{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 6. Model comparison (part II)\n", "\n", "Slides introducing this section are available [here](model_comparison_part2_slides.pdf)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model\n", "\n", "We again consider the sine model with gaussian measurement errors.\n", "\n", "$$ y = A_1 \\sin\\left(2 \\pi \\left(\\frac{t}{P_1} + t_1\\right)\\right) + B + \\epsilon $$\n", "\n", "where $\\epsilon \\sim \\mathrm{Normal}(0, \\sigma)$\n", "\n", "We want to test if this is preferred over pure noise.\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from numpy import pi, sin\n", "\n", "def sine_model1(t, B, A1, P1, t1):\n", " return A1 * sin((t / P1 + t1) * 2 * pi) + B\n", "\n", "def sine_model0(t, B):\n", " return B + t*0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "The model has four unknown parameters per component:\n", "\n", "* the signal offset $B$\n", "* the amplitude $A$\n", "* the period $P$\n", "* the time offset $t_0$\n", "\n", "## Generating data\n", "\n", "Lets generate some data following this model:\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "np.random.seed(42)\n", "\n", "n_data = 50\n", "\n", "# time of observations\n", "t = np.random.uniform(0, 5, size=n_data)\n", "# measurement values\n", "yerr = 1.0\n", "y = np.random.normal(sine_model1(t, B=1.0, A1=0.9, P1=3, t1=0), yerr)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Visualise the data\n", "\n", "Lets plot the data first to see what is going on:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAEECAYAAAArlo9mAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAAAaw0lEQVR4nO3db4wcZ30H8O/3ro5zl1Aa7MRFquw7IgVOSm0iBpRCQowoEiUvEkCVItxAQuoF1BLxBqE2KQxSAwikNoBUpOFFIIqjFKkt4k8CKEi2oMRBa0SmEUcQ9BwIqmLiiJBgxzH2ry9mN3fe27nbPzPPM8883490ut292Z1ndud++8zz/J7noZlBRETab8Z3AURExA0FfBGRSCjgi4hEQgFfRCQSCvgiIpEINuCT7Pgug086fh2/7zL4pOOf7PiDDfgAov7AoePX8cdNxz+BP6q6FFXYvn27LSwsbLjN/Pw8kiSJdhCBjl/Hr+PX8Q8+fuTIkafM7OKy5zUy4C8sLKDb7W64TZIkm27TZjp+Hb+OX8c/iOTjGz0v2CadTifuKzodv44/Zjr+yY6fTZxaIUkSi/nbW0RkEiSPmFlS9vdga/giIjIeBXwRkUgo4IuIREIBX0QkEgr4IiKRUMAXEYmEAn5T5ClwL1d/8tRveUSkdRo50jZKu1Pg2MHi9l8e9FgQEWkr1fBFRCKhgC8iEgkFfBGRSCjgi4hEQgFfRJopT5W5VjFl6YhIMylzrXJeavgkzyOZk1zwsX8RkRj5atL5MIB5T/sWEYmS84BP8pUAFgB83/W+RURi5jTgk5wB8CkA/1jy9w7J7vLyMpIkQZZlLosnIhKkLMuQJAkALJHskhy6BqLTJQ5Jvg/AC2Z2F8kvAUjN7OjgdtEucfjg3uK3OqhECvqfGMtmSxy6ztJ5E4CXk3wPgFcBeBXJt5nZ047LISISHadNOmZ2g5ldY2Z7AXwLwA0K9iXyVDnIIlIpb3n4ZnaTr30HQTnIIlKxdo+0zVPVkkVEeto90jbkWnKeAscOFbfvJXD5x4rjERGZULsDfsh2p8Bjdxa3//q3HgsiIm3R7iYdERF5kQK+iEgkFPBFRCKhgC8iYcpTZeGNSZ22TbFyAHjqMHD2FPDVBWDPHb5LJNJsIWfheaIafhOsHAB+2CmCPQCceLy4f+YFv+USkVZRwG+CR24Dzpw497EzJ4Czz/spj4i0kgJ+E5z4Zckf3M1kKiLtp4DfBPM7S/5Ap8UQiVKeRtP5q4DfBHvuAGYHVnycnQcwA5x+ZuMTMU+jOVlFarE7BS65pvh5l7V6ChNl6TTB4r7i98O3FB2387uKL4Hu3wF/eA64+KryLARlKkhbDctc6/+vyERUw2+KxX3A9iuLWsb1R3ViS9zKMtdWDvgtV+AU8EWkecoy1x65zU95WkIBX0SapyxzrTSjTUahgC8izVOWuVaa0SajcBrwSW4jeT/Jh0h2SV7hcv8iEoiyzLXQpxzJU69Zda6zdG4F8CMzu53k9QBSANc5LoOMK0+BRz++el+rb0ndyjLXQk9m8JxV5zrgPwDgVyQJYCeAJxzvXyah1E/xYXEf8IsvFrd13lXCaZOOmR02s18D+AaATwO4a+3fSXZIdpeXl5EkCbIsc1m8Zlk5AJz+HWBnilxkpaOJSIksy5AkCQAs9ZrLO8O2c1rDJ3kxgN+a2bUkXwvgKyQvNTMDADPLAGRJkli323VZtGbp5yD359I5e6p3H+Ff0opI5TqdDjqdDkgum1lStp3rLJ3PALild/s4gK217q0/Uu/YoWKkXii1ZOUgi0gNXLfhpwDuJrm/t+/9/dp95cpG6gHNryUrB1lEauA04JvZUQBvdLKzjWrJTQ/4W14GnD4+/HERkQm1d+BVyLXkslmRmzhbcp5qts62ylN9ti3T3tky53cWzTjDHm+6F54e73GflLLZXtN8tnmqsRsN1N6Av+eO3rqwa5p1fIzUy9PxT/yNvqyGvZ5I06gi0EjtDfhNGak3yYm/0ZfV4r71r/fg3ipKKhIWzZc/tvYGfMD9SL08reYytn/SPnQjAANmtgKvy3Qyi/SFnIXnUXs7bX2ocqm0xX3Alj8GOFssjKKTWGSVxqpMRAFfRMITchaeR+0J+Hk6eQrZNM8VEfc0X/5E2tOGP01WgDIKRMJSZRZeRJ2/7anhu5Cnbq8EzrxQzJa50VxAoc4XJDKNxX1FIsNMbzqu+V2TJTZEtlh6e2r4LtR5JZCnRdAGii+TP3sHcPbk6t/XZiH0KVMhXnmqgU1VZOGFPAXLBBTwm2J3eu4/7FcX1m/TPxEv7P0tspNV1lAzZDUi6/xVwG+qjU7EfsCP7GQVrK/Zz+/yVZJ2CHkKlgmoDb+pRslCUKZCM+Rp/X07/X30g/38rmK8R//LXybT1sXSSyjgN9WwE27wRIzsZG2sKgfcjbIPBfrqVNX5GwgF/KZa3AfMzK3eH3YiRnayitRicV8xmv2Sa4Drj9b7/+M5q04B35c83bwZYPa8YmqFjU5EFyerUj/Fhzwtzrljh9oxILIBKaDqtPUllCwLpX6KL4OZa6FrQFad0xo+yTmS95D8Acmc5NUu9y8TcD1JVZ5qmgtppwZk1bmu4e8H8KyZvZ7kGwB8DsBrHJehkKfr09vUEbae65M0lCsfkXE1IAXUdRv+YwA+37v9BIBZx/tfNZhZoWA/XOnJaKu18OeOuiyRVClPdUXlSgOy6pwGfDP7tpn9hOQrANwD4Pa1fyfZIdldXl5GkiTIssxl8WSYspP0Ja/Sl2UbuEgplUKNWXVZliFJEgBYItkl2Rm2nfNOW5LXAfgIgA+a2ZG1fzOzDECWJIl1u13XRZNhypaK7M9hIiKjq2kVvk6ng06nA5LLZpaUbee60/ZaADcC2DsY7KXBNkr9DDVlM0/VlLGZUD/bvjzVZzzAdQ3/vQAuA/AdkgCwYmY3Oy5DGPIUOP1McfvYoeJ+0y63Tz4ZbsqmOoc3Nm06bhPmmNdnvI7rNvx3mtmfm9ne3k/7g/2ktaR+2+qWlxa/+8G+SbWu369oXdG2miYdtwEDjGS4do+0zVO/I/WqPvHLXu/kk9WUd1z9cgzSbJ3hmyYdVwuMN1a7R9oOjtTL0yLw91Wdez94GXv6uclH1uXp6oIo/Sad//3S8Nf7/Qowt6OKIxjPzNbhQV+zdYZvmpzxBgwwkuHaXcMfVGfu/bDa9+njw7cd5cTfnRZl7Jd3d1r+vLKadt0uWPSeVyw1mSZnXNN2b+y5o6utDo5bHuIK+HUadhlbZtITv+x5/bxe1+Z2aLZO1/rBov9T16C3aXLGGzDAqNEuXFjtm3M89qE9AX+azswqOkJHvVyd5sQv+0e6YHGy16uCy6llm8xVra0fLPoBA6gv9XDSz1bTdjdWO9rwp0khqyq1sKzN87xtwB+eO3fQ0qQnvgZBNdeFC8Dp3wIXvdptCuCFC6tNk01KPaxpgJFMpx01/GmyAsZJLdzoSqCs9v2az1ZbA66yRp2nGpgyqjzVe9U0edqu+fIdaEcNf5qsgFFTCze7iiirfa+t6TSNBqaMrmnv1ZkXVjPCZrb6bdbzpW3z5TvQjhr+NFkBZR2eg88d5SpC7dniwpkXgLMnVysfZ08Bz/5MA5tkU+0I+NNkBYyaWqjc4rDkaTubYE4+WQT7dc5qYJNsqh0Bf5qsgFFTC6vOLc5TtT/WyeW0v/2+ndPPFL/rqGmvHAB+89/Asz8t30aVD9lEOwI+MF1zyijPrTq3eHe6ml6necjDNdi3c/ZU9fPG9Pdhf9h4Ow1smkyeTlb5ytPgriLb0WnrwkadsnXJ09XpFe4lcPnH1n8xjLKN1MfFwtQjDeqb0cCmSU3a+du0jvwRKOCPo8rc4pUDwOnfAbDy6WNHORGVqeCXi76dUV7rJZcpSUA21Z4mnZD0L9FhxX1NHxsuF/PGbPhaM8Vykz4mz5PgKOD7oOljyzVpvv9RuJg3Ztg+ih0VNXsFexlRvE06g1MZz865+8dRiudw066y5MNg387M1urnjRncBwjMnA9sf111+5AoxFnDHzZ/zrM/c7eQSOjTxw7Wwqt630K98ulneW15afG7ji+ntZlkW/4YmD2vmtcN7YpKpuI84JOcJXkTyftc7/tFw+bPwdnicRdCnj525QBw+OaBL8vHqgn6uvJxS0sRupenxZfr6WdWFzZyyGnAJ7kNwKMAPuVyv+uUzZ/jaiGR/kAx9Fbfavr0sXm6mqf80N8AdnpgA6vmyzL0Kx+gmCY5lNzsaa+o8jScY22KYQsbOeR6EfPjZrYE4AaX+12nbP4clwuJLO4rLs23vLT58+70T9J3GV78khpUxZelyyufupoyLlxwN8J3WtNeUbkczTyJ0Jqr8rT2L9BGteGT7JDsLi8vI0kSZFlWz46GzZ+DmThnHBxXnatuuVo4w1dTRp42q0bchiuqMiE2V03xBZplGZIkAYAlkl2SnWHbNSpLx8wyAFmSJNbtduvb0dwO4PLbzx016zJLJzR5Cjz68dX73DLQrFPhl6WLhTNcjI4dpmkjM/fcUQTBte9FKH1Jm/H1GXvS6XTQ6XRActnMkrLtGlXDd2pw/hwF+3KDNY8r78I5/Q+h5YKrc7jQ5qUI9RkPFVfAryudMDaD/Q8hBXug3U0Z42rrGg76jIfyEvDN7KCZue24Hdam5zL3Xpoj5LRYGU2TP2OPncnx1PCHzjjoMPe+rfI0vHn9Q27KOPlkMelef+79OisseRreZ9vX1M/Yc2dyozpta1XWducq976tQp2ts+rO4X4gPnaovjVmTz5ZXJX2J907e6pYEOW5nxdz5ZfNujqpaT7bPPU/bbeLBIBxee5MjqeGX2c64UbytNpaUtWvJ9NbOTAkENewxuzvVwCcXf94f2GUJqUerh270cQcfV88dybHE/CHzjjoIPe+6hO/ytcLbWCKTxu9V4/chvWBuIY1Zke5Gg1h7qGYee5M3jTgk/wWybeTDLv5Z1ibXtXphHkaTu07xIEpvmz2XrmqtY16NRp56mGjee5MHqWG/yEAVwA4SPITJMMdjlp37n1Il7Ghzkzpw2bvlata2wWLGOlfNvLUw0bz3Jm86dljZj81s48CeHNv+5+Q/CbJPbWXTurT9oEpVTZXbfZe7bkD6/+Valhjdm5HcVX64nxGs1g3t1FTUg+lnMexD6M06fwFyS8AOAzgWQCLAN4H4F9rLtt48nTy5pRpnjup/pq2p5/x037e5oEpVTdXbfZeLe47NxDPbK1vjdm5HauD3i65CnjJK5uXeiiNNUq7/EcB/BuAvzezM/0HSTYr4E+TQuY6tbBsTVvA3T+r5lEZ3Sjv1dwO4Pn/Ay569URFntjcjtWmyaakHsZicNW8KlNiazJKk85fmdnX1wb73uNfr69YDZWn1VwJNKH9vKkDU6pQdXNVm98rmUygSQ9hZ964VtWVQFPaz5s4MKUK8zuLf8Bhj0+qae/VmedXBzYBxZeQuBPobJzx5OE3SZvbz5ugyfOoVGX2/NVssEuuKRZeEXeaUmkbkwK+DzEEJJ/a3ATz3NGio//0M80f69FmgVba1KTjQz/wPHQjACsCUgAdPkFx2QSTp6vNK8cOFZ9n1TXutfsAin1cf7S4/eDeavclmws06UE1fF9CWtNWNja4MHUdzStrB/WpCce/QK8iVcOX8fXHEMCqSUfL03OXUKyjhixStaZ15I9ANXxf8jTMttiyMQTTpKMNLqEYcrA/+WQ8E9Jp8r3gqIbvS9MWtB5VoOloTrw4X31v5kwfA+pcKctDB9p3rK44GMjltIbPwp0kHyZ5mORbXe5fKlB3OlqehjPj6KBh89WvHVDXphpxEwYPtomjgVyua/hvAbAbwJUALgXwXZILZmaOy9GMFXlCsbbmwVng3EHXharS0UJdQQson6/+xC/bVyMONA+9sRxdObtuw78CwPes8HMUs01td1yGQkhTGfs0GKiGBXtuaXw6mhNl89XP72xujThPJ7uiCjQPvbEcfYG6DvjnA3h6zf3jAOb6d0h2SHaXl5eRJAmyLHNcPFln6OLva8zvAq68K8xaatWGzVffz81uao140oqPBg9Wa8ov0CzLkCQJACyR7JLsDNvOdcB/HsC2Nfe3AzjZv2NmmZklS0tL6Ha76HSGlllc2iggeZjPu9H689UPy81uW4040Dz0xpryC7TT6aDb7QLAspklZja0tuw64P8YwFW9zttLUeT2PeW4DDIOX4u/1y1P6+kcntsxfHGLNtaIPS7kMZI8DScBwNEXqOtO2+8AuBbAw7377/PSYSujKxtCHmrNtM9153D/H/fhW4r+EE2nUb/QEgAcDORyGvB7wf1Wl/uUKZUFqv6JKaMLcGSmtItG2srmmn7pLiIjiSvg52k4bXoiIhWLa2qF0Nr0RKR98tTboM+4Ar5I6PJ0fbCQsHiseCrgi1QhT92sMTsYLNbuV1OEyCYU8EWqsDYQu1yBSs2UMoa4Om3lXHmqTuxR5aneKwmeavgxU+1wdHqvpAVUwxcRiYQCvrRTnqoJRmSAmnR8yVNlV9RJTTAi6yjg+6KAJBK2PA2u0qaAL/45WLxZpHIBVtrUhi9+OVq8WUQU8MW3pq71KtJCCvjiV1PXehVpIQV88atta72KNJgCvvjVxrVeRRrKacAnOUvyJpL3udyvVCxPqxvU5GLx5jwtytn/ydPqXlskIM7SMkluA/B9ABcBOOhqv1KDqtPR6l7rdXcKHDtY3+uvlafB5WZPLE/jOdaWcBbwzew4gCWSewG839V+RZwKMDd7YjEdqwt5WvsXaKPa8El2SHaXl5eRJAmyLPNdJJHq5Knm95Fyu1PgXbb6M0awz7IMSZIARaW6S7IzbDuaWSVlPedFi529e+Dhu80s69fwzeyGsucnSWLdbrfycsmE8hR49OOr9+u4dO8vGlJXk0vdry/SACSPmFlS9vdamnTMLAOg6nlb6NJdpBUa1aQjIiL1cT55mpkdhLJ0REScUw1fRMSnPHU2TkTTI4uI+ORwnIhq+CIikVDAFxGJhAK+iEgkFPBFRCKhgC8iEgkFfBGRSCjgi4hEQgFfRCQSCvgiIpFQwBcRiYQCvohIJBTwRUQioYAvIhIJBXzxL0/rXet15QDw1OHi9b+6UNwXiZCmRxb/6lxCceUA8MMOcPZUcf/E48V9AFjcV88+RRpKNXxpt0duA86cOPexMyeKx0Ui4yzgk5wjeQ/JH5DMSV7tat8SsRO/HO9xkRZzWcPfD+BZM3s9gA8AuNPhviVW8zvHe1ykxVwG/McAfL53+wkAsw73LbHacwcwO3/uY7PzxeMikXEW8M3s22b2E5KvAHAPgNsHtyHZIdldXl5GkiTIssxV8aStFvcBr8uAma3F/fldxX112EqLZFmGJEkAYIlkl2Rn2HY0s8p33tvZuwcevhvAkwA+AuCDZnak7PlJkli32628XBKxB/cWv2teJFpkIhWdnySPmFlS9vda0jLNLANwTvWc5LUAbgaw18xeqGO/IiLB6Y8TOXuqGCey547arkBd5uG/F8BlAL5DEgBWzOxmh/sXEWkWx+NEnAV8M3unq32JiARho3EiNQR8DbwSEfHF8TgRBXwREV8cjxNRwBcR8cXxOBEFfBERXxyPE9FsmSIiPi3uA37xxeJ2zeNEVMMXEYmEAr6ISCQU8EVEIqGALyISCQV8EZFIKOCLiERCAV9EJBIK+CIikVDAFxGJhAK+iEgkFPBFRCKhgC8iEgkFfBGRSDgL+CS3kbyf5EMkuySvcLVviVyeAscOFT/3srgvEiGX0yPfCuBHZnY7yesBpACuc7h/idXutPgRiZzLgP8AgF+RJICdAJ5wuG8Rkeg5a9Ixs8Nm9msA3wDwaQB3DW5DskOyu7y8jCRJkGWZq+KJiAQryzIkSQIAS70m886w7Whmle+8t7N3Dzz8dQD/YmanSb4WwL8DuNSGFCBJEut2u5WXS0SkkR7cW/yecsUrkkfMLCn7ey01fDPLzOyqtT8AlgDc0tvkOICtdexbRESGc9mGnwK4m+T+3n73D6vdi4hIPZwFfDM7CuCNrvYnIiLn0sArERGf8tTZOBGXTToiIjLI4TgR1fBFRCKhgC8iEgkFfBGRSCjgi4hEQgFfRCQSCvgiIpEINuDHPrGajl/HHzMd/2THr4AfKB2/jj9mOv7Jjr+W2TKnRfI3AB7fZLMlAMsOitNUOn4dv44/XmXHv8vMLi57UiMD/ihIdjeaBrTtdPw6fh2/jn/c5wXbpAMg7ms6Hb+OP246/gkEW8MXEZHxhFzDFxGRMSjgi4hEIqiAz8KdJB8meZjkW32XyQeSsyRvInmf77K4RHKO5D0kf0AyJ3m17zK5RnIbyftJPtRbrPoK32XygeR5vXNgwXdZXOrFwKMkD/Z+bhvn+aHNh/8WALsBXAngUgDfJbkQ01KJJLcB+D6AiwAc9Fsa5/YDeNbMXk/yDQA+B+A1nsvk2q0AfmRmt5O8HsXSodd5LZEfHwYw77sQHuwCcMjM3jPJk4Oq4QO4AsD3rPBzAASw3XOZnDKz42a2BOAG32Xx4DEAn+/dfgLArMey+PIAgC+QJICdKN6HqJB8JYAFFBWf2LwawKUkD5H8Zu+9GFloNfzzATy95v5xAHOeyiKOmdm3AYDkKwB8GcDtfkvknpkdBgCS3wTwZgBX+S2RWyRnAHwKQAfAZzwXx4enAXwSwP0A3oHi/+DKUZ8cWg3/eQDb1tzfDuCkp7KIBySvA3APgA+Z2Td8l8c1kheT3GJm1wK4GsBXerX9WOwH8DUz+43vgnhyBMC3es3Y/4Witj9yHA8t4P8YwFW9jotLARiAp/wWSVwheS2AGwHsNbMjvsvjyWcA3NK7fRzAVo9l8eFNAG4ieRDAWwHcR/Jlfovk1CcBfLB3+3IAT5jZ2VGfHNTAq15N5rNYvYT5mJk94LFI3pDcC+D9ZhZNWz7J/wBwGYpABwArZnazxyI518tKuRvABSiaZP/BzO73WihPSH4JQGpmRz0XxRmSLwdwL4A/QdHi8QEz+/HIzw8p4IuIyORCa9IREZEJKeCLiERCAV9EJBIK+CIikVDAFxGJhAK+iEgkFPBFRCKhgC8yApJ/S/I/e6O8P0Hyn3yXSWRcGnglMoLeKO8vAzgF4E8BXDfOkHaRJghttkwRL8zMSH4awP8AeLuCvYRITToiIyB5HoAvoFhs5BMkL/FcJJGxqYYvMpp/BnC/mX2N5IUA7ib5NtX0JSRqwxcRiYSadEREIqGALyISCQV8EZFIKOCLiERCAV9EJBIK+CIikVDAFxGJxP8Dygm5HJN49poAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "\n", "plt.figure()\n", "plt.xlabel('x')\n", "plt.ylabel('y')\n", "plt.errorbar(x=t, y=y, yerr=yerr,\n", " marker='o', ls=' ', color='orange')\n", "t_range = np.linspace(0, 5, 1000)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A beautiful noisy data set, with some hints of a modulation.\n", "\n", "Now the question is: what model parameters are allowed under these data?\n", "\n", "First, we need to define the parameter ranges through a prior:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "parameters1 = ['B', 'A1', 'P1', 't1']\n", "\n", "def prior_transform1(cube):\n", " # the argument, cube, consists of values from 0 to 1\n", " # we have to convert them to physical scales\n", " \n", " params = cube.copy()\n", " # let background level go from -10 to +10\n", " params[0] = cube[0] * 20 - 10\n", " # let amplitude go from 0.1 to 100\n", " params[1] = 10**(cube[1] * 3 - 1)\n", " # let period go from 0.3 to 30\n", " params[2] = 10**(cube[2] * 2)\n", " # let time go from 0 to 1\n", " params[3] = cube[3]\n", " return params\n", "\n", "parameters0 = ['B']\n", "\n", "def prior_transform0(cube):\n", " # the argument, cube, consists of values from 0 to 1\n", " # we have to convert them to physical scales\n", " \n", " params = cube.copy()\n", " # let background level go from -10 to +10\n", " params[0] = cube[0] * 20 - 10\n", " return params\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define the likelihood, which measures how far the data are from the model predictions.\n", "More precisely, how often the parameters would arise under the given parameters.\n", "We assume gaussian measurement errors of known size (yerr).\n", "\n", "$$\\chi^2 = \\sum\\left(\\frac{m_i-y_i}{\\sigma}\\right)^2 $$\n", "$$\\log \\cal{L} = -\\chi^2 / 2$$\n", "\n", "where the model is the sine_model function from above at time $t_i$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def log_likelihood1(params):\n", " # unpack the current parameters:\n", " B, A1, P1, t1 = params\n", "\n", " # compute for each x point, where it should lie in y\n", " y_model = sine_model1(t, B=B, A1=A1, P1=P1, t1=t1)\n", " # compute likelihood\n", " loglike = -0.5 * (((y_model - y) / yerr)**2).sum()\n", " \n", " return loglike\n", "\n", "def log_likelihood0(params):\n", " B, = params\n", " \n", " y_model = sine_model0(t, B=B)\n", " # compute likelihood\n", " loglike = -0.5 * (((y_model - y) / yerr)**2).sum()\n", " \n", " return loglike\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Solve the problem:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "import ultranest\n", "\n", "sampler1 = ultranest.ReactiveNestedSampler(parameters1, log_likelihood1, prior_transform1)\n", "\n", "sampler0 = ultranest.ReactiveNestedSampler(parameters0, log_likelihood0, prior_transform0)\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ultranest] Sampling 400 live points from prior ...\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "ada51289bb094f5a9c41631f39f21860", "version_major": 2, "version_minor": 0 }, "text/plain": [ "VBox(children=(HTML(value=''), GridspecLayout(children=(HTML(value=\"
&nb…" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "[ultranest] Explored until L=-2e+01 [-20.7186..-20.7186]*| it/evals=6660/177951 eff=3.7510% N=400 00 \n", "[ultranest] Likelihood function evaluations: 177973\n", "[ultranest] logZ = -32.7 +- 0.1201\n", "[ultranest] Effective samples strategy satisfied (ESS = 2385.8, need >400)\n", "[ultranest] Posterior uncertainty strategy is satisfied (KL: 0.46+-0.05 nat, need <0.50 nat)\n", "[ultranest] Evidency uncertainty strategy is satisfied (dlogz=0.24, need <0.5)\n", "[ultranest] logZ error budget: single: 0.16 bs:0.12 tail:0.01 total:0.12 required:<0.50\n", "[ultranest] done iterating.\n", "\n", "logZ = -32.722 +- 0.238\n", " single instance: logZ = -32.722 +- 0.156\n", " bootstrapped : logZ = -32.698 +- 0.238\n", " tail : logZ = +- 0.010\n", "insert order U test : converged: True correlation: inf iterations\n", "\n", " B 1.02 +- 0.26\n", " A1 0.89 +- 0.31\n", " P1 3.7 +- 6.1\n", " t1 0.48 +- 0.45\n" ] } ], "source": [ "result1 = sampler1.run(min_num_live_points=400)\n", "sampler1.print_results()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ultranest] Sampling 400 live points from prior ...\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "6c9b9b07d34d429eb649fcc80c127e6f", "version_major": 2, "version_minor": 0 }, "text/plain": [ "VBox(children=(HTML(value=''), GridspecLayout(children=(HTML(value=\"
&nb…" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "[ultranest] Explored until L=-3e+01 [-31.7136..-31.7136]*| it/evals=2960/3465 eff=96.5742% N=400 0 \n", "[ultranest] Likelihood function evaluations: 3470\n", "[ultranest] logZ = -35.87 +- 0.07029\n", "[ultranest] Effective samples strategy satisfied (ESS = 1243.0, need >400)\n", "[ultranest] Posterior uncertainty strategy is satisfied (KL: 0.46+-0.07 nat, need <0.50 nat)\n", "[ultranest] Evidency uncertainty strategy is satisfied (dlogz=0.16, need <0.5)\n", "[ultranest] logZ error budget: single: 0.10 bs:0.07 tail:0.04 total:0.08 required:<0.50\n", "[ultranest] done iterating.\n", "\n", "logZ = -35.885 +- 0.162\n", " single instance: logZ = -35.885 +- 0.096\n", " bootstrapped : logZ = -35.868 +- 0.157\n", " tail : logZ = +- 0.038\n", "insert order U test : converged: True correlation: inf iterations\n", "\n", " B 1.15 +- 0.14\n" ] } ], "source": [ "result0 = sampler0.run(min_num_live_points=400)\n", "sampler0.print_results()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot the parameter posterior probability distribution\n", "\n", "A classic corner plot of the parameter pairs and the marginal distributions:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from ultranest.plot import cornerplot\n", "cornerplot(result1)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "cornerplot(result0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you want, you can also play with the posterior as a pandas frame:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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BA1P1t1
count7065.0000007065.0000007065.0000007065.000000
mean1.0168140.8928153.7340010.475235
std0.2603520.3093816.0885070.445044
min-3.3375170.1010841.0109370.000062
25%0.9010840.7308722.8992820.042637
50%1.0083280.8855603.0328140.151977
75%1.1143001.0515493.1758490.957797
max7.3906076.46728498.3021790.999996
\n", "
" ], "text/plain": [ " B A1 P1 t1\n", "count 7065.000000 7065.000000 7065.000000 7065.000000\n", "mean 1.016814 0.892815 3.734001 0.475235\n", "std 0.260352 0.309381 6.088507 0.445044\n", "min -3.337517 0.101084 1.010937 0.000062\n", "25% 0.901084 0.730872 2.899282 0.042637\n", "50% 1.008328 0.885560 3.032814 0.151977\n", "75% 1.114300 1.051549 3.175849 0.957797\n", "max 7.390607 6.467284 98.302179 0.999996" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "df = pd.DataFrame(data=result1['samples'], columns=result1['paramnames'])\n", "df.describe()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot the fit:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To evaluate whether the results make any sense, we want\n", "to look whether the fitted function goes through the data points." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.title(\"1-sine fit\")\n", "plt.xlabel('x')\n", "plt.ylabel('y')\n", "plt.errorbar(x=t, y=y, yerr=yerr,\n", " marker='o', ls=' ', color='orange')\n", "\n", "\n", "t_grid = np.linspace(0, 5, 400)\n", "\n", "from ultranest.plot import PredictionBand\n", "band = PredictionBand(t_grid)\n", "\n", "# go through the solutions\n", "for B, A1, P1, t1 in sampler1.results['samples']:\n", " # compute for each time the y value\n", " band.add(sine_model1(t_grid, B=B, A1=A1, P1=P1, t1=t1))\n", "\n", "band.line(color='k')\n", "# add 1 sigma quantile\n", "band.shade(color='k', alpha=0.3)\n", "# add wider quantile (0.01 .. 0.99)\n", "band.shade(q=0.49, color='gray', alpha=0.2)\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "\n", "\n", "## Model comparison methods\n", "\n", "We now want to know:\n", "\n", "**Is the model with 2 components better than the model with one component?**\n", "\n", "What do we mean by \"better\" (\"it fits better\", \"the component is significant\")?\n", "\n", "a) Which model is better at predicting data it has not seen yet?\n", "\n", "b) Which model is more probably the true one, given this data, these models, and their parameter spaces?\n", "\n", "c) Which model is simplest, but complex enough to capture the information complexity of the data?\n", "\n", "\n", "## Bayesian model comparison\n", "\n", "Here we will focus on b, and apply Bayesian model comparison. \n", "\n", "For simplicity, we will assume equal a-prior model probabilities.\n", "\n", "The Bayes factor is:\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "K = 23.66\n", "The 1-sine model is 23.66 times more probable than the no-signal model\n", "assuming the models are equally probable a priori.\n" ] } ], "source": [ "K = np.exp(result1['logz'] - result0['logz'])\n", "print(\"K = %.2f\" % K)\n", "print(\"The 1-sine model is %.2f times more probable than the no-signal model\" % K)\n", "print(\"assuming the models are equally probable a priori.\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "N.B.: Bayes factors are influenced by parameter and model priors. It is a good idea to vary them and see how sensitive the result is." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For making decisions, thresholds are needed. They can be calibrated to desired low false decisions rates with simulations (generate data under the simpler model, look at K distribution)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calibrating Bayes factor thresholds\n", "\n", "Lets generate some data sets under the null hypothesis (noise-only model) and see \n", "how often we would get a large Bayes factor. For this, we need to fit with both \n", "models." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "import logging\n", "logging.getLogger('ultranest').setLevel(logging.FATAL)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "K_simulated = []\n", "LR_simulated = []\n", "var_simulated = []\n", "\n", "import logging\n", "logging.getLogger('ultranest').handlers[-1].setLevel(logging.FATAL)\n", "\n", "# go through 100 plausible parameters\n", "for i in range(20):\n", " # generate new data\n", " y = np.random.normal(sine_model0(t, B=1.0), yerr)\n", " \n", " # analyse with sine model\n", " sampler1 = ultranest.ReactiveNestedSampler(parameters1, log_likelihood1, prior_transform1)\n", " results1 = sampler1.run(viz_callback=False)\n", " lnZ1 = results1['logz']\n", "\n", " # analyse with noise-only model\n", " sampler0 = ultranest.ReactiveNestedSampler(parameters0, log_likelihood0, prior_transform0)\n", " results0 = sampler0.run(viz_callback=False)\n", " lnZ0 = results0['logz']\n", " \n", " # store Bayes factor to K_simulated\n", " # the difference of the lnZ values is the ln of the Bayes factor\n", " print()\n", " print(\"Bayes factor: %.2f\" % ...) # TODO by you:\n", "\n", " K_simulated.append( ... ... ) # TODO by you:\n", "\n", " \n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercise 1 (10 points):**\n", "\n", "* Plot the distribution of Bayes factors.\n", "* How many false positives and false negatives would you have if you applied a threshold of Bayes factor 10?\n", "* Where does the real Bayes factor lie? Do you trust the result?\n", "\n", "**Homework exercise 1 (20 points):**\n", "\n", "* Make a [ROC curve](https://en.wikipedia.org/wiki/Receiver_operating_characteristic), by plotting the false positive vs false negative rates as a function of thresholds.\n", "* Add a ROC curve of likelihood ratios (hint: the highest log-likelihood found is in `sampler.results['maximum likelihood']['logl']`).\n", "* Can you think of another method to identify a second sine signal? Compute its indicator as well, and add a ROC curve. Which method is better overall? Which method is more efficient (lower false negative rate) at a 5% false positive rate?\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "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": "3.9.7" } }, "nbformat": 4, "nbformat_minor": 2 }