta in (-0.1, 0.1):\n", " plt.axhline(1 + delta, ls=\":\", color=\"0.5\", zorder=0)\n", "plt.ylim(0.5, 1.5);" ] }, { "cell_type": "markdown", "id": "quiet-watch", "metadata": {}, "source": [ "We see that the bootstrapped bands are a bit wider in the tails. This is caused by non-linearities that are neglected in error propagation." ] }, { "cell_type": "markdown", "id": "following-campaign", "metadata": {}, "source": [ "## Which is better? Error propagation or bootstrap?\n", "\n", "There is no clear-cut answer. At the visual level, both methods are usually fine (even with a small number of bootstrap samples). Which calculation is more accurate depends on details of the problem. Fortunately, the sources of error are orthogonal for both methods, so each method can be used to check the other.\n", "\n", "* The bootstrap error is caused by sampling. It can be reduced by drawing more samples, the relative error is proportional to $N^{-1/2}$.\n", "* The propagation error is caused by using a truncated Taylor series in the computation." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3.8.13 ('venv': venv)", "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": "3.10.8" }, "vscode": { "interpreter": { "hash": "bdbf20ff2e92a3ae3002db8b02bd1dd1b287e934c884beb29a73dced9dbd0fa3" } } }, "nbformat": 4, "nbformat_minor": 5 }