2-Gaussian mixture fit Bayes vs NLS

2-Gaussian mixture fit Bayes vs NLS.ipynb

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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Generate the data"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import numpy as np\n",
      "from scipy.stats import distributions\n",
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline\n",
      "import seaborn as sns\n",
      "import pymc as pm"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nsamples = 1000\n",
      "mu1_true = 0.3\n",
      "mu2_true = 0.55\n",
      "sig1_true = 0.08\n",
      "sig2_true = 0.12\n",
      "a_true = 0.4"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.random.seed(3)  # for repeatability\n",
      "s1 = distributions.norm.rvs(mu1_true, sig1_true, size=round(a_true*nsamples))\n",
      "s2 = distributions.norm.rvs(mu2_true, sig2_true, size=round((1-a_true)*nsamples))\n",
      "samples = np.hstack([s1, s2])\n",
      "bins = np.arange(-0.2, 1.2, 0.01)\n",
      "data, _ = np.histogram(samples, bins=bins, density=True)\n",
      "x_data = bins[:-1] + 0.5*(bins[1] - bins[0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(x_data, data, '-o');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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SZ8QEqJYFYdXWBWFOsRBJQtvcpe05C+PckHM2jc1+vt4z7S4wi0ZkFPPtw81e\nnjMgwtVV1HSrEM0vrO0IgQvD64W4uMhMmBcWhQA556XlFbuP++R1WZw9swjANJJZS6nNTSJqhqDX\ndwpQZAmZVBSl8gHD2lUdUUW2LwSoEkbGCXrOJPQECWuXWoiQuFW8iuUa3nXPfXhqzb+1o+45N1Zr\nR5V6WHu/WFcbcwuaRD0GZ3jh5TkDQDIuRlyax3fPcq5v11g85oez8hlo74WK98yA2cZ9/sIW3nXP\nfXjy4g7KVb2hQt2JeP8vbRUwnY5BliQ757x5gJwzPWcyrtA4k9AjwtqZVMz2nIu+Oefmj7SXitfW\nXgm//6kHfY/pnsnszDnbYe28UwrUFdaOBDTOluecdHvOiQiKpap9fF/POaCEZ7lD4+z3nv3Bp78F\noFkdTCAMaalcs41yLKpgIhE5cFhbXICwnYqMEwxrk9CzX6hAkkxDJEmmKFe5KazdPufcCfVqbX/j\nvFeooFQxDY7bc45Y1dq6YXhWNQvqnnO04fFUPAID9aiBX0FYUAlPEfbPWAVh7TxtPwyrAD0R929Z\nE0w78vrTmfjBC8LoOZMxhJ4zCT3m0IsoZFmyhS7c85xbec4nr2uW6cxm4nZPshci5yzCys6c84TV\nq2vmnPOYSseacsaiT7rWxnsWbVBNOWfrvpC9bOc5F9p4zmLwRTopvNDWhs7vPXvdj50AUK8od+NM\nKwjPWdzOFatNtQJ+GIbZOmXmnM3XPOgFBSHDCI0zCT17+Yqd5wVM78w/rN3s0Z09s9hQnZ3NxHHu\nztvtnmQvnCIkQGPOWZFlO0y7sVP0bMuKirB4m7GRfjlncV+IpvjlnIN7zmbPsCLLiMeUtiHis2cW\nbcESAJhKx3DuztvtkZ1+rVQJl1qafdsy1EFVwqqOiyFxIUDPmYwTNM4k1Oi6gVyx0tCjLIQunNTD\n2t4f6btPn0I2E2/rMQtEz3LVo88ZMIvTruwUYcBbbazuebf2nAt+1dqBPefG8ZJ+VKo1+70Rwy/a\ncfqlN9i3z7zM9JiLZW/pToEzrJ1NN4a1geCjI53vN8PaZBxhzpmEmnypCsNoFBCJRRVbNUxge84+\nOefj8xmcu/P2wMe1PWeXtrZtnFNRXNoyc6heoycjEblhPz9sz9mjlQoAdq3xk+1zzq3btspVHdGo\nMM4RFAKoijnnNYvjFK3pXom4X5+zM6xd97yz1u2gnnODcQ5YkU7IKEHPmYQa4Tk2hLUtoQsnpYoZ\ntpV9wr88eHqyAAAgAElEQVSdYnu+1eY+ZwDIJOuGx2uIRtRVUOaHXa3tyuEmbc/ZNKIR+XDV2pWq\nbnvOyYCes9PLFbcLHXjO7oIwAIHnOjvTCPScyThC40xCja0O5jCGQujCafjK1ZqvAMlBaG6lMg2D\nMLpOT95Lp9v2nNsZ51IVybjSdFEhwtXi4uSw1dqmcTaNXCKmoFzVbYETP5yGVCh+CQPpVxAWb1EQ\nZr5OueUx7fXWnGFttlKR8YPGmYQapwCJQBR9OT2pcqXWUle7U/zlO+thbcDMcc94qGV14jm7i8GA\nutEVBWF+Oedk4D7nmn3BkAhYYOU0pCIcLfbx9Zxj9QsA5zCP7AE95whzzmRMYc6ZhBanstdXvrWK\nV956LYC6YShXakAyiqXlFaxvF+19hMzkYah7zs3znAHgXx5dN9dQ1fHBv/hG0zGjHeScZz2MuzDY\ntufsE65PxBRIUmvP2TAMVCr1sLboUS6WaphIRH33c+aHRVhbSGj65Zw/8+Unze3KtYa/xUc+dx4A\n8MAjl/G2//Jl+2LCKQvqxHkxFI8pkBzH9pMVJWSUoOdMQolbcvPilZwtuRl3eM7u7YTMZCtpziC4\nq63tMKsiY2l5BZe36oIaXse0RUxaGGd7lnPC33Pea+M5S5KEVDzSss+5WjNgAI6cc7Aw8fZ+Celk\nFLGobE+ZauU5Ly2v4ILjPRDvy2/+6QN4+Kn63yhXrDbJgrr/Xs6csyxJVvtXzVdW9LB/b0LCBo0z\nCSWtJDdjjslUB5HmDELE1edcdXjOQY5ZH5zh3+csZjm3CmuLnLtfzlls28pztvPljpwz0H4E49Ze\nCdPpOLLpuB2ObtVK5fe+PLm62/Y47r+XuwBPtH/16u9NSNigcSZDR0NYu0e4c8aVqo6IIrWU4my1\nvxd+E6mA5oIrv5GRgFk81irnbPeAR+uGDmjtORdKVRTLNUxnYphOx7GXK6Na01GwWqmSPmHtbuH0\nnM01RwJN0iJkVKBxJqGkleSmM6x9EGnOICh2K1U95yy8uCDHDJJz9lMHA+oznevr8f+qphIRlCo1\n3wuBsquYTeSLRc+yFyLfnE2bwi0GzJ7rVp6z3/ty/cKk73HENu6/l7sALxlXevr3JiRs0DiTUNJK\nctM5NvLsmcWGSu4g0pxBaPKcLZ3ndmsTuAdneNHKcwYavdNIq7B2G5GOiq2e1hjWblX9LFqnspl4\ng7pXsVxDNCLbCmpO/N6X977hhQ2PO4MPqXjE8+/lLsBLxCKoVHX8u597XoOsaNJnf0KGHRpnElre\n9tqbAZiVyk7PSHjOYojCjyw+C4Bp5LrlQSkeYe2oQxq0nRxokD7nQgvP2f24X0EYUBcs8cs713PO\njQVhrcLEogBsOh2v9yjvl1Ao13xnOQP+78vdp09hdiqBbCaOO151k31BdetNx7zX7JFzBswLite8\n5Hp7uxfceMR3LYQMM2ylIqHlaDYJAHjO9800eEZxR0EYUG8z+tWffm7XPKioXdBVN87O9qF2cqDR\nANXawpi6ZzkLnMbZr5XKuZ1f3rlccYe123vOogBsOhO3vVjTc676znIG/N+X4/MZfPx9r8D6ullV\nPT+bwvs//kDDBY+Tes5ZePv1CnPDqBfZ6a3nihAytNBzJqFly/LenCFRAA1hbXO7uiHpFnUREkfO\nuYX32rR/AM/ZDmvHvXuNU44e5HY5Z6CV59w4FCSI4pboa86m47ZG9ta+Gdb2EyDpBHsmdt5b49vt\n7TsvKFY38k3rJGTUoOdMQovIezplIIFmz7luSGLoFk3ynTXd18vzohPPuWs5Zz/P2aeVKkhB2HQm\njorjfS512TjvF/yMs39Ye20zbz8XdJAGIcMGPWcSWuyKYbfnbOecdXu7WFTuanuP03M2DKMp59x+\n//Z9znXP2SesnXCGtf2P/Y/fuAgA+NBfPYSl5ZWm5ysHaKXa3itBkSVkUlFMWRdHlyyj6KcO1gnx\nqIKIImO/4K217c4528IppSpWN3KYnIjhaDZJ40xGFhpnElq2bM+50SOuh7VN47K9V0I2HYcUsAc5\nCNFIPedctQxsR8Y5EsRzNr1GP885FcBzXlpewcUrOfu+l2KWO+csLmJaVmvvlzCVjkGWJEQjMtLJ\nqB1O7obnLEmm4fcPa7v7nM1j7uUruLJdxMJMCtl0HIVSjQMxyEhC40xCi51L9g1r66jWdOzmK03b\nHBbFEZZ2G4ogRJUOcs5+xjnRvlo7iGKWWIO7lcqv9Uo3DGzvl5FNN7ZF1aU7uxOhSCejvmHtalNY\n2zzmU5f2YMAc01mvIg826YqQYYLGmYQWZ6+tE2cr1Y5P0dhhkSUJiiyhqutNIdYgRF3yn14I4+g3\nfjFotXY7RM5YFIQpsoxoRPb1nPfyFdR0w3PkI4AGcZTDkE5GUSzXPIVavERIANhSoPOzE3YB4DaL\nwsgIQuNMQsv2fgkRRWoQGQGAeMz82JYqNV/vuhtEFBnVqtFUORx0X6BNWLtYRSLWPMtZ0JBz9vGc\ngyhmuRXCACBpaVV7YRfiNQiKOOZpd8lzzqT8i8Ka+5zNYz5thevnZ1J2AWDQMZSEDBM0ziS0bO+X\nMe2RS1ZkGRFFQqlS8zQk3SKiSKjW9CYvLti+AcLaPhOpBEFyzk2qXOlmtTIv45yIRXxztVsehXjO\ni59u5JyB1hXbftXa4lwWZlP0nMlIQ+NMQomuG9jZL/sa3XhUQalc8zQk3SKiyI3GuZOccxBt7WLV\nt1IbaOxzjrSo1r779Cn7eG/4CbXpeeH5i2legGns/KZSbXsU4jn/Dt2qireNc745Z+wc0SnWK4hG\nZMxOJuy/OT1nMorQOJNQspsvQzcM33B1PKY0es5d7HEW2Mb5IDlnW/7Tu5VKNwwUSq2Nc7IhrO2f\ncz4+n8ErX3SttV3zGj0953gEpXINutG8PufQC0EvPOdMyvyb7Xl4zlWXtrbzguBYNgVZluoFYfSc\nyQhC40xCiVOhyot41DLOHoakW0QUCZWa0VQ5HGhfqxXLryCsWKqZs5wT3upgQHBtbcAM8wLAmkM9\nS1CpNCqEAXUDW/Lwnre8cs4DCGs7R3Q6jynOdTJltnqxWpuMIjTOJJTUc8neHrEd1ra2m+qFcY7I\nqB0w56zIMiTJP6wtepxbhYgbRka2qdZemJ0AAKxu5JqecyuEAa0nUzmHXgicaYOutVKJgjCPXme3\n6EvcwzjLsoSpdIwSnmQkoXEmoaSdRxyPKihXdWzulZBORjsynEGJKDIqB8w5A6Yx9ysI+6PPfhsA\n8D+/veap6gUA//kvv2nf/oNPP+i5jeDYjDkkZNXLc3YphC0tr+DrD18GAHzor77VsO3S8gq+9eQG\nAOCez9Sf++O//rZ9+y/vfbzlWoKSaeU51xq1zJ3vxT9r6/bt6XQc2/slz/A8IcMMjTMJJe0KvYQn\ndWW72JNiMMCq1q4aB8o5A6Yx9wprLy2v4MmLu/Z9L1WvpeUVnHcIjDz81HbTNk4SsQhmJuO27rQT\n58WF+3WfeGbXfl33c2Jdv/mnD+Dhp+qPP3lxt+VagtIurC3eb/e6nrmSs4+fzcRR0w1fMRNChhUa\nZxJKtveaQ6tOhBBJq6KxwxJVZOiGYedlIx0aZ7NPutk4B1H1CrKNm4WZFLb2Sk3KX86CsFav6/ec\nEP7oZC1BsCdT+eWcrTB8qzVnWRRGRhQaZxJK2omLOHOQWZ+89GERRVgiL9ux59wirN0L5q2886Wt\nRu+5Uq0hGpG7qj3eDWJRBfGo4p9zDpBGEDUJHIBBRg0aZxJKtvdKSMYjDUbYSdzRs9srz1kYZ+GJ\nRpXOqpT9POcgql5BtnEzP2MWSrnzzuWqbldqt3pdv+euX5jseC1BMfW1vfucowHWLP72LAojowaN\nMwkl2/ullrnkBuPcw5wzABQsJa1OPWezoKy5UOnsmcWG1qBsplnVq0n5y2MbN6KK2W2cK5W6oXO/\nbjyq2K979swiJhy91eKY733DCzteS1DSqWhTWNs9orPVeyH+9jTOZNSgcSaho1ypIVes2trJXjSE\ntfvlOXcc1pZ8+5yfd8MRAKa+tJ8HevfpU8hm4oG9VNFOteZqpypXa/ZEKvG6UxPme3vi6qmGbW+/\neR4AMJGINByz07UEJZOMolzRUarUW7q8RnT6HT/LyVRkROnedHpCusR2gGEW/Qxr50sHzDkrMipV\nHYZhNOV7hUjJr//iC3F0Oum5//H5DM7deXvg402nY4jHFKxuunPOOiYcw0OOz2fwgbfehrd84B+b\n+rBlyTzHf/dzz2vwjDtdS1BEr3OuULH/pl6ta37HFx41c85k1KDnTEKHl0KVm3i0/tHtWSuVZYyL\nds65w7C2tX9Nbw5t27Ocu6RTDQCSJGFhJoVLm3nojmN6FVdFFBmZiViTLnUvp3x5YVdsO4rCOmld\nS8TMojJWa5NRg8aZhI4gwyxEWFuRJdv76jYRS5XroGFtezKVR1GYPcu5S7ORBQuzKVRrBq7sFACY\n+VtnQZiT6XQM2/slGA4Bj+29EiQAUz3QKvfCS4ikkxGdkiRhOhPn8AsycgT6tVFV9VZVVe/1ePwd\nqqo+pKrqvda/G7u/RDJOLC2v4MN/fR4A8D++cdF3u//+1acBmF7pB//iGz1Zi/B88wfNOdvDL5qN\nc75kznJWWkybOgiPP2P2JL/7j7+KpeUV+9jRaPNFQDYdR7miN/RFb+2XkJmItdXy7hZpe/hFPWfc\niVzq0vIKLm3msZev4AOf8FZaI2QYafvpV1X11wB8BICXG3MLgNdrmvYj1r9Hu71AMj64laC+e3nf\nU4lqaXkF3728b9/3UtjqBt3ocwa8Ped8sfUs54OwtLyC9e2Cff/8hS38hz/6nwDg7Tm7Kp0Nw8D2\nXqknE778qI+NdHrOweRSm1XUevM5IGQQBPm1eRzAawF4KRi8AMB7VFX9J1VV393VlZGxI6gq1kHU\nsw6CaKU6qOccaeE5txsXeRC83hdRxey1dnelc6FURbmq96z63QsvCc+gOed+fQ4IGQRtfx00Tfu0\nqqrX+Tz9CQD3ANgD8BlVVX9K07QvtHq9ubnD90YOMzz/FucvAfCYXyDLUuN+Qbc7JNOTZhW1kO9c\nmJ9qqBJvR8YycpnJpL2uubkMdN2c5XzdVVPd/Tz4vC8AMJlONB3rmqvMNqoqzPftqTUzJD4/l+7Z\n59T9urmqueCqUX9ubdeaNOZ43zzp0+egW4RxTf1k3M+/Uw576f57mqbtAoCqql8AsAigpXFeXx/f\nkNPcXIbn3+L8Tx7PNoQpAbMo7K7X3NywX9DtDkup2CiOsb2Vs+cLB6FSMT3uy+v7SCqSff6FUhW6\nAURlqavr9XpfJlNR7OYrqNVqTcdSrEKw767uYH19D9952tw3GZF78jn1+vtXiqbXvr6Zt5+7csVM\nWVTKla58XsIAv/s8/045cNWHqqpTAL6lquqEqqoSgJcBeOCgr0dIUFWsg6hnHQQR1ha3OzHMgCPn\n7AprizaqVrOcD4L7fZlKx/D2n3seAO+cs9hWVDoHaWHrNp5h7YA5Z/f5puKRnnwOCBkEnRhnAwBU\nVX2dqqp3aJq2A+DdAO4F8GUAD2ma9sUerJGMEXe99mYAgKJILZWoeqVY5cRZsXyQedF2tbarIEzk\nsLtdEAaY74sIvZ/+oRtaVj6Lwi/RI9zvHmfAfI+TceVAOWfAPF8hOfpDpxZ6s0hCBkCgXwdN0y4A\nuM26/QnH45+AmXcmpCsczZp53lPXz7b0gHqlWOXEOSKyUwESwL8gLG+Fy7tdEAaY78vrfuwEPv7f\nH4EBA2W7Z7g5V55ORhFRZFtdaztAf3kvMIdfNHvOQUZ0Hp/P4M3/+jn4z3/5zZ71uxMyCChCQkKF\naKlJJwf/Q3tYz9lPhKSXnjPgmE61mUelYh7bK6wtSRKm0zE7nC086H62UgFAOhnDXr5ii6F00ucM\n1M+tXOnfeE5Ceg2NMwkVYkJRGLyghpyzh+fZjnY55154zkB9OtXaRh7lqr9xBsz88k6uDF03sL1f\nQkSR+35hlElFUa3Vh1/Uc87B3vOYFcYXUQJCRgEaZxIqwuQ5O0PZBwlrC+PcFNbuseecScWQTkax\nupFrGdYGzF5nwwB2cmVsWQIk7iEdvcYtRNJJzhlwGGd6zmSEoHEmoULIOIbBOCsNYe3ODZbwvKuu\nmc6FHlVrO5mfTWF9u4iCNVErFvXxnK3ir83dInZy5b5WagOmytf9D60BAP7wsw8B6DysHbfD2vSc\nyehA40xChSgMyiT7m/f04vCec+MIREGvPWcAWJhJQTcMPLO+b63Fe/2i+OvpS3swjN7NxvbCLb/5\nndU9vOue++yhHUHfc+E5lzxkUgkZVmicSaiww9ohyDkrjpzzwQrCzP2bjHOPc84AsDA7AQB4+lJr\n4zydMS+CvrNqCkT0s43KT37zgUfWAXQS1qbnTEYPGmcSKvZsz3nwxrnBcz5IQZhfK5XtOffuHOet\norBnLLWtWIucMwB8x5Lu7HcblReGpckZpJUKqJ8bjTMZJWicSajIhala22EcghqKhv3b9Dl3e5az\nkwWrnUrku/09Z9MYX7ySs+73L51w8rps02PZTBwnj5uPB/WcZVlCRJHtynRCRgEaZxIq9goVyJLU\n02KpoERkR1j7ENXaXjnneA9mOTs5Mp2A4li/byuV5TlbLcZ9zTm75TdlWcK5O2+3Fc46ec/jUZme\nMxkpaJxJqNjPV5BORjrWse4FDQphhxEh8ehz7mW+GQAUWcYxy3sGgKjPNK14VGlYS7+rtYUMqyJL\nkGCgpusdV2sDZlEYW6nIKEHjTELFfqGCdGrwldpAFxTC7D5nVytVqdrTSm3BgsM4+3nOQGOeuZ8F\nYUBdhvXWm46hpgNXdood9zkD5vmVKEJCRggaZxIadN1ArlAJRY8z0KgQdrDBF1afsyOsrRsG8qXe\ne85AvSgMaG2chVxnKh7paF51NxGqZqsbefv96iSsTc+ZjBo0ziQ05IoVGAhHpTbg8pwP0+fsCGuX\nyjUYRm/bqAQLDuPc6uJChLIHWak9P2O2fq1t5FGp6lBkCbIcPLURY86ZjBg0ziQ07IeoUhuAlQc1\nOUyfs9Nztnuc+xDW/vt//p59+/c++aDvdtrT2wCAZ67ksLS80vN1eVH3nHOoVPWO3+9YREFNN5oq\n4wkZVmicSWjYC5GuNmBObRISnt0qCLN7nOO9Pcel5RVbWAQAzj+1hXfdcx+eWttr2u7KTrG+3QXv\n7XrN0WwSsiSZk7RqnRtnEY53V8YTMqzQOJPQsB8iARKB0NQ+UM7ZY/CF3ePcY8/ZT33r9z/14IG2\n6zURRcbcdMIOa3fsOVMljIwYNM4kNIQtrA3Uvd+D5JxFWNzpzdU958H3cYeNhdkJ7Bcq2MmVO36/\nhUoY9bXJqEDjTELDXl5MpApHKxXgMM4H8JwlSUIkIjd4zoU+DL0A/NW37j596kDb9QNRXU7PmRAa\nZxIi7LB2qDzng4e1zf1lVKr1Pud+DL0AmtW3spk4zt15O47PZw60XT9w9mV3bpw505mMFjTOJDTs\nh6wgDDic5wyYvc5Vr4KwPlRrC/Wtdp5w0O16jZikBXSeRhB93PScyajAxBcJDWIiVSiN8wFyzoBp\n1CsDaqUS6lvd2q7XzAfsy/ZCVGuXqRJGRgR6ziQ07BcqUGQJidhgVKq8qHvOB1tTRJG9PWcWhDWR\nTkbtlEan7zfD2mTUoHEmoWE/X0E6FYUUgqEXgkPnnN0FYcXez3IeZkTeudMRnSKsXWJYm4wINM5k\nICwtr+CNv/MPeOPv/IOtSrVXqISqx3lpeQWPfW8HAPDnf6sdaP9n1nPIFav2OQrPuZeznIeZy9sF\nAMADj1zuSK3M9px9Wqm8Pm+EhBkaZ9J3lpZXcP7CFgwABkxVqnf+wVdQKFVDk28WaxQ8cXG3I+Us\n9/7nL2zhl97/JWztlXo+y3lYWVpewfZ+2b7fiVpZq1Yqr8/bIFTQCOkE/kKQvuOlSiV+lMMyLvKw\nylle+2/sFHF5K898sw+Hec/rOedm4xwWFTRCOoHGmYSKMIW1e4Fh9KdSe9yIR1qHtQkZNmicSd/x\nUqUS4eywhLUPq5zltf/sVAIGWKntx2HecxHW9ioIC5MKGiFBoXEmfefsmcWGdqlkXMEvvkIFEB5d\n7cMqZ7n3l2UJH/q1lwGgcfbjMO95q1aqs2cWGy76ptOxgamgERIUGmcyEL5vof7DODedDOVEqsMq\nZ4n9oxEZum7g0afN3CfD2v4c9D23FcJ8REh+8OZ5+/a/fbl6uEUS0gf4K0EGwm6+gnhMwTVzaTxx\ncQerG3kA4fGcgcMrZ4n9v/LgKj72Nw/j7x/4LoDez3IeZg76nrcTIXFOq5qcCEfRISGtoOdM+o6u\nG7i0WcDCTAqLNx6BYQBfPb8GAMiEaCJVt3jes2chScD9D64CAJIJ9jh3m3ba2mvWxR9Q13AnJMzQ\nOJO+c2W3iGpNx/xsCrecmAMA7IVw6EW3yKRiuPHqadtw0HPuPlE7rO3tOa9u5Ozbe4Wy5zaEhAka\nZ9J31qwfyoWZFI7NpOxKWwD46BfOD2pZPWU7V7Jv/9ODFwe4ktFEkiTEorKn51woVbG9X4Yim1Ks\nor6BkDBD40z6jsgvL8xOYGl5pSFP+MjT2yOn3rS0vIJLmwX7/upGfuTOMQzEIoqn57y2aX7erj1m\nFiEyrE2GARpn0neEcZ6fTY2FetM4nGMYiPt4ziLffOLqKQD10aSEhBkaZ9J31jZykCTgWDY56KWQ\nESIWVTyN8+qmmUY5cfU0AHrOZDigcSZ9Z3Uzj7mpJKIRZSzUm8bhHMNALKI0tEwJRKTm+qsmIUsS\nc85kKKBxJn1lv1DBXr6C+Vlzbu9hlbiGgXE4xzAgCsIMw2h4fG0jj2RcwXQ6hnQqyrA2GQponElf\nEcU5C5ZxBg6vxDUM3H36FGanEiN9joMmFlVgGEC1VjfONV3Hpa085mcmIEkSMskocjTOZAigQhjp\nK6LfdGF2wn7ssEpcw8Dx+Qw+/r5XYH2dFdq9winhKfqer+wUUa0Z9sVgOhnFxSs56LoB2WqtIiSM\n0HMmfUVUzs7PpNpsSUhnxD0kPFddn7d0MgoDQK5I75mEGxpn0lfqPc40zqS7CDEbZ8X2muvzJrTb\nWRRGwk4g46yq6q2qqt7r8firVVX9uqqq96uq+qbuL4+MGqubeUwkIsikRk9DmwyWWMT0nJ0zndes\nNqp5K40i5GH32E5FQk5b46yq6q8B+AiAuOvxKIAPAvhxAC8F8GZVVY/2YpFkNPj1P7wPlzbzyBWr\nWFpeGfRyyIhhT6ay2qmWllfw5W+aw0b+3//vUQD1kaT0nEnYCeI5Pw7gtQDc1RMnATyuadqOpmkV\nAF8B8JIur4+MCEvLK3jw8Sv2/fMXtihhSbqKM6y9tLyC8w5ltoefMj9vxUoVAI0zCT9tjbOmaZ8G\nUPV4ahLAjuP+HoCpLq2LjBiUsCS9RoS1yxXd9/P2dw88AwDYy3MyFQk3h2ml2gHgVFHIAGj+RriY\nmxtv4YWxPX8JgNH8sCxLY/WejNO5etHL85+1KrITyZjv501RzABgDf3/3PFvP97n3ymHMc6PADih\nqmoWQA5mSPsD7XYa5z7PubnM2J7/91+bxcNPNV67ZTNx3PWam8fmPRnnvz/Q+/MvW+1R65v7OHk8\n2xDWBszP2+tffiN+/1PfwvpGrq9/C/7tef6d0kkrlQEAqqq+TlXVO6w88zsBfAnA/QA+qmnaascr\nIGPBK2+9tuE+JSxJt4k5+pzPnllEKl73PcTnTb3W1DmnhCcJO4E8Z03TLgC4zbr9Ccfjnwfw+Z6s\njIwUK4+uAzCrZSMRmRKWpOs4FcIA4NabjuLelYtIJ6P25y0RUxBROPyChB/Kd5KeoxsGVh67gsmJ\nGD545+2UTSQ9IeZSCDOsBpNf+4VFXD2XBgBIkoR0MsqxkST0UCGM9JzvXNzFTq6MF900T8NMeoZb\nIWx7rwQADRPBACCdjDGsTUIPjTPpOSuPmf3NL37u/IBXQkaZeKTRc97aLyEakRtyzwCQSUVRKFVR\nrTXPfiYkLDCsTXrG0vIKHr6wBQOAJAHPV49idzs/6GWREUV4zqVq3XPOpuOQpMZojZDwzBUqmEo3\netWEhAV6zqQnCIUm0WpqGMBbfvvvqAhGekY951xDTdexmytjOtNsfMXwC4a2SZihcSY9wUuhaWOn\nSEUw0jOcCmE7+2UYAKbTzQNWbH1tFoWREEPjTAgZCeyCsGoNW/vexWBAPazNdioSZmicSU84eV22\n6bHZqQT7m0nPiCgyFFlCuaJje8/Uzp72yCkzrE2GARpn0hPOnllE1vHDmM3E8fH3vYKKYKSnxKIy\nypUatlt4zpmkGere5/ALEmJonEnP+OWfOgkAiFIRjPSJWERBqapjy+px9vSck/ScSfihcSY9I2pN\nAHr5D1xDj5n0Bbfn7FmtzZwzGQJonEnPWN0we5rnrVF+hPSaWFRBuVKzPeesR7W2yDmzWpuEGRpn\n0jOEcV6YnRjwSsi4EIsoKFd1bO+XkE5GEbXaq5zEowpiEZmeMwk1VAgjPWN1MweAnjPpH/GojIqV\ncz4ylfDcZml5BeWqjgtre1haXsHZM4u+24l+/ZPXZX23I6QX0HMmPWNtI4+piRhSCV4Dkv4gVMKK\n5Zpnvlko1wnOX9jCu+65r0m5zqlwZ7TYjpBeQeNMekKpUsPGThELs/SaSf8QM50B70ptL+W6rb1S\nk3Jd0O0I6RU0zqQnXNrMwwAwz3wz6SPCcwbQ0GdPyLBB40x6wtqmVQzGfDPpI07P2UuAxEu5LpuJ\nN/XhB92OkF5B40x6wppdqU3jTPqH03P2CmufPbPYYLSTMQXn7ry9qQ//7JlFJGJK2+0I6RU0zqQn\nrFqe8zyNM+kjYvgF4O05A8Ddp09hcsLsf77xmmnf1zp+rG6IZ30qvwnpFTTOpCesbuQQi8iYmeSP\nGkpjGt0AABVgSURBVOkfsYjTc24WIAGA4/MZLL31Niiy1FLCczdfxkQighuvmcYz6znsWKpjhPQD\nGmfSdXTDwNpmHvMzKciSNOjlkDFChLUVWUJmwts4A+YEq6PZJNY28jAMo+n5ak3H5a0C5mdTuOXG\nORgAvvH4lV4tm5AmaJxJ19naLaFc0RnSJn1HhLWn0rG2F4YLsxPIl6rY9ZDxXN8uoKYbWJiZwOKJ\nIwCAlcdonEn/oHEmXWVpeQX//g/vBwA8eXF3wKsh48bfP/A9AMDmbglLyysttxXFimsbuabnnAWN\nc9NJxKMKHnxiA2/8nX9o+7qEdAMaZ9I13OpLV3aKVFUifWNpeQXPXKkb2naqXkJWVmjAO7ELGmdS\nWFpeQalSA0C1MNI/aJxJ16CqEhkknX7+xEAWT+NsedPzsyl+rslAoHEmhIwltue86R3WVmQJc9PJ\nfi+LEAA0zqSLUFWJDJJOP3+pRARTEzE7vywwrG6Do9kkIorMzzUZCDTOpGucPbPY0FuazcSpqkT6\nhlv9K8jnb2E2hY2dIspWThkA9vIV5IpV27N2v+50OsbPNek5NM6kq/zsD98AwBxoT8+C9Ju7T59C\nNhMP7NnOz07AAHBpq2A/JvLNC46hLXefPmW3ab3ux27s7qIJ8YCDdklP+N9e9mx6FqTvHJ/P4Nyd\ntwfefsGu2M7hmqNp8/Zmsy788fkMfvLW4/irr3wHqTh/NknvoedMuoqofOU0KjIM1Hud63lncdst\nojNthba39ijjSXoPjTPpKpxGRYYJYYCFtwz4X2CKKVfb1NgmfYDxGdJVVjfzSMYVe+oPIWHm//6b\nRwAAXzt/CXv5MgDYQjof+quHcPbMor2tKArbonEmfYCeM+kaNV3Hpc085mcmIHHgBQk5S8srePip\nusDI+QtbDQp3biUwYZy3GdYmfYDGmXSNK9tFc1gAQ9pkCPBS/nLjVAKbSEQQUWSGtUlfoHEmXcOr\nypWQUUGSJEynYywII32Bxpl0DbvKdWaizZaEDB4v5S837n7p6UwcO7kydL15BjQh3YTGmXSNungD\nPWcSfrwUxdopjGXTcRgGsJMr93WtZPygcSZdY3UzD1mScDTLYQFkOHArirVTGLOLwph3Jj2GrVSk\na6xt5DFnDQsgZBjwUhRrpTBm9zrvlYCFni6NjDn8FSVdYS9fxn6hQmUwMtJMZ8z+ffY6k15D40y6\nwqqP5CEho0SWKmGkT7QMa6uqKgP4EIBTAEoA3qRp2hOO598B4I0A1q2H3qJp2qM9WisJMWub1NQm\now/1tUm/aJdz/hkAMU3TblNV9VYA56zHBLcAeL2maSu9WiAJP0vLK7ay0r0rz+CHnnfVgFdESG9o\nyDkT0kPahbVvB/BFANA07WsAXuh6/gUA3qOq6j+pqvruHqyPhBynYQaAC2t7DZKHhIwS8aiCVDyC\n7X22UpHe0s44TwLYddyvWaFuwScAvAXAywD8oKqqP9Xl9ZGQ4yWB6JQ8JGTUyGbiDGuTntMurL0L\nIOO4L2uapjvu/56mabsAoKrqFwAsAvhCqxecm8u0enrkGbnzlwB4iCXJsuR5riN3/h3C8x/+85+b\nSeGZKzlkppJIxIJ3o47CuR+GcT//Tmn3yboPwKsBfFJV1RcDsN0hVVWnADyoqupNAPIwveePtjvg\n+vr4hjvn5jIjd/4nj2cbwtqA6Vnc9Zqbm851FM+/E3j+o3H+E3EFAPD4hQ0cywYrgByVcz8oPP/O\nL0zahbU/A6Coqup9MIvB3qGq6utUVb1D07QdAO8GcC+ALwN4SNO0L3a8AjLUnD2zCEWuj4f0kjwk\nZJTg6EjSD1p6zpqmGQB+1fXwo47nPwEz70zGlI0dc0xkRJGQScU8JQ8JGSVExTaFSEgvoXwnORQr\nj5kt7q/70RP4kVuuHvBqCOk9thDJHiu2Se+gQhg5FCuPXQEAPP/E3IBXQkh/oBAJ6Qc0zuTA7Bcq\n0J7exvctTDaM2iNklJmmhCfpAwxrk8AsLa/Yfc2pRAS5YhUAkCtUBrksQvrKn3z+PADgfz1yGef/\ny5eRt74HJ6/L4uyZxUEujYwQ9JxJIIQSmAGzrVkYZgC4vF2gKhgZC5aWV/DwU/XWwVyxan8nzl/Y\n4veAdA0aZxIILyUwJ1QFI+MAvwekX9A4E0IIISGDxpkE4uR12ZbPZzNx9jiTkYffA9IvaJxJIH7l\nJ0823JfqomBUBSNjw9kziw2dCc7vQSwq83tAugaNMwmE6GdOxSPIZuK441U3IZuJ01MgY8fdp0/Z\nn/07XnUTptMxAMDRgDrbhASBrVQkEEIJ7P1vfBFmJhMAgBc/Z36QSyJkIByfz+Dcnbfb91/8nHn8\nxw9/lVrbpKvQcyZtyRdNsZHr5jO2YSaE1FmYSWG/UMFenpKepDvQOJO2PPjEBmq6gcUbKdFJiBcL\ns2ZIe3UjP+CVkFGBYe0xxan25adsJLYxrPu3nDjSxxUSMjzMW8Z5bTOPG6+ZHvBqyChAz3kMcat9\neSkbObcRfPAvvkn1I0I8WJidAACsbuQGvBIyKtA4jyFeKkduZSPPbfapfkSIF/MzDGuT7kLjTAgh\nhySdjCKTimKNxpl0CRrnMcRL5cjdrxxkG0JInYWZFNZ3CqhUa4NeChkBaJzHkLNnFpGK12sB41Gl\nSdno7JlFZFJR+z5VwAhpzfzsBAwDuLRVGPRSyAhA4zymPM9ReT2RjHpuc/P1s/bz9JgJaY1op2Jo\nm3QDGucxpWDNY1avmcbmbtGzyvSJi7umXvBbb6PHTEgb7F7nTRpncnhonMeU1Y0c0skofuh5CwCA\nf3l0ven5S5t53Px9s4hFlUEskZChYt5qp1pjOxXpAjTOY0ilqmN9u4iF2RRO3XAEsiTZgy0Ewlgv\n3kjhEUKCcGQygYgis52KdAUqhA0pfgpfQZS/Lm8XoBsGFmZTSCejSMQVPHlxF2/8nX9AKhFBvli1\nxUdO3UDjTEgQZFmCIgMX1vYavksA8LwTc7j79M1N+wT5vpLxhJ7zEOKn8PWbf/pAW+UvoB52m5+Z\nwNLyiv0DYgDIOQwzAPynj32dqmCEBGBpeQWlig6g8btkAPjGY+stVfhafV/JeELjPIT4KXw9ubrr\n+bhb1UuE3eZnU56v1W5/QkgznX6Xgij1kfGFxnkMEcZZVJcSQggJFzTOQ4ifetf1C5Oej7t7lNc2\n84goEo5MJTxfq93+hJBmOv0uUYWPtILGeQg5e2YRaYdwyOREFOfuvB3vfcMLkc3E7ccTsWblL8Mw\nsLaZw7FsCoos4+yZxYZ9JKl+HKqCERKcVt+lTCrmqcI3kajX5Hp9X8n4QuM8pPyr5xyzb//Ei47b\nt9/0qpvs28ePNX/Jd3JlFEo1e/4sANx9+hSymTiymTjueNVN9m1ewRPSGe7vUsa6iH7uDTOe2zuj\nXSeunurLGslwwFaqIaVUqYvr14x6fXVUqV9v7ebLTft55ZuPz2dw7s7b7fsvfs58V9dKyLjg/i69\n6OQxvOMPvoKHL2xBNwzIDne6WtPx+MVdzEzGsZurYDdfGcSSSUih5zykOIUOnNKbztuXtwqo1vSG\n/UQb1cLMRI9XSAiRZQnPe/YRbO+V8OTFxm4K7bvbKJSqWDwxh/mZJNY28zAMw+eVyLhB4zykrG7k\nMTuZgCJLDUL7Qtf3aDaJmm5gfbvQtB+AhrA2IaR33HJiDgCw8lijRO6KpcJ3y4kjmJ9JoVSuYXu/\nOdpFxhMa5yFkL1/GfqGCq+cmMDedxOpG/YpbGGrxg+CekCOM9/wMjTMh/eCm67KIxxSsPFqXyDUM\nAyuPXcFEIoIT10zbutxeA2jIeMKc8xCytinyxhOQZQlrm3ns5SuYnIhhdTOPdDKKE1dP4YtfN42x\nEAQUikQAcM9nvkWpQEL6QCyqIBFTsLaZt2U9c5Yq39REDBFFrk+02sjjpuuai8cGIfN5mGO69/3d\nt72kJ2scZeg5DyFrjtD0vP2lzqFa07G+VWh4XGzrNMwApQIJ6RdLyyvYscLVQtZTsJMr41333Gc9\n4z0LehAyn4c5pte+v/T+L/G3pkNonIeQ1c16xbUo7FrdzOPyljXQYiaFuekkFFnC6qYZJqNUICGD\nIYis5yfvfQIA7O9ru/17/d09zDG99t3YKfK3pkMY1h5C1jYcYW2rNWNtI49MMmY/HlFkHM0msbbB\nClBCwo4kSchm4hw3SWzoOQ8hqxs5pJNRpJNRR1g7jzXrqls8Nj+TQq5YxV6+QqlAQgZEUFnPhdkU\ntvZKKJarDc8P4rurXjt94GN6rXdmMsHfmg6hcR4yKlUd69tF2wBPJKJmIdhGrklgZMFRAfpvX642\nvA6lOQnpD2fPLGJ2KmHf95PIFSmqS5uN7Y9ve22jUYtG5J5/d3/8B65puD+RiAQ+5tkzi0glGoOy\nd/7c8/hb0yE0zkPG5e16XlmwMJPCxk4RT1/aswdaAHUjvbqZt3ssU4kIPWZC+sx7f+XWthK5zuJO\nJw99ZxOAqb0tS4AE8yK9l4i2r1TcNLLXdmhYjx9NN+z/1W+tdnF14wFzzkOGrfA1W1f4WphNQfvu\nNr63nsOzjkxAkc1rLmfF9pMXdyFJwG+/+cXIpGL9XzghY8yzr55uK5HrbKdyIi6s//3rFvG185fw\nt//ru3jk6S3cfP1sT9aq6wa+8fgVTE3EcO6u2/GeD38VT17cRaVaQzSitN2/XKnhidVdHJtJ4bfe\ndCveec99+Pr5Nfz8D98AWZba7k9M6DkPGV4KX/MOQ+18XHjX2tPbeOKZHZy4epqGmZCQYqehNuvG\nuabr+ObjV5DNxHF8PoPFE0cAACuPXfF8jW7w+DM72C9UsHjiCGRJwi0n5lAq1/DwU62rzgXnn9pC\nuaLjlhNHIMsSnv/sI9jZL+OJizs9W/Mo0tI4q6oqq6r6R6qq3q+q6r2qqt7gev7Vqqp+3Xr+Tb1d\nKgG8B1c41b6ct1NWPvqpS3swYMoEEkLCyXQ6hnhMsaNjAPDYd3eQK1bx/GebhvLZV08hnYxi5bF1\n6D3qwvgXS1Z08UZTZfD51u/Gvzwa7IJgxbX/LTdaFxQB9ycm7cLaPwMgpmnabaqq3grgnPUYVFWN\nAvgggBcCyAO4T1XVv9Y07bLfi/3GH92Pbzpyn3mrGd95W1T6iV45v+16tX8v1zKRjCJXqBzq+ELA\n4M++qOHfv85U7Pn8/Rfs93jlsSs4/VLzGmppeQW7ubpW7/OtLwshJHyc+4tvoFSu4XvrOXzgEyuQ\nJNjCQcLrVGQZEUXC9n4Zb/rdezHRg98uA4AsAd9/rfkaz37WFBRZwpe/eRH/9M2LgfZXZAnXX2WO\nwzx5PAtZAr749afxpa8/PfDf4X7YhG6ouEmtemBVVT0H4Guapv2ldf97mqZdbd0+BeB3NU37Cev+\nBwHcr2naf/N7vVe/67NsuO0i2Uwc2XQcT67uBn787tOnBlY1OTeXwfr6+KoE8fzH9/zbnbtbwc8L\nv+91rxC/F5/8x8fbrq0X+w87zt/bublMx8n2djnnSQDOT0JNVVXZ8ZwzibAHgNPC+8jWXsnzi9rq\ncar0EBI+2qmIAf7f614hfi+CrK0X+w87h/29bRfW3gXgdLNkTdNEDf+O67kMgPH8KwwRW3ulZ+bm\nMlcP6vhzc+Pd68jzH9/zb3XuBqDD7JIKFVt7pWcAXIUDru2w+w87h/m9bWec7wPwagCfVFX1xQCc\nlwGPADihqmoWQA7ASwB8oNWLfe7cT4/lH4gQQlrxuXM/zc4Z0kC7nLME4EMARKf8LwN4AYC0pmkf\nUVX1VQDeBzM8/lFN0/6wx+slhBBCRp6WxpkQQggh/YehFEIIISRk0DgTQgghIYPGmRBCCAkZNM6E\nEEJIyOjpVCpVVZMA/hzAHEyRkjdomnbFtc07APy8dfdvNE17fy/X1A8soRZR5V4C8CZN055wPP9q\nAL8BoArgY5qm/clAFtoDApz76wC8Hea5fwvAWzVNG5mqxHbn79juwwA2NE37j31eYk8J8Pf/AZgy\nwBKAZwD8oqZpZa/XGkYCnP9rALwHgAHzu/9HA1loD7Gknn9H07QfcT0+sr97Tlqcf0e/fb32nH8V\nwDc1TXsJgD8D8F7nk6qqXg/gFwD8K03TXgzg5aqq3tzjNfUDW5McwLth/hgBaNAk/3EALwXwZlVV\njw5klb2h1bknAfwfAH5Y07QfhKko96qBrLJ3+J6/QFXVtwB4Lswf6FGj1d9fAvBhAL+kadoPAfh7\nAN83kFX2jnZ/f/Hdvx3Au1RVHSlVRVVVfw3ARwDEXY+P+u8egJbn3/FvX6+N8+0Avmjd/iKAH3M9\n/zSAVziuHqIACj1eUz+wz1vTtK/BHA4iOAngcU3TdjRNqwD4CkwBl1Gh1bkXYV6IFa37EYzG39tJ\nq/OHqqq3AXgRgD/GaKomtTr/GwFsAHinqqr/CGBa0zSt7yvsLS3//gAqAKYBJGH+/UftAu1xAK9F\n82d71H/3BH7n3/FvX9eMs6qqb1RV9VvOfzCvDoQYbJP2tqZpVU3TNlVVlVRVXQLwL5qmPd6tNQ2Q\ncdYk9z13TdMMTdPWAUBV1bcBmNA07e8GsMZe4nv+qqouwBTtuQujaZiB1p/9IwBuA/BfYV6o/6iq\nqj+C0aLV+QOmJ/3PAB4C8DlN0/onlt0HNE37NMywrZtR/90D4H/+B/nt61rOWdO0jwL4qPMxVVU/\nhbr+dgbAtns/VVUTAD4G8w/31m6tZ8CMsyZ5q3MXObn/C8CzAZzu89r6Qavz/1mYBupvAMwDSKmq\n+rCmaX/W5zX2klbnvwHTe9IAQFXVL8L0LO/t7xJ7iu/5q6p6LcwLs+Mwx+z+uaqqP9tqkt8IMeq/\ne23p9Lev12Ht+wD8pHX7JwB82fmklYP67P/fzh2jNBQEARj+RVALL2AnWOwFrAQPYWtjZWGZUk9g\nK57ARlsvIVpY2A6IB8gJtBAsdiOviM8ovOe6+T94RSDFDhtm9k2GBZ4i4qShwaDPuPvuJE8prZFb\nO/fjL3EwfbFDbueuAwedFk9Lvow/Ii4jYrcMipwD140VZujf/xdgM6W0Uz7vk98gW9IX/wbwDryV\ngj0lt7iXQet5bxE/yn2DXt9Z/gS/ArbIk4uHETEtE9rPwCpwQ96kWZvvNCIeBlvUCJb5TvK+2IHH\n8nQPaRcRcTvqIgf03d53vncEpIg4G3+Vw1ngtz87mKwAdxEx+ZuVDmOB+CfkIdhXcg48joh5beB/\nK6W0TT547pUJ5ebzXte8+PlF7vNubUmSKuMlJJIkVcbiLElSZSzOkiRVxuIsSVJlLM6SJFXG4ixJ\nUmUszpIkVeYDPAclB0QdBf0AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x170e4a20>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Least-squares histogram fit"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Model definition"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import lmfit\n",
      "\n",
      "peak1 = lmfit.models.GaussianModel(prefix='p1_')\n",
      "peak2 = lmfit.models.GaussianModel(prefix='p2_')\n",
      "model = peak1 + peak2\n",
      "\n",
      "model.set_param_hint('p1_center', value=0.2, min=-1, max=2)\n",
      "model.set_param_hint('p2_center', value=0.5, min=-1, max=2)\n",
      "model.set_param_hint('p1_sigma', value=0.1, min=0.01, max=0.3)\n",
      "model.set_param_hint('p2_sigma', value=0.1, min=0.01, max=0.3)\n",
      "model.set_param_hint('p1_amplitude', value=1, min=0.0, max=1)\n",
      "model.set_param_hint('p2_amplitude', expr='1 - p1_amplitude')\n",
      "name = '2-gaussians'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Fit"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fit_res = model.fit(data, x=x_data, method='nelder')\n",
      "print fit_res.fit_report()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " - Adding parameter \"p1_fwhm\"\n",
        " - Adding parameter \"p2_fwhm\"\n",
        "[[Model]]\n",
        " Composite Model:\n",
        "    gaussian(prefix='p1_')\n",
        "    gaussian(prefix='p2_')\n",
        "[[Fit Statistics]]\n",
        "    # function evals   = 503\n",
        "    # data points      = 139\n",
        "    # variables        = 5\n",
        "    chi-square         = 8.886\n",
        "    reduced chi-square = 0.066\n",
        "[[Variables]]\n",
        "    p1_amplitude:   0.40397393 (init= 1)\n",
        "    p1_center:      0.30130651 (init= 0.2)\n",
        "    p1_fwhm:        0.19268109  == '2.3548200*p1_sigma'\n",
        "    p1_sigma:       0.08182412 (init= 0.1)\n",
        "    p2_amplitude:   0.59602606  == '1 - p1_amplitude'\n",
        "    p2_center:      0.55926808 (init= 0.5)\n",
        "    p2_fwhm:        0.28679204  == '2.3548200*p2_sigma'\n",
        "    p2_sigma:       0.12178937 (init= 0.1)\n",
        "[[Correlations]] (unreported correlations are <  0.100)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = plt.subplots()\n",
      "x = x_data\n",
      "ax.plot(x, model.eval(x=x, **fit_res.values), 'k', alpha=0.8)\n",
      "plt.plot(x_data, data, 'o');\n",
      "if  fit_res.model.components is not None:\n",
      "    for component in fit_res.model.components:\n",
      "        ax.plot(x, component.eval(x=x, **fit_res.values), '--k',\n",
      "                alpha=0.8)\n",
      "for param in ['p1_center', 'p2_center']:\n",
      "    ax.axvline(fit_res.params[param].value, ls='--', color='r')\n",
      "ax.axvline(mu1_true, color='k', alpha=0.5)\n",
      "ax.axvline(mu2_true, color='k', alpha=0.5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "<matplotlib.lines.Line2D at 0x19d21128>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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i+39XrvwOk8nMqFFjnPp4TZkylb/+9UU++ugDBg68TetyhHAKMnMWTi8+Pg6g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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x17360780>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Bayesian Inference: MCMC"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "samples.size, nsamples"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "(1000, 1000)"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sigmas = pm.Normal('sigmas', mu=0.1, tau=1000, size=2)\n",
      "centers = pm.Normal('centers', [0.3, 0.7], [1/(0.1)**2, 1/(0.1)**2], size=2)\n",
      "#centers = pm.Uniform('centers', 0, 1, size=2)\n",
      "\n",
      "alpha  = pm.Beta('alpha', alpha=2, beta=3)\n",
      "category = pm.Categorical(\"category\", [alpha, 1 - alpha], size=nsamples)\n",
      "\n",
      "@pm.deterministic\n",
      "def mu(category=category, centers=centers):\n",
      "    return centers[category]\n",
      "\n",
      "@pm.deterministic\n",
      "def tau(category=category, sigmas=sigmas):\n",
      "    return 1/(sigmas[category]**2)\n",
      "\n",
      "observations = pm.Normal('samples_model', mu=mu, tau=tau, value=samples, observed=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gen_model = pm.Normal('gen_model', mu=mu, tau=tau)  # generative model"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Some debug plots:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t3 = pm.rbeta(alpha=6, beta=2, size=1e5)\n",
      "t4 = pm.rbeta(alpha=2, beta=3, size=1e5)\n",
      "plt.hist(t3, bins=bins, alpha=0.5);\n",
      "plt.hist(t4, bins=bins, alpha=0.5);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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APPDeEEIO+Apwez3b/J3A3dSmpZ03Wa19kuVQAUuiSn3G+ufqlBMF7xjjDvBT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\nliQpZQzekiSljMFbkqSUMXhLkpQy/x/M6EvFzSgBTAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x174e0ac8>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t1 = pm.rnormal(0.3, 1/(0.1)**2, size=1e4)\n",
      "t2 = pm.rnormal(0.55, 1/(0.1)**2, size=1e4)\n",
      "plt.hist(t1, bins=bins, alpha=0.5)\n",
      "plt.hist(t2, bins=bins, alpha=0.5);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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+511NK5PJ8KWXnyU5m9RiHeIrStQiPbJWKnKaF8nVFnmlfopEVXOv+p13Na0L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\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x174d5c88>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model = pm.Model([observations, mu, tau, category, alpha, sigmas, centers])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mcmc = pm.MCMC(model)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mcmc.sample(100000, 30000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  0%                  ] 861 of 100000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
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       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------98%----------------- ] 98804 of 100000 complete in 62.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------99%----------------- ] 99576 of 100000 complete in 62.6 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 100000 of 100000 complete in 62.9 sec"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pm.Matplot.plot(mcmc)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Plotting alpha\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " centers_0\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " centers_1\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " sigmas_0\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " sigmas_1\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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qt70h9vZ7BlC0O3jwoaKiokHnqm+f1pK4iYjUJ1ZyNhE438wqx+quNrPLga7u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\nzsoxKJM6qgzOLgWOj4i17emTI+IkYFlmnh8RbwS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       "text": [
        "<matplotlib.figure.Figure at 0x19d545c0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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9nepSV6Iqmr/Zz76Mw8/eH08/+zppyS245EIpvioOHcGaIiYNGOTaJgdjqph6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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x19e0b828>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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tTy3wOj5vWatCevuzCztKnIiwcfvuoGtPhYZYOwXBSXJqBsmpGWHtm7o7dl0B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       "text": [
        "<matplotlib.figure.Figure at 0x517cc2e8>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    }
   ],
   "metadata": {}
  }
 ]
}

View the notebook here