{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Testing look-elsewhere effect by creating 2d chi-square random fields with a Gaussian Process\n", "\n", "by Kyle Cranmer, Dec 7, 2015\n", "\n", "The correction for 2d look-elsewhere effect presented in \n", "*Estimating the significance of a signal in a multi-dimensional search* by Ofer Vitells and Eilam Gross http://arxiv.org/pdf/1105.4355v1.pdf\n", "\n", "is based on the fact that the test statistic\n", "\n", "\\begin{equation}\n", "q(\\nu_1, \\nu_2) = -2 \\log \\frac{ \\max_{\\theta} L(\\mu=0, \\nu_1, \\nu_2, \\theta)}{ \\max_{\\mu, \\theta} L(\\mu, \\nu_1, \\nu_2, \\theta)}\n", "\\end{equation}\n", "\n", "is a chi-square random field (with 1 degree of freedom). That means that, for any point in $\\nu_1, \\nu_2$, the quantity $q(\\nu_1, \\nu_2)$ would have a chi-square distribution if you repeated the experiment many times.\n", "\n", "That is what you expect if you have a background model $p_b(x|\\theta)$ and you look for a signal on top of it with signal strength $\\mu$. Creating that scan is somewhat time consuming, so here we make realizations of a chi-square random field by using a Gaussian Process. \n", "The main trick we will use is that a chi-square distribution for one degree of freedom is the same as the distribution of $x^2$ if $x$ is normally distributed. As you might have guessed, a Gaussian Process (GP) is like a chi-square random field, but it is Gaussian-distributed at each point.\n", "\n", "Note, the distributions are not independent at each point, there is some covaraince. So if the $q(\\nu_1, \\nu_2)$ is high at one point, you can expect it to be high near by. We can control this behavior via the GP's kernel.\n", "\n", "For more on the theory of Gaussian Processes, the best resource is available for free online: [Rasmussen & Williams (2006)](http://www.gaussianprocess.org/gpml/). We will [`george`](http://dan.iel.fm/george/current/) -- a nice python package for Gaussian Processes (GP).\n", "\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "//anaconda/lib/python2.7/site-packages/matplotlib/font_manager.py:273: UserWarning: Matplotlib is building the font cache using fc-list. This may take a moment.\n", " warnings.warn('Matplotlib is building the font cache using fc-list. This may take a moment.')\n" ] } ], "source": [ "%pylab inline --no-import-all" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The main trick we will use is that a chi-square distribution for one degree of freedom is the same as the distribution of $x^2$ if $x$ is normally distributed. Here's a quick demonstration of that:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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9+u+TzDnX1PffffROP6E6/dCFzGwCgJldwLEbiZIg59w+d6zr42fAf0tnPNnG\nzM6gN8n/wjm3vm9zQp/PdCR69d8nkZkV9P22x8zOBq4F3k9vVFnp+HEiLwIVfd/fCaw/fgcZUL/3\nsi8RRdyCPp+JWgPUOed+ErMtoc9nOtsrf8Kx9sofDXsQHmFmk+i9inf0Tmnxn3o/E9M3TqQcGAeE\ngKVAFfAr4GKgkd72tdZ0xZgtBngvZ9JbW+6htxXwW5H6spyamX0ZeAv4K73/xh2wGHgHeJ44P59p\nSfQiIjJ8dDNWRMTjlOhFRDxOiV5ExOOU6EVEPE6JXkTE45ToRUQ8ToleRMTj/j8h7rmmBmYZ7QAA\nAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.stats import chi2, norm\n", "chi2_array = chi2.rvs(1, size=10000)\n", "norm_array = norm.rvs(size=10000)\n", "_ = plt.hist(chi2_array, bins=100, alpha=.5, label='chi-square')\n", "_ = plt.hist(norm_array**2, bins=100, alpha=.5, color='r', label='x^2')\n", "plt.yscale('log', nonposy='clip')\n", "plt.legend(('chi-square', 'x^2'))\n", "#plt.semilogy()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Ok, now to the Gaussian processes." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import george\n", "from george.kernels import ExpSquaredKernel" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "length_scale_of_correaltion=0.1\n", "kernel = ExpSquaredKernel(length_scale_of_correaltion, ndim=2)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Create the Gaussian process\n", "# gp = george.GP(kernel)\n", "gp = george.GP(kernel, solver=george.HODLRSolver) #faster" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "n_scan_points=50\n", "aspect_ratio = 10. # make excesses look like stripes\n", "x_scan = np.arange(0,aspect_ratio,aspect_ratio/n_scan_points)\n", "y_scan = np.arange(0,1,1./n_scan_points)\n", "xx, yy = np.meshgrid(x_scan, y_scan)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# reformat the independent coordinates where we evaluate the GP\n", "indep = np.vstack((np.hstack(xx),np.hstack(yy))).T" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[1, 3],\n", " [2, 4]])" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# illustration of what is being done here\n", "np.vstack([[1,2],[3,4]]).T" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# slow part: pre-compute internal stuff for the GP\n", "gp.compute(indep)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# evaluate one realization of the GP\n", "z = gp.sample(indep)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# reformat output for plotting\n", "zz = z.reshape((n_scan_points,n_scan_points))" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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J6FEieuRg+SwRvd0qa2gM6YZSyrkDY88S0Q0D8zkE73S8khop9Wp8mVerKqp5jClfLlvc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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot the chi-square random field\n", "plt.imshow(zz**2, cmap='gray')\n", "plt.colorbar()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now lets histogram the values of the random field.\n", "Don't get confused here... if you pick a single point and histogram the value of over many instances, you expect a Gaussian. However, for a single instance, you don't expect the histogram for the value of the field to be Gaussian (because of the correlations). Thought experiments: if you make `length_scale_of_correaltion` very small, then each point is essentially independent and you do expect to see a Gaussian; however, if `length_scale_of_correaltion` is very large then you expect the field to be nearly constant and the histogram below would be a delta function." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot the gaussian distributed x and chi-square distributed x**2\n", "plt.subplot(1,2,1)\n", "count, edges, patches = plt.hist(np.hstack(zz), bins=100)\n", "plt.xlabel('z')\n", "plt.subplot(1,2,2)\n", "count, edges, patches = plt.hist(np.hstack(zz)**2, bins=100)\n", "plt.xlabel('q=z**2')\n", "plt.yscale('log', nonposy='clip')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Ok, now let's repeat that several times and test lee2d" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from lee2d import *" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from scipy.ndimage import grey_closing, binary_closing\n", "\n", "def fill_holes(array):\n", " zero_array = array==0.\n", " temp = grey_closing(array, size=2)*zero_array\n", " return temp+array" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generate 25 realizations of the GP, calculate the Euler characteristic for two thresholds, and use the mean of those Euler characteristics to estimate $N_1$ and $N_2$" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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yXGheijxd1p2283WJ9eRveR08fWh5KjzeiFp4xcqjh4IQQraTyUVFSc0dry0H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PivrKxgsVicOSeeF/+BRTGRioooNHJB4X/YjuM402YQUXHp0qVTvvE8+C7Py9PcLABroGRXVg2O\nEE6/jZOITpUbB+OYjoMtEZ1yAUhCoyQ6JCGiBW3WBGhy8SpcW0pxKNoi/f5cf0jzHcdxnOkyiKjY\n2NjA4eHhydOrNrBI1gpusQROWl0XTdGuWzvbhYsxaDplVBMM0ro0o0a7f0lgSEGummCUppiO6f6o\nsZJYZgPM2ezc98yAPmbGdE36+9W0x5gvv5JiviLnsa/W4rNe2jOIqFhfXz8RFLlgkKYPaulcWFgs\nGCnpoN+15ULbjkgDlDQLhttn2S7NiuGsEE2DXfO8vN01sVcSgkO7tRzHcZxmDCIqvvjFL2Jzc5MV\nA9zTqPZEq1kn8gFJ8sNLA2fqzmhD7XXyY7k65QN0fg+LxQJra2unzpesDVIsiFYniYODA6yvr5/K\ny+tqTUv7ue0x2NnZwfb29tjVcDrmIv2uF+lenXEYRFTs7e3hwQcfZAf/XBwA+hROi2sjvXZuztIG\ny5LpyzrQLhYL1UzIDZDWa0vWgRijIV2zZB2x1IXLv3fvnlrfHKs4aCpy+mLs8i8SaR/xdu8Ob0tn\nCAYRFXfu3MHrr78uDihdPoVysxPy/Fpzf+0fIydmciz3rB3D7eva/2xpj6Ojo5OXm9W2n1U4+D9D\nx3GceTCIqAD6C5Tsi7YDnDZbQruOdMwYbSW5cfrOlxhTXLz1rW/FV7/6VTz66KODljtGmWOVexHu\n9ZFHHsHu7u4gZeV4Hz6/5Q5d5osvvijuo74HKyKarnJwZkkIYVB14X3Y6Rrvw87ckfpw76LCcRzH\ncZyLgU/KdRzHcRynE1xUOI7jOI7TCb2LCiJ6OxF9noj+hYie7rGc3yeiPSL6bJJ3jYj+ioj+mYj+\nkoi+peMyHyOiTxDRPxHRPxLRe/oul4guEdHfEdGnl2X+at9lZuWvENGLRPTRIcsdE+/DvZQ7Wj/2\nPux9uKNyvQ8z9CoqiGgFwO8A+EkAbwHwLiL63p6K+7/LclKeAfCxEML3APgEgF/quMxDAO8LIbwF\nwI8A+Pnl/fVWbgjhHoAfDSH8AIDvB/A/ieiH+iwz470APpdsD1XuKHgf7qfckfux92Hvw63xPiwg\nvZWyiwXADwP4i2T7GQBP91je4wA+m2x/HsCNZXoLwOd7vt8/BfDjQ5ULYBPA3wP4wSHKBPAYgL8G\nsA3go2O08dCL9+H+yx2yH3sf9j7cU5neh5dL3+6PbwPwlWT735d5Q3E9hLAHACGEXQDX+yqIiJ7A\nsVr9JI5/3N7KXZq+Pg1gF8BfhxA+1XeZS34TwC8CSKcMDVHumHgf7qnckfqx92Hvw12W530446IF\navYyf5aIrgD4MID3hhDuMOV0Wm4I4Sgcm9weA/BDRPSWvsskop8GsBdCeAmANsfe5yj3y7now8Dw\n/dj78GTwPtyQOfThvkXFfwD4jmT7sWXeUOwR0Q0AIKItAK90XQARreG4I38ghPCRocoFgBDCfwHY\nAfD2Acp8G4B3ENEXAPwRgB8jog8A2B3iXkfE+3DPv+uA/dj78DHehzvG+/Ab9C0qPgXgu4nocSLa\nAPC/AXy0x/IIp9XbRwH87DL9MwA+kp/QAX8A4HMhhN8aolwieiRG9hLRZQA/AeDlPssEgBDCL4cQ\nviOE8J04/h0/EUL4PwD+rM9yJ4D34R7KHaMfex/2Ptxlgd6HBfoO2sCxcvtnAP8K4Jkey/lDAF8F\ncA/AvwH4OQDXAHxsWf5fAbjacZlvA7AA8BKATwN4cXm/b+qrXADftyznJQCfBfAry/zeymTq8CTe\nCBAarNyxFu/DvZQ7aj/2Pux9uINyvQ8zi7+m23Ecx3GcTrhogZqO4ziO4/SEiwrHcRzHcTrBRYXj\nOI7jOJ3gosJxHMdxnE5wUeE4juM4Tie4qHAcx3EcpxNcVDiO4ziO0wkuKhzHcRzH6YT/BonJgASS\nB+IZAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n_samples = 100\n", "z_array = gp.sample(indep,n_samples)\n", "\n", "q_max = np.zeros(n_samples)\n", "phis = np.zeros((n_samples,2))\n", "\n", "u1,u2 = 0.5, 1.\n", "\n", "n_plots = 3\n", "plt.figure(figsize=(9,n_plots*3))\n", "for scan_no, z in enumerate(z_array):\n", "\n", " scan = z.reshape((n_scan_points,n_scan_points))**2\n", " \n", " q_max[scan_no] = np.max(scan)\n", " \n", " # fill holes from failures in original likelihood\n", " scan = fill_holes(scan)\n", "\n", " #get excursion sets above those two levels\n", " exc1 = (scan>u1) + 0. #add 0. to convert from bool to double\n", " exc2 = (scan>u2) + 0.\n", " #print '\\nu1,u2 = ', u1, u2\n", " \n", " #print 'diff = ', np.sum(exc1), np.sum(exc2)\n", " \n", " if scan_no < n_plots:\n", " aspect = 1.\n", " plt.subplot(n_plots,3,3*scan_no+1)\n", " aspect = 1.*scan.shape[0]/scan.shape[1]\n", " plt.imshow(scan.T, cmap='gray', aspect=aspect)\n", " plt.subplot(n_plots,3,3*scan_no+2)\n", " plt.imshow(exc1.T, cmap='gray', aspect=aspect, interpolation='none')\n", " plt.subplot(n_plots,3,3*scan_no+3)\n", " plt.imshow(exc2.T, cmap='gray', aspect=aspect, interpolation='none')\n", "\n", " phi1 = calculate_euler_characteristic(exc1)\n", " phi2 = calculate_euler_characteristic(exc2)\n", " #print 'phi1, phi2 = ', phi1, phi2\n", " #print 'q_max = ', np.max(scan)\n", "\n", " phis[scan_no] = [phi1, phi2]\n", "\n", "plt.savefig('chi-square-random-fields.png')" ] }, { "cell_type": "code", "execution_count": 71, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(14.359999999999999, 13.76)" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ "exp_phi_1, exp_phi_2 = np.mean(phis[:,0]), np.mean(phis[:,1])\n", "exp_phi_1, exp_phi_2" ] }, { "cell_type": "code", "execution_count": 72, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "7.34442273108 14.81882537\n" ] } ], "source": [ "n1, n2 = get_coefficients(u1=u1, u2=u2, exp_phi_1=exp_phi_1, exp_phi_2=exp_phi_2)\n", "print n1, n2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With estimates of $N_1$ and $N_2$ predict the global p-value vs. u" ] }, { "cell_type": "code", "execution_count": 73, "metadata": { "collapsed": false }, "outputs": [], "source": [ "u = np.linspace(5,25,100)\n", "global_p = global_pvalue(u,n1,n2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Generate 5000 instances of the Gaussian Process, find maximum local significance for each, and check the prediction for the LEE-corrected global p-value" ] }, { "cell_type": "code", "execution_count": 74, "metadata": { "collapsed": true }, "outputs": [], "source": [ "n_samples = 5000\n", "z_array = gp.sample(indep,n_samples)\n", "\n", "q_max = np.zeros(n_samples)\n", "\n", "for scan_no, z in enumerate(z_array):\n", " scan = z.reshape((n_scan_points,n_scan_points))**2\n", " q_max[scan_no] = np.max(scan)" ] }, { "cell_type": "code", "execution_count": 75, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 75, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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7qZupnISp8zJsKOWtpXOnd0hLdWUZYgMcZkODyoH3JEkpJgdJUorJQZKUYnKQJKWYHCRJ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\nTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bins, edges, patches = plt.hist(q_max, bins=30)\n", "icdf = 1.-np.cumsum(bins/n_samples)\n", "icdf = np.hstack((1.,icdf))\n", "icdf_error = np.sqrt(np.cumsum(bins))/n_samples\n", "icdf_error = np.hstack((0.,icdf_error))\n", "plt.xlabel('q_max')\n", "plt.ylabel('counts / bin')" ] }, { "cell_type": "code", "execution_count": 76, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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VL2XF1lwWA69XV/OwC4svgQct+EfS4hXRckf+MsAVNQ0ABT+r8MOChbfJMiK2UWdydesx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\nSJEP6/hrURcPqFw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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot the p-value \n", "plt.subplot(121)\n", "plt.plot(edges,icdf, c='r')\n", "plt.errorbar(edges,icdf,yerr=icdf_error)\n", "plt.plot(u, global_p)\n", "plt.xlabel('u')\n", "plt.ylabel('P(q_max >u)')\n", "plt.xlim(0,25)\n", "plt.subplot(122)\n", "plt.plot(edges,icdf, c='r', label='toys')\n", "plt.errorbar(edges,icdf,yerr=icdf_error)\n", "plt.plot(u, global_p, label='prediction')\n", "plt.xlabel('u')\n", "plt.legend(('toys', 'prediction'))\n", "#plt.ylabel('P(q>u)')\n", "plt.ylim(1E-3,10)\n", "plt.xlim(0,25)\n", "plt.semilogy()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Study statistical uncertainty\n", "\n", "Outline:\n", " 1. generate `n_samples` likelihood scans using the GP\n", " 1. make exclusion sets, calculate phi1, phi2 for levels u1, u2\n", " 1. look at histogram of phi1, phi2 (notice that they are narrower than Poisson)\n", " 1. look at 2-d scatter of phi1, phi2 (notice that they are positively correlated)\n", " 1. look at 2-d scatter of coefficients n1, n2 (notice tha they are negatively correlated)\n", " 1. Compare three ways of propagating error to global p-value\n", " 1. Poisson, no correlations: estimate uncertainty on Exp[phi1] as sqrt(exp_phi_1)/sqrt(n_samples) \n", " 1. Gaus approx of observed, no correlations: estimate uncertainty on Exp[phi1] as std(exp_phi_1)/sqrt(n_samples) \n", " 1. Gaus approx of observed, with correlations: estimate covariance of (Exp[phi1], Exp[phi2]) with cov(phi1, phi2)/n_samples -- note since it's covariance we divide by n_samples not sqrt(n_samples)\n", " \n", "Conclusions:\n", "\n", "The number of islands (as quantified by the Euler characteristic) is not Poisson distributed. \n", "Deviation from the Poisson distribution will depend on the properties of the underlying 2-d fit (equivalently, the Gaussian Process kernel). In this example, the deviation isn't that big. It is probably generic that the uncertainty in phi is smaller than Poisson because one can only fit in so many islands into the scan... so it's probably more like a Binomial.\n", "\n", "Unsurpringly there is also a positive correlation between the number of islands at levels u1 and u2.\n", "This turns into an anti-correlation on the coefficients n1 and n2.\n", "\n", "The two effects lead to the Poisson approximation over estimating the uncertainty on the global p-value." ] }, { "cell_type": "code", "execution_count": 142, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from scipy.stats import poisson" ] }, { "cell_type": "code", "execution_count": 143, "metadata": { "collapsed": false }, "outputs": [], "source": [ "n_samples = 1000\n", "z_array = gp.sample(indep,n_samples)\n", "phis = np.zeros((n_samples,2))\n", "\n", "for scan_no, z in enumerate(z_array):\n", " scan = z.reshape((n_scan_points,n_scan_points))**2\n", "\n", " #get excursion sets above those two levels\n", " exc1 = (scan>u1) + 0. #add 0. to convert from bool to double\n", " exc2 = (scan>u2) + 0.\n", "\n", " phi1 = calculate_euler_characteristic(exc1)\n", " phi2 = calculate_euler_characteristic(exc2)\n", " phis[scan_no] = [phi1, phi2]" ] }, { "cell_type": "code", "execution_count": 147, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 147, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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uwj1VY5n12la8PJ3n1DkipBuXy1Sm2ndjUYkJ6faVLXaFad3WcleFGLr+735i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\nPw6//go+PvaL093IUEqR+66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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bins = np.arange(0,25)\n", "counts, bins, patches = plt.hist(phis[:,0], bins=bins, normed=True, alpha=.3, color='b')\n", "_ = plt.hist(phis[:,1], bins=bins, normed=True,alpha=.3, color='r')\n", "plt.plot(bins,poisson.pmf(bins,np.mean(phis[:,0])), c='b')\n", "plt.plot(bins,poisson.pmf(bins,np.mean(phis[:,1])), c='r')\n", "plt.xlabel('phi_i')\n", "plt.legend(('obs phi1', 'obs phi2', 'poisson(mean(phi1)', 'poisson(mean(phi2))'), loc='upper left')" ] }, { "cell_type": "code", "execution_count": 149, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Check Poisson phi1 14.628 2.87256261899 3.82465684735\n", "Check Poisson phi1 13.88 2.38528824254 3.72558720204\n", "correlation coefficients:\n", "[[ 1. 0.43701228]\n", " [ 0.43701228 1. ]]\n", "covariance:\n", "[[ 8.25987588 2.99735736]\n", " [ 2.99735736 5.6952953 ]]\n" ] } ], "source": [ "print 'Check Poisson phi1', np.mean(phis[:,0]), np.std(phis[:,0]), np.sqrt(np.mean(phis[:,0]))\n", "print 'Check Poisson phi1', np.mean(phis[:,1]), np.std(phis[:,1]), np.sqrt(np.mean(phis[:,1]))\n", "\n", "print 'correlation coefficients:'\n", "print np.corrcoef(phis[:,0], phis[:,1])\n", "print 'covariance:'\n", "print np.cov(phis[:,0], phis[:,1])" ] }, { "cell_type": "code", "execution_count": 150, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 150, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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ygKbpMAwNkYiK8+cVHD1qptQK0jqhSA1DRySiwelUoSjKenYVdz9CYIsCNlHt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\n/LiZiA8dq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iAIgBgEQRAEoYoYBEEQBAEQgyAIgiBUEYMgCIIgAGIQBEEQhCpiEARBEARA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\nCAIgBkEQBEGo8v8BiZGazfXNIKMAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x, y = np.random.multivariate_normal([np.mean(phis[:,0]),np.mean(phis[:,0])], np.cov(phis[:,0], phis[:,1]), 5000).T\n", "_ = plt.scatter(phis[:,0], phis[:,1], alpha=0.1)\n", "plt.plot(x, y, 'x', alpha=0.1)\n", "plt.axis('equal')\n", "plt.xlabel('phi_0')\n", "plt.ylabel('phi_1')" ] }, { "cell_type": "code", "execution_count": 151, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 151, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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YYFkmQSC5fr1Cr5dBiAxB0OP4+JBOJ8FolGV/v02jkWFzc41MJoWUGb71re9h288zM2Mz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\n0PUSjcYcw+E+ExMxFy5MEwQBL7/8A3Z2PDQNlpddhsMdcjm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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "toy_n1, toy_n2 = np.zeros(x.size),np.zeros(x.size)\n", "for i, (toy_exp_phi_1, toy_exp_phi_2) in enumerate(zip(x,y)):\n", " n1, n2 = get_coefficients(u1=u1, u2=u2, exp_phi_1=toy_exp_phi_1, exp_phi_2=toy_exp_phi_2)\n", " toy_n1[i] = n1\n", " toy_n2[i] = n2\n", "plt.scatter(toy_n1, toy_n2, alpha=.1)\n", "plt.xlabel('n1')\n", "plt.ylabel('n2')" ] }, { "cell_type": "code", "execution_count": 152, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# now propagate error exp_phi_1 and exp_phi_2 (by dividing cov matrix by n_samples) including correlations\n", "x, y = np.random.multivariate_normal([np.mean(phis[:,0]),np.mean(phis[:,1])], \n", " np.cov(phis[:,0], phis[:,1])/n_samples,\n", " 5000).T\n", "\n", "'''\n", "# check consistency with next cell by using diagonal covariance\n", "dummy_cov = np.cov(phis[:,0], phis[:,1])/n_samples\n", "dummy_cov[0,1]=0\n", "dummy_cov[1,0]=0\n", "print dummy_cov\n", "x, y = np.random.multivariate_normal([np.mean(phis[:,0]),np.mean(phis[:,1])], \n", " dummy_cov,\n", " 5000).T\n", "'''\n", "\n", "toy_global_p = np.zeros(x.size)\n", "for i, (toy_exp_phi_1, toy_exp_phi_2) in enumerate(zip(x,y)):\n", " n1, n2 = get_coefficients(u1=u1, u2=u2, exp_phi_1=toy_exp_phi_1, exp_phi_2=toy_exp_phi_2)\n", " u = 16\n", " #global_p = global_pvalue(u,n1,n2)\n", " toy_global_p[i] = global_pvalue(u,n1,n2)" ] }, { "cell_type": "code", "execution_count": 153, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# now propagate error assuming uncorrelated but observed std. on phi_1 and phi_2 / sqrt(n_samples)\n", "x = np.random.normal(np.mean(phis[:,0]), np.std(phis[:,0])/np.sqrt(n_samples), 5000)\n", "y = np.random.normal(np.mean(phis[:,1]), np.std(phis[:,1])/np.sqrt(n_samples), 5000)\n", "\n", "toy_global_p_uncor = np.zeros(x.size)\n", "for i, (toy_exp_phi_1, toy_exp_phi_2) in enumerate(zip(x,y)):\n", " n1, n2 = get_coefficients(u1=u1, u2=u2, exp_phi_1=toy_exp_phi_1, exp_phi_2=toy_exp_phi_2)\n", " u = 16\n", " #global_p = global_pvalue(u,n1,n2)\n", " toy_global_p_uncor[i] = global_pvalue(u,n1,n2)" ] }, { "cell_type": "code", "execution_count": 154, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# now propagate error assuming uncorrelated Poisson stats on phi_1 and phi_2\n", "x = np.random.normal(np.mean(phis[:,0]), np.sqrt(np.mean(phis[:,0]))/np.sqrt(n_samples), 5000)\n", "y = np.random.normal(np.mean(phis[:,1]), np.sqrt(np.mean(phis[:,1]))/np.sqrt(n_samples), 5000)\n", "\n", "toy_global_p_uncor_pois = np.zeros(x.size)\n", "for i, (toy_exp_phi_1, toy_exp_phi_2) in enumerate(zip(x,y)):\n", " n1, n2 = get_coefficients(u1=u1, u2=u2, exp_phi_1=toy_exp_phi_1, exp_phi_2=toy_exp_phi_2)\n", " u = 16\n", " #global_p = global_pvalue(u,n1,n2)\n", " toy_global_p_uncor_pois[i] = global_pvalue(u,n1,n2)" ] }, { "cell_type": "code", "execution_count": 156, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 156, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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9mmeeeYZZs2YRFhbmqdngLSsri6FDh9KwYUNiY2MZNmwY2dnZnunWWsaPH0+d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\nRBwpSYiIiCMlCRERcfT/0EVOmIXoDcUAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "counts, bins, patches = plt.hist(toy_global_p_uncor_pois, bins=50, normed=True, color='g', alpha=.3)\n", "counts, bins, patches = plt.hist(toy_global_p_uncor, bins=bins, normed=True, color='r', alpha=.3)\n", "counts, bins, patches = plt.hist(toy_global_p, bins=bins, normed=True, color='b', alpha=.3)\n", "\n", "plt.xlabel('global p-value')\n", "#plt.ylim(0,1.4*np.max(counts))\n", "plt.legend(('uncorrelated Poisson approx from mean',\n", " 'uncorrelated Gaus. approx of observed dist',\n", " 'correlated Gaus. approx of observed dist'),\n", " bbox_to_anchor=(1., 1.3))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Conclusion: The two effects lead to the Poisson approximation over estimating the uncertainty on the global p-value." ] } ], "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": "2.7.11" } }, "nbformat": 4, "nbformat_minor": 0 }