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{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"---\n", | |
"# Rechnernutzung in der Physik\n", | |
"**Institut für Experimentelle Teilchenphysik** <br>\n", | |
"**Institut für Theoretische Teilchenphysik** <br>\n", | |
"Priv. Doz. R. Wolf, Prof. Dr. M. Steinhauser <br>\n", | |
"Dr. A. Mildenberger, Dr. Th. Chwalek <br>\n", | |
"A. Heidelbach <br>\n", | |
"[Ilias Seite zum Kurs](https://ilias.studium.kit.edu/ilias.php?ref_id=1253214&cmd=frameset&cmdClass=ilrepositorygui&cmdNode=ug&baseClass=ilrepositorygui) <br>\n", | |
"WS 2020/21 – Blatt 03 <br>\n", | |
"Abgabe: Mi. 02.12.20 23:59 Uhr\n", | |
"\n", | |
"---" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Auf dem dritten Übungsblatt beschäftigen Sie sich mit einem der wichtigsten Grundbegriffe der modernen Parameteranpassung - die Maximum Likelihood Methode. Sie haben, mit großer Wahrscheinlichkeit, im Laufe Ihres Studiums oder Privatlebens bereits die Maximum Likelihood Methode (oder ihre Abwandlungen) verwendet, um die Steigung einer Geraden oder andere Parameter einer Messung zu bestimmen. Falls Sie es noch nicht getan haben, schauen Sie mit diesem Übungsblatt nochmal ganz genau in die Methodik rein und nehmen hoffentlich mit, auf welchem Prinzip die ganzen eingebauten Fitfunktionen in *Scipy*, *kafe2*, *probfit* und vielem mehr (ja, auch Excel) aufgebaut sind. Sie werden merken, dass sich hinter all den angesprochenen Methoden keine schwarze Magie befindet, sondern die Umsetzung und Überführung auf eigene Programme ganz einfach ist. Mit einem guten Verständis der Maximum Likelihood Methode können Sie dann nicht nur die Methode der kleinsten Quadrate verstehen, sondern auch schon bald Anpassungen wie diese durchführen.\n", | |
"\n", | |
"" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"---\n", | |
"# Aufgabe 1: Poisson-Likelihood <a id=\"Aufgabe1\"></a>\n", | |
"---\n", | |
"\n", | |
"In der ersten Aufgabe beschäftigen Sie sich mit einem vermutlich bereits bekanntem Beispiel aus dem Praktikum: Sie haben eine radioaktive Quelle erhalten und messen elektronisch die Klicks eines Geiger-Müller-Zählrohrs in aufeinanderfolgenden, gleich langen Zeitintervallen. Die Messdaten haben Sie in der Datei *Geiger_Zaehler.txt* abgespeichert und wollen nun für die weitere Auswertung die Anzahl der radioaktiven Zerfälle pro Zeitintervall bestimmen. \n", | |
"\n", | |
"Bei der Auswertung der Daten erinnern Sie sich an die Rechnernutzung Vorlesung und die Parameterschätzung mithilfe der Maximum Likelihood Methode und beschließen, statt *kafe2* zu nutzen, die gesuchte Zahl selbst abzuschätzen. Sie schauen zurück in die Folien der Vorlesung und entdecken die Funktion\n", | |
"\n", | |
"$$ \n", | |
"L\\left(\\left\\{x_i\\right\\},\\theta\\right)=\\prod_{i\\leq n}p\\left(x_i,\\theta\\right).\n", | |
"$$\n", | |
"\n", | |
"Sie erinnern sich daran, dass $\\left\\{x_i\\right\\}$ ihre Messungen sind, $p(x,\\theta)$ die zugrunde liegende Wahrscheinlichkeitsdichte und $\\theta$ der gesuchte Parameter ist." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## a) Maximum Likelihood\n", | |
"\n", | |
"Im ersten Aufgabenteil überprüfen Sie graphisch die Form der Likelihood Funktion.\n", | |
"> Frage: Warum ist es gerechtfertig die Poissonverteilung als zugrunde liegende Wahrscheinlichkeitsdichte für den Ausgang des Zählexperiments zu wählen? Welche Abweichungen von der Annahme gibt es beim Aufbau und der Messung?" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"> Antwort: Sehr viele Atome mit jeweils sehr kleiner Zerfallswahrscheinlichkeit -> Poissonverteilung" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Implementieren Sie die Likelihoodfunktion $L\\left(\\left\\{x_i\\right\\},\\theta\\right)$. Es bietet sich an, die Wahrscheinlichkeitsdichte als Argument der Funktion zu übergeben. Denken Sie daran, dass Sie einen gewissen Parameterereich abdecken müssen. Es bietet sich also an nicht nur $x$, sondern auch $\\theta$ als Array zu behandeln." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 1, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"import numpy as np\n", | |
"import matplotlib.pyplot as plt\n", | |
"import seaborn as sbn\n", | |
"from scipy.stats import poisson\n", | |
"\n", | |
"sbn.set()\n", | |
"\n", | |
"def Lp(x, theta):\n", | |
" return np.array([np.product(poisson.pmf(x, t)) for t in theta])\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Betrachten Sie nun die Likelihoodfunktion für eine steigende Zahl an Messergebnissen $L\\left(\\left\\{x_i\\right\\},\\theta\\right)$. Stellen Sie dafür die Likelihoodfunktion für $\\theta$ im Intervall $[2,9]$ dar für\n", | |
"* nur den ersten Messwert\n", | |
"* den ersten und den zweiten Messwert\n", | |
"* die ersten 10 Messwerte\n", | |
"* die ersten 100 Messwerte.\n", | |
"\n", | |
"Sie können mithilfe von *np.loadtxt(\"filename\")* die Messdaten aus dem Verzeichnis laden, indem sie das Notebook ausführen. Sollten Sie also das Notebook von ihrem eigenen PC in [jupytermachine.etp.kit.edu](jupytermachine.etp.kit.edu) laden oder lokal auf ihrem Rechner arbeiten, denken Sie daran, zuerst die Datei *Geiger_Zaehler.txt* herunterzuladen." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 2, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
}, | |
{ | |
"data": { | |
"image/png": 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7jNXPdjByyiunrED4eQVBNWSjOaKjfU6cOIHnnnsOu3btwqRJkwLLs7KyIAi+UxUVFcHpdKKxsTGSpyYKuDWpW/gXfH37c2ZPUq6IFf9Tp05hw4YNeOmllzB16tQ+65qamgKv33vvPQiCgKysrEidmqiPwHTOt9HnD/hG/LDPn5QqpG6frVu3ora2Fi0tLVi1ahWMRiNqampQXFyMkpIS5Ofno6KiAt3d3di0aVNgv6qqKuTm5mLjxo2wWq1QqVTQ6XT4+c9/joSEqFxuIILN6UZyYgIS1LfXtklL1aKrxwN3rweahNC7KInkIKQKXFZWhrKysn7L9+zZE3i9b9++Qfd//fXXh5+MKEy3e4OXn/8uX5vTDZOexZ+UhXf4kuLYnO7IFH/e5UsKxuJPiuOb1O32LvYCnNyNlI3FnxTH1hWZbp/A/D58ohcpEIs/KYooirA7b29GT7/AzJ7s9iEFYvEnRenq6YXHK0ak5Z+oUUObIHC4JykSiz8pSiTm9fFTqVR8kDspFos/Kcqt4n/73T6A70Hu7PYhJWLxJ0WJ1N29fvoULWwc7UMKxOJPihKY1ycCQz0B34gftvxJiVj8SVGi0vJ3uiGKw59RliiWsfiToticbt8oHU1kpmPQp2jg8Ypw9vRG5HhEsYLFnxQlUvP6+N260YtdP6QsLP6kKJGa18dPz+JPCsXiT4pii9DdvX7++X38Q0iJlILFnxTF1uVCWnIEW/6c4oEUisWfFEMUxYi3/HUpGqjAbh9SHhZ/UowetwfuXm9E+/zVgoDUZA062e1DChO0+FdWVuLhhx9Gbm4uvvjiiwG38Xg8qKiowCOPPIIFCxZg7969Ia0jiiR/v7wugsUf8F305V2+pDRBH+M4f/58rFy5EsuXLx90m+rqaly7dg21tbVob29HUVERZs+ejbFjxw65jiiSIj2vj58+hfP7kPIEbfnPmDEDFotlyG0OHz6M7373uxAEASaTCY888gj++Mc/Bl1HFEmRvrvXLy1Fy24fUpyI9Pk3NDQgOzs78LPFYkFjY2PQdUSRFL2WP7t9SHmCdvvEiowMXdj7ms1pEUwSfXLKG0tZRcHXqMgZl46UpIFb/+HktWTq4PykF8b0FGgSIjNtRChi6bMNhZzyyikrEJ28ESn+FosF9fX1mD59OoC+rf2h1g2H1WqH1zv8ybXM5jQ0N9uGvZ9U5JQ31rI2NNuRoBZg7+yCw9bdb324eQX4vneXrrbCpE+67ZyhiLXPNhg55ZVTVuA2vreCashGc0S6fRYtWoS9e/fC6/WitbUVR44cwcKFC4OuI4ok/7w+KpUqosflXb6kREFb/lu3bkVtbS1aWlqwatUqGI1G1NTUoLi4GCUlJcjPz0dhYSFOnjyJb33rWwCAJ598EuPGjQOAIdcRRVKk5/Xx8xd/jvghJQla/MvKylBWVtZv+Z49ewKv1Wo1KioqBtx/qHVEkRTpu3v90lJvTvHAi76kILzDlxTD5nQF5uKJJLb8SYlY/EkxotXyT9KqoUkQYHOwz5+Ug8WfFKHH7UGP2xOVPn+VSsW7fElxWPxJEfx39+qj0PIH/Hf5sviTcrD4kyIE7u5NjU7x16dqecGXFIXFnxQhWvP6+OlTtBznT4rC4k+K0HnzYmzUun1SNeh0uCCKw7/LnCgWsfiTIti6ot/y93hFdPX0RuX4RCONxZ8UweZwQ5sgIFETnYnXbo31Z9cPKQOLPylCZ5Tm9fHjXb6kNCz+pAjRusHLL9DyZ/EnhWDxJ0XodLqgj9IwTwCBY9s41p8UgsWfFMHudCEtOToXewFAd/PY7PMnpWDxJ9kTRRGdTnfUbvACgAS1gNSkBN7lS4rB4k+y1+3ywN3rjdowTz/e5UtKwuJPsmfriu4NXn58kDspCYs/yZ6/IEe75Z+WqkUHiz8pBIs/yV5gUrcot/yNqVq0s/iTQgR9jCMAXL58GaWlpWhvb4fRaERlZSUmTpzYZ5vnn38e58+fD/x8/vx57Nq1C/Pnz8eOHTvw5ptvIjMzEwBw3333oby8PHLvguJaZ5Snc/Yz6LTocXnQ7epFkjak/zpEMSukb3B5eTkeffRRFBYW4uDBg9i0aRPeeOONPttUVVUFXp87dw6PPfYY5s6dG1hWVFSEjRs3Rig20S3RntHTz6hLBAB02F1IMrH4k7wF7faxWq04c+YMFi9eDABYvHgxzpw5g9bW1kH3+e1vf4uCggJotdFtiREBvm6fRK0a2ijN6+Nn0Pm+z+32nqieh2gkBG2+NDQ0ICsrC2q17z+WWq1GZmYmGhoaYDKZ+m3vcrlQXV2N119/vc/ympoaHDt2DGazGU899RTuvffeYQXNyNANa/uvMpvTwt5XCnLKGwtZXR4RRl1iSFluJ++kXt90zqKgHpH3HQuf7XDIKa+csgLRyRvxv12PHDmC7Oxs5OXlBZYtW7YMa9euhUajwfHjx7F+/XocPnwY6enpIR/XarXD6x3+XOpmcxqam23D3k8qcsobK1mb25xITUoImuV283rdvumcrzV0oHmsPuzjhCJWPttQySmvnLIC4ecVBNWQjeag3T4WiwVNTU3weDwAAI/Hgxs3bsBisQy4/b59+7BkyZI+y8xmMzQaX3/snDlzYLFYcOHChZDfBNFQbA5X1C/2AkBqUgIS1Cp0sNuHFCBo8c/IyEBeXh4OHToEADh06BDy8vIG7PJpbGzExx9/jIKCgj7Lm5qaAq/Pnj2Luro65OTk3G52IgC+0T66KF/sBQCVSgVDqhbtdg73JPkLqdtn8+bNKC0txe7du6HX61FZWQkAKC4uRklJCfLz8wEA+/fvx7x582AwGPrsv23bNpw+fRqCIECj0aCqqgpmsznCb4XikVcUYXO6YYjivD5fZdAlosPBlj/JX0jFf/Lkydi7d2+/5Xv27Onz87p16wbc3//LgijS7F1ueLziyBX/VC1utHWNyLmIool3+JKsdd7sgjHcHIMfbUZdIod6kiKw+JOs+efaGbluHy0c3b1w93pH5HxE0cLiT7Lm73/334AVbYG7fNnvTzLH4k+yNuIt/5vn6eCIH5I5Fn+StQ67C4ka9YhNtOZv+XO4J8kdiz/JWofDNWKtfuBW9xK7fUjuWPxJ1jrsPdCPUH8/4Js2WqViy5/kj8WfZG2kW/6CoII+RcspHkj2WPxJ1jpHuPgDgDEtEW0s/iRzLP4kW+5eLxzdvSN2g5efKS0RbZ0s/iRvLP4kW50jPMzTz5SWhFYbiz/JG4s/yVa7/wavkS7++kR09fSiq6d3RM9LFEks/iRbt+b1Gdnin57m62ZqY+ufZIzFn2TLf3fvSDzI5atM+iQAQKute0TPSxRJLP4kW222HqhUErb8edGXZIzFn2SrzdYDQ6oWamFkv8b+4s+LviRnLP4kW222bqSnJY34eRPUAvSpWrSx24dkLKTif/nyZSxduhQLFy7E0qVLceXKlX7b7NixA7Nnz0ZhYSEKCwtRUVERWNfV1YVnnnkGCxYswKJFi/Duu+9G7A1Q/Gqzu2BKG9kx/n6mtES0stuHZCykqRDLy8vx6KOPorCwEAcPHsSmTZvwxhtv9NuuqKgIGzdu7Lf8tddeg06nwzvvvIMrV65g+fLlqK2tRWpq6u2/A4pbbbZu3DUhXZJzp6cl8nGOJGtBW/5WqxVnzpzB4sWLAQCLFy/GmTNn0NraGvJJ/vCHP2Dp0qUAgIkTJ2LatGn405/+FGZkItwcZ+8J9L+PNJOeN3qRvAUt/g0NDcjKyoJarQYAqNVqZGZmoqGhod+2NTU1KCgowOrVq3HixInA8vr6eowZMybws8ViQWNjYyTyU5zyj7GXrPin8UYvkreIPQFj2bJlWLt2LTQaDY4fP47169fj8OHDSE+PzJ/lGRm6sPc1m9MikmGkyCmvVFmvt/q6XHLGpQ8rQ6TyThhjBACICeqofQZy+h4A8sorp6xAdPIGLf4WiwVNTU3weDxQq9XweDy4ceMGLBbL18KZA6/nzJkDi8WCCxcuYObMmcjOzkZdXR1MJhMA318Ts2bNGlZQq9UOr1cc1j6+XGlobrYNez+pyCmvlFmvXG8HAKg8npAzRDJv4s2/mS9ctiJFrYrIMb9KTt8DQF555ZQVCD+vIKiGbDQH7fbJyMhAXl4eDh06BAA4dOgQ8vLyAoXcr6mpKfD67NmzqKurQ05ODgBg0aJFeOuttwAAV65cwWeffYa5c+cO+80Q+fmHWUrV7TPKmAwAaG7nRV+Sp5C6fTZv3ozS0lLs3r0ber0elZWVAIDi4mKUlJQgPz8f27Ztw+nTpyEIAjQaDaqqqgJ/DTz++OMoLS3FggULIAgCtmzZAp0u/G4cojZbD3TJGmgS1JKcX5+igVYjoKWDY/1JnkIq/pMnT8bevXv7Ld+zZ0/gtf8XwkBSUlLw0ksvhRGPaGCtth7JxvgDgEqlwihDMlv+JFu8w5dkqd3WA6OExR8AzIYktvxJtlj8SZZabT2S9ff7jTL6Wv6iOPyBCERSY/En2el29cLe5cYow8jP6/NVZkMSul0eOLo51p/kh8WfZMd6s6slQ+rizxE/JGMs/iQ7/n52syFZ0hwc7klyxuJPsuMv/lJ3+/jPz4u+JEcs/iQ7LR1d0CT45tSXUnJiAnTJGrSw5U8yxOJPstPS3o1RhiSoVJGfVmG4zMZkNHFqZ5IhFn+SnZaOboySuL/fz5KRgsZWp9QxiIaNxZ9kp6WjS/L+fj9LRgrabD2c2plkh8WfZKWrpxeO7l6MMsZG8R9tSgEANLWx9U/ywuJPsuIfVhkr3T6jM3yPIm2wsviTvLD4k6z4L65mpcdG8c80JkNQqVj8SXZY/ElWGq0OAEBWeorESXw0CQLMxqRALiK5YPEnWWls7YJJn4hErTTz+A9ktCkFDRzxQzLD4k+y0tTmjJlWv58lIxVNrV1hPWaUSCos/iQboiii0eoMjLCJFaMzUtDr8aKlgzd7kXyw+JNs2LvccPb0IivGiv+YUb4RP3XN7Pcn+QjpMY6XL19GaWkp2tvbYTQaUVlZiYkTJ/bZZteuXTh8+HDgGb4bNmwIPKS9tLQU77//PtLT0wH4Hui+bt26yL4TUrymVl/LerQpNkb6+I0166ACcO2GHfdOMUsdhygkIRX/8vJyPProoygsLMTBgwexadMmvPHGG322mT59OlavXo3k5GScO3cOK1aswLFjx5CU5LsZ54knnsCKFSsi/w4objT4R/rEWMs/UatGlikF15psUkchClnQbh+r1YozZ85g8eLFAIDFixfjzJkzaG1t7bPd3LlzkZzsa5Hl5uZCFEW0t7dHPjHFrevNDmg1guTz+A9kfJYOX96wSx2DKGRBi39DQwOysrKgVvuG1qnVamRmZqKhoWHQfQ4cOIDx48dj9OjRgWW//OUvUVBQgPXr1+PixYsRiE7x5nqzHWNG6SAI0s/m+XXjMnVo6eiGs9stdRSikITU7TMcH374IbZv345f/OIXgWUbNmyA2WyGIAg4cOAA1qxZgyNHjgR+oYQiI0MXdiazOS3sfaUgp7wjlVUURVxvdmB2vuW2zhmtvPlTMrHvfy+h0+XFhHGROYecvgeAvPLKKSsQnbxBi7/FYkFTUxM8Hg/UajU8Hg9u3LgBi8XSb9sTJ07gueeew+7duzFp0qTA8qysrMDroqIivPjii2hsbMSYMWNCDmq12sMaR202p6G5WT59sXLKO5JZ2+09sDldMOsTwz5nNPMaEn0NmZPnmjBan3jbx5PT9wCQV145ZQXCzysIqiEbzUG7fTIyMpCXl4dDhw4BAA4dOoS8vDyYTKY+2506dQobNmzASy+9hKlTp/ZZ19TUFHj93nvvQRCEPr8QiILx96ePNadKnGRgBl0iMvRJuFjXIXUUopCE1O2zefNmlJaWYvfu3dDr9aisrAQAFBcXo6SkBPn5+aioqEB3dzc2bdoU2K+qqgq5ubnYuHEjrFYrVCoVdDodfv7znyMhIeI9TqRg1/3FPzP87r9ou2OsAeevtUEUxZh4yhjRUEKqwJMnT8bevXv7Ld+zZ0/g9b59+wbd//XXXx9+MqKvuNpkQ4Y+EalJGqmjDOqOMQZ8cKYJrZ09yIiRh80QDYZ3+JIsXKzrxKRsg9QxhjR5jB4A8Dd2/ZAMsPhTzGu398Da2Y3J2XqpowxprFkHrUZg8SdZYPGnmOe/iDp5TGy3/BPUAu4cY8DZq21SRyEKisWfYt7F+k4kqFUYnxX7Y7On5mSgvsWB1s5uqaMQDYnFn2Le3+o6MCErDZqE2P+6TsvxDYE+fbk1yJZE0or9/00U17p6enG5vhNTxhuljhKSMeZUGHRanL7C4k+xjcWfYtr5L9vh8YqYNtEUfOMYoFKpkJ+Tgc8utcLd65U6DtGgWPwppp2+3AptgoA7xhqljhKyGd8wo6unl10/FNNY/ClmiaKIk39rwTcmpMuiv9/vrokmpCYl4MNzTcE3JpKIfP5HUdy51mRHS0c37pfZ07ES1ALuzzXjxIUW9Lg8UschGhCLP8Wsv567AUGlkuWjEf/PNAt6XB78+Uyj1FGIBsTiTzHJ4/Xiz6cbMTXHBF1y7M7nM5g7xxowPkuH//7oOkRx+FORE0Ubiz/FpFMXrWiz9eChe7KljhIWlUqFR+4fh7oWBz67xAu/FHtY/Ckm1X74JdLTEjF9cobUUcI2664sjDIkYd//XgzrQURE0cTiTzHn/LU2nP+yHYtmjUeCWr5fUU2CgCUPTcaXN+w49tngz7wmkoJ8/2eRInm8Xrx55ALS0xLx0N3y7PL5qpl5mZgyzoj/+u8LuNHeJXUcogAWf4opNe9fxZc37Ph/8++EVqOWOs5tU6lUKF58F1QqFXb/7jM4u3uljkQEgMWfYshfz93AwWOXMXtqFu7Pld/wzsFkGJKwtnAq6loc+OneT9HpcEkdiSi04n/58mUsXboUCxcuxNKlS3HlypV+23g8HlRUVOCRRx7BggUL+jz2cah1RKIo4o8fXMMrB09j8lgDVi76huKegZs/KQNrC6fiWpMdFa//FZ9eaOEQUJJUSM/wLS8vx6OPPorCwkIcPHgQmzZtwhtvvNFnm+rqaly7dg21tbVob29HUVERZs+ejbFjxw65juJXV08vTl5swdsffImrTTbcN8WMx/9vHhIV0N0zkPtzM/F9QzJerT6Nl/adwoSsNMy924JpOSaYjcmK+4VHsU0lBml+WK1WLFy4EB988AHUajU8Hg9mzZqF2tpamEy3Zlp84okn8A//8A9YtGgRAGDLli3Izs7GmjVrhlwXKqvVPuzhcr0eL640O9Ha5hhw/dffuYh+C4b6sc+Cr+8brFE32Ln1aUno/NqDQIK966//E4qD/jDQexh832DvITU1EXb7raxDfz5Aj9sDm9MFm9ON+hYH6lsc8HhFmI1JKHwwB7Onjo5qATSb09DcbIva8UPV6/Hi2KkG/PfH11HX4vtupqVokGVKwShDElKTNMjMSIXH7YFarUKCoIJaLUAtqCAIKvT7hFRf/7HvgmAfaSQ+c72+//c2Vskpq0Yt4OFZE9DaOnANG4ogqJCRoRt0fdCWf0NDA7KysqBW+1pjarUamZmZaGho6FP8GxoakJ19a3SGxWJBY2Nj0HWhGupNDOb9U/V48Vd/HfZ+FD3JiQkw6LTINuswa5oFM/KykDfRBEEYmVav2RwbTwP77mgD/nFBLuqa7Tj5RTMu1XeirtmOSw02OJwuOHhhmG4alZGKe3MzI37ckLp9YkE4Lf87LWl4pXQ+brTY+yz/apkZbqtoqFZX/3VD7zvQsTJMOlhb7RFtvX191XBzDvYeMzJ0QVskXz20NkGAJqF/l47Vau+3LBpipeX/VYkqYGauGTO/doHblKHD9bp2eEURHo8XHq+IXq/Y7/9AsOsG/f/CDLJBmNJNqWgLo3UqBTll1SQImDolM6zv7W23/C0WC5qamuDxeALdPjdu3IDFYum3XX19PaZPnw6gb2t/qHXRlm3WQRO04yR2mE0pUHnkMROkQZcIVxdHrkSDWlAhJUk2bTOYzWlIUcvjmoWcskZT0NE+GRkZyMvLw6FDhwAAhw4dQl5eXp8uHwBYtGgR9u7dC6/Xi9bWVhw5cgQLFy4Muo6IiEZeSE2LzZs3o7S0FLt374Zer0dlZSUAoLi4GCUlJcjPz0dhYSFOnjyJb33rWwCAJ598EuPGjQOAIdcREdHICzraJ1aE0+cPxGY/71DklFdOWQF55ZVTVkBeeeWUFQg/b7A+f97hS0QUh1j8iYjiEIs/EVEcks1Ystu5CWikbiCKFDnllVNWQF555ZQVkFdeOWUFwssbbB/ZXPAlIqLIYbcPEVEcYvEnIopDLP5ERHGIxZ+IKA6x+BMRxSEWfyKiOMTiT0QUh1j8iYjiEIs/EVEcks30DsPV1taG559/HteuXYNWq8WECROwZcuWfg+hiRXr16/H9evXIQgCUlJS8G//9m/Iy8uTOtaQdu7ciR07dqC6uhpTpkyROs6gHn74YWi1WiQmJgIAnn32WcydO1fiVAPr6enBD3/4Q/z5z39GYmIi7rnnHvzgBz+QOtaArl+/jieffDLws81mg91ux4cffihhqsG9++672L59O0RRhCiK+Od//ufAM0Zi0f/8z/9g+/bt6O3thcFgwIsvvhjZ56CICtXW1ib+5S9/Cfz8ox/9SPzXf/1XCRMNrbOzM/D6nXfeEYuKiiRME9znn38uPv744+K8efPE8+fPSx1nSHLI6PeDH/xA/Pd//3fR6/WKoiiKzc3NEicK3datW8WKigqpYwzI6/WKM2bMCHwPzp49K95zzz2ix+ORONnA2tvbxZkzZ4qXLl0SRVEUDxw4IK5evTqi51Bst4/RaMSsWbMCP99zzz2or6+XMNHQ0tLSAq/tdvuQD2SXmsvlwpYtW7B582apoyiKw+HAgQMH8PTTTwf+/UeNGiVxqtC4XC5UV1djyZIlUkcZlCAIsNl8D0Wx2WzIzMyEIMRmCbx69SpGjRqFnJwcAMBDDz2EY8eOobW1NWLnUGy3z1d5vV785je/wcMPPyx1lCG98MILOH78OERRxH/+539KHWdQ27dvx3e+8x2MHTtW6ighe/bZZyGKIu6//378y7/8C/R6vdSR+vnyyy9hNBqxc+dOfPDBB0hNTcXTTz+NGTNmSB0tqKNHjyIrKwtTp06VOsqAVCoVfvazn2H9+vVISUmBw+HAq6++KnWsQeXk5KClpQWnTp3C9OnTUV1dDQBoaGiIXNd1RP+OiFGbN28W161bF7N/4n3d/v37xTVr1kgdY0CffPKJuHLlykC3hBy6VOrr60VRFMWenh5x06ZN4ve+9z2JEw3s888/F6dMmSL+/ve/F0VRFD/99FPxm9/8pmiz2SROFtyaNWvEX/3qV1LHGJTb7RYfe+wx8aOPPhJFURQ/+ugj8aGHHhLtdrvEyQZ3/PhxcdmyZeLf//3fiz/96U/FGTNmiGfPno3Y8RVf/H/0ox+Jq1atEnt6eqSOMiz5+flia2ur1DH6eeWVV8Q5c+aI8+bNE+fNmyfm5eWJDz74oPjee+9JHS0k586dE+fNmyd1jAFZrVbxrrvuCvxiFUVR/Pa3vy2eOnVKwlTBNTY2infffXdMfl/9Tp06JX7729/us2zRokXiyZMnJUo0PM3NzeK0adNEh8MRsWPGZodXhGzbtg2ff/45du3aBa1WK3WcQTkcDjQ0NAR+Pnr0KAwGA4xGo3ShBvHEE0/g2LFjOHr0KI4ePYrRo0fjtddew4MPPih1tAE5nc5AP68oijh8+HDMjqIymUyYNWsWjh8/DgC4fPkyrFYrJkyYIHGyoe3fvx8PPfQQ0tPTpY4yqNGjR6OxsRGXLl0CAFy8eBFWqxXjx4+XONngmpubAfi6rbdt24Zly5YhJSUlYsdXbJ//hQsX8Morr2DixIlYtmwZAGDs2LHYtWuXxMn66+rqwtNPP42uri4IggCDwYCXX345pi/6yoXVasVTTz0Fj8cDr9eLyZMno7y8XOpYg6qoqMD3v/99VFZWIiEhAVVVVTF5feKr9u/fjxdeeEHqGEMym83YvHlzn4vpP/zhD2OygeX3s5/9DJ988gncbjfmzJmDZ599NqLH55O8iIjikKK7fYiIaGAs/kREcYjFn4goDrH4ExHFIRZ/IqI4xOJPRBSHWPyJiOIQiz8RURz6/9aG2/cznU4eAAAAAElFTkSuQmCC\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"xi = np.loadtxt(\"Geiger_Zaehler.txt\")\n", | |
"m = [xi[:1], xi[:2], xi[:10], xi[:100]]\n", | |
"\n", | |
"theta = np.linspace(2, 9, 1000)\n", | |
"\n", | |
"for i, val in enumerate(m):\n", | |
" plt.figure(i)\n", | |
" plt.plot(theta, Lp(val, theta))" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"> Frage: Erläutern Sie das Verhalten des Maximums der Likelihoodfunktion. Schätzen Sie den Wert des gesuchten Paramters ab." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"> Antwort: $\\theta\\approx 5$" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## b) Negative Log Likelihood (NLL)\n", | |
"\n", | |
"Beachten Sie die $y$-Skala bzw. den Wertebereich der Likelihoodfunktion für die vier verschiedenen Anzahlen an Messpunkten. Für eine große Anzahl an Messpunkten nimmt die Funktion immer kleinere Werte an. Testen Sie die obige Aufgabe gerne mit allen Messpunkten aus.\n", | |
"\n", | |
"In der Vorlesung wurde eine häufig angewandte Lösung des vorliegenden Problems behandelt. Statt nach dem Maximum der Likelihoodfunktion zu suchen, wird häufig nach dem Minimum der negativen Log Likelihood gesucht. \n", | |
"\n", | |
"$$ \n", | |
"-\\ln\\left(L\\left(\\left\\{x_i\\right\\},\\theta\\right)\\right)=-\\sum_{i\\leq n}\\ln\\left(p\\left(x_i,\\theta\\right)\\right).\n", | |
"$$\n", | |
"\n", | |
"Wiederholen Sie den ersten Aufgabenteil mit der NLL Methode. Implementieren Sie dazu eine neue Funktion, die die NLL ausgibt. Betrachten Sie den gleichen Parameterbereich aber diesmal für \n", | |
"* nur den ersten Messwert\n", | |
"* den ersten und den zweiten Messwert\n", | |
"* die ersten 10 Messwerte\n", | |
"* alle Messwerte\n", | |
"\n", | |
"Stellen Sie Ihr Ergebnis geeignet dar." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 3, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"def Lplog(x, theta):\n", | |
" return np.array([np.sum(-np.log(poisson.pmf(x, t))) for t in theta])\n", | |
"\n", | |
"for i, val in enumerate(m):\n", | |
" plt.figure(i)\n", | |
" plt.plot(theta, Lplog(val, theta))\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## c) Parameterschätzung\n", | |
"\n", | |
"Bestimmen Sie nun den gesuchten Parameter und schätzen Sie dessen graphisch Varianz ab. \n", | |
"\n", | |
"Für den ersten Schritt kann die *numpy* Methode *np.argmin()* hilfreich sein. Sie gibt den Index des Arrays am Minimum aus. <br>\n", | |
"Den zweiten Schritt erhalten Sie, indem Sie diejenigen Punkte finden, deren NLL Wert um $1/2$ größer sind als der des Maximums und anschließend die Differenz mit dem gefunden Parameter bilden. Hier eine schnelle Illustration:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 4, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"x = np.linspace(0, 10, 1000)\n", | |
"y = (x-3)**2+0.2\n", | |
"\n", | |
"dots_x = [3-1/np.sqrt(2), 3, 3+1/np.sqrt(2)]\n", | |
"dots_y = [0.7, 0.2, 0.7]\n", | |
"\n", | |
"plt.plot(x,y,'b-', label='NLL')\n", | |
"plt.hlines(0.7, 1, 5, color='green', label=r'NLL$[\\hat{\\theta}]$+0.5')\n", | |
"plt.plot(dots_x, dots_y, 'ro')\n", | |
"\n", | |
"colors = ['gold', 'orange', 'tomato']\n", | |
"labels = [r'Unterschranke $\\hat{\\theta}-\\sigma$', r'Minimum $\\hat{\\theta}$', r'Oberschranke $\\hat{\\theta}+\\sigma$']\n", | |
"for i in range(3):\n", | |
" plt.vlines(dots_x[i], 0, dots_y[i], linestyle='dashed', color=colors[i], label=labels[i])\n", | |
"\n", | |
"plt.ylim(-0.1,1)\n", | |
"plt.xlim(1,5)\n", | |
"plt.xlabel(r'$\\theta$')\n", | |
"plt.ylabel(r'NLL $-\\ln L\\left(\\left\\{x_i\\right\\},\\theta\\right)$')\n", | |
"plt.legend(bbox_to_anchor=(1.05, 1), loc='upper left')\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Es bietet sich an die Schritte als Funktion zu implementieren, damit sie erneut verwendet werden kann." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 5, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"lambda: 5.02002002002002, variance: [0.02102102 0.02102102]\n" | |
] | |
} | |
], | |
"source": [ | |
"def find_estimator(Llog, theta):\n", | |
" index_min = np.argmin(Llog)\n", | |
" theta_min = theta[index_min]\n", | |
" Llog_min = Llog[index_min]\n", | |
"\n", | |
" intersect = np.argwhere(np.diff(np.sign(Llog - (Llog_min + 0.5)))).flatten()\n", | |
" std = np.abs(theta_min - theta[intersect])\n", | |
" \n", | |
" return theta_min, std, Llog_min\n", | |
"\n", | |
"[lambda_final, lambda_variance, blub] = find_estimator(Lplog(xi, theta), theta)\n", | |
"\n", | |
"print(\"lambda: {}, variance: {}\".format(lambda_final, lambda_variance))" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"---\n", | |
"# Aufgabe 2: Profile Likelihood <a id=\"Aufgabe2\"></a>\n", | |
"---\n", | |
"In der zweiten Aufgabe schauen Sie sich ein vielleicht bereits bekanntes Beispiel aus dem Praktikum an: Der Myon Zerfall. Das Myon hat die gleichen Eigenschaften wie das Elektron, nur ist es ca. 200 Mal schwerer. Myonen entstehen bspw. als Zerfallsprodukte kosmischer Strahlung und können dann am Boden bspw. durch mehrere Szintillatorschichten nachgewiesen werden. Dabei Zerfallen sie größtenteils gemäß dem folgenden Graphen:\n", | |
"\n", | |
"\n", | |
"\n", | |
"Bei Experimenten treten häufig Störparameter auf, die für das physikalische Ergebnis irrelevant sind, aber dessen Unsicherheit beeinflussen. Die Berechnung und Analyse der Profile-Likelihood für den jeweils interessierenden physikalischen Parameter ist eine einfache Möglichkeit, die durch Störparameter verursachten Unsicherheiten zu berücksichtigen.\n", | |
"\n", | |
"In der Datei *tau_mu.dat* finden Sie 150 Werte gemessener Lebensdauern von Myonen, die im oder in der Nähe eines Myondetektors gestoppt wurden. Die Zeitdifferenz zwischen dem Nachweis des einfallenden Myons und dem Eintreffen des Elektrons aus dem Zerfall ist die Messgröße. Bedingt durch das Messverfahren sind nur Zeiten zwischen $\\Delta t_{min}=1.0\\,\\mu$s und $\\Delta t_{max}=11.5\\,\\mu$s erfasst. Als Störgröße bei den Messungen tritt ein Untergrund aus Zufallskoinzidenzen von Signalen auf, die im Bereich von $[\\Delta t_{min},\\Delta t_{max}]$ als flach verteilt angenommen werden können.\n", | |
"\n", | |
"In den folgenden Teilaufgaben soll die Myonenlebensdauer $\\tau_{\\mu}$ bestimmt werden. Sie werden dabei bemerken, wie einfach es ist, mit dem Wissen aus der Vorlesung und der [ersten Aufgabe](#Aufgabe1) eine reele Größe abzuschätzen." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## a) Verteilungsdichte der Zeitdifferenzen\n", | |
"\n", | |
"Zunächst soll die zugrunde liegende Wahrscheinlichkeitsdichte der Messdaten erstellt werden. Aus dem Aufbau der Messung ist zu entnehmen, dass die Verteilung der gemessenen Zeitdifferenzen aus der Summe einer Exponentialverteilung und einer Gleichverteilung besteht. \n", | |
"* Die **Exponentialverteilung** ist charaketerisiert durch die Myonenlebensdauer $\\tau_{\\mu}$ und beinhaltet die noch zu bestimmende Normierungskonstante $C_n$. Außerdem wird der Störparameter $f_b$ (in %) berücksichtigt durch den Faktor $(1-f_b)$.\n", | |
"* Die **Gleichverteilung** ist durch den relativen Anteil $f_b$ an der Gesamtanzahl gemessener Zeitdifferenz als Störparameter skaliert.\n", | |
"\n", | |
"$$\n", | |
"pdf(t)=C_n(1-f_b)\\exp\\left\\{-\\frac{t}{\\tau_{\\mu}}\\right\\}+\\frac{f_b}{\\Delta t_{max}-\\Delta t_{min}}\n", | |
"$$\n", | |
"\n", | |
"Zur Vorbereitung der Auswertung führen Sie folgende Schritte aus:\n", | |
"1. Implementieren Sie eine Funktion, die die Wahrscheinlichkeitsdichte ausgibt. Beachten Sie, dass die PDF auf Eins normiert sein muss. Bestimmen Sie dazu die Normierungskonstante $C_n$.\n", | |
"2. Implementieren Sie eine Funktion, die die NLL der PDF ausgibt, falls diejenige, die Sie in der [ersten Aufgabe](#Aufgabe1) geschrieben haben, nicht ausreichen sollte.\n", | |
"3. Lesen Sie die Daten aus der gegebenen Datei ein und histogrammieren Sie diese, damit Sie eine grobe Vorstellung des Problems erhalten." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 6, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"def pdf(t, fb, tau):\n", | |
" Cn = 1/(tau*(np.exp(-1/tau)-np.exp(-11.5/tau)))\n", | |
" return ((Cn * (1-fb) * np.exp(-t/tau)) + (fb / 10.5))\n", | |
"\n", | |
"def Llog(t, fb, tau):\n", | |
" return np.array([np.sum(-np.log(pdf(t, f, tau))) for f in fb])\n", | |
"\n", | |
"ti = np.loadtxt(\"tau_mudat.sec\")\n", | |
"\n", | |
"plt.hist(ti, bins=30)\n", | |
"\n", | |
"plt.xlabel(r'Zeitdifferenzen $\\Delta t$ in $\\mu$s')\n", | |
"plt.ylabel(r'Relative Häufigkeit')\n", | |
"\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## b) Bestimmung der Profile Likelihood\n", | |
"\n", | |
"Zur Bestimmung der Profile Likelihood wählen Sie 1000 Werte $\\tau_i$ für die Lebensdauer $\\tau_{\\mu}$ im Intervall zwischen $1.5\\,\\mu$s und $2.9\\,\\mu$s. Minimieren Sie für jeden Wert die NLL $-\\ln L(\\Delta t;\\tau_i,f_b)$ bezüglich des Parameters $f_b$. Die Untergrundrate $f_b$ können Sie durch 200 Werte im Intervall $[0,0.3]$ wählen – dies entspricht einem kleinen Untergrundanteil von ca. 0-30%. <br>\n", | |
"Stellen Sie die Profile Likelihood geeignet dar. Zeichnen Sie ebenfalls die Linie ein, die die Abschätzung der Standardabweichung zeigt." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 7, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"tau = np.linspace(1.5, 2.9, 1000)\n", | |
"fb = np.linspace(0, 0.3, 200)\n", | |
"\n", | |
"LlogE = np.array([find_estimator(Llog(ti, fb, tau_i), fb)[2] for tau_i in tau])\n", | |
"\n", | |
"plt.plot(tau, LlogE)\n", | |
"\n", | |
"plt.axhline(np.amin(LlogE) + 0.5)\n", | |
"\n", | |
"plt.xlabel(r'Myonenlebenszeit $\\tau_{\\mu}$ in $\\mu$s')\n", | |
"plt.ylabel(r'NLL $-\\ln L\\left(\\left\\{\\Delta t_i\\right\\};\\tau, f_b\\right)$')\n", | |
"\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## c) Parameterschätzung\n", | |
"\n", | |
"Bestimmen Sie als letzten Schritt \n", | |
"* den bestmöglichen Schätzer für die Myonenlebenszeit $\\hat{\\tau}_{\\mu}$, \n", | |
"* dessen Abschätzung über die Standardabweichung nach oben und unten \n", | |
"* und den bestmöglichen Schätzer für die Untergrundrate unter der Annahme $\\hat{\\tau}_{\\mu}$\n", | |
"\n", | |
"und stellen Sie die histogrammierten Zeitdifferenzen, die Verteilung des Signals unter der Annahme der bestmöglichen Schätzer und alle Ergebnisse in einem Plot dar." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 9, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"tau: 2.1264264264264265, std_tau: [0.40640641 0.57457457], fb: 0.11155778894472361, std_fb: [0.06331658 0.07386935]\n" | |
] | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"[tau_final, tau_variance, res] = find_estimator(LlogE, tau)\n", | |
"[fb_final, fb_variance, blub] = find_estimator(Llog(ti, fb, tau_final), fb)\n", | |
"\n", | |
"print(\"tau: {}, std_tau: {}, fb: {}, std_fb: {}\".format(tau_final, tau_variance, fb_final, fb_variance))\n", | |
"\n", | |
"t = np.linspace(1.5, 11.5, 1000)\n", | |
"\n", | |
"plt.plot(t, pdf(t, fb_final, tau_final))\n", | |
"\n", | |
"plt.xlabel(r'Zeitdifferenzen $\\Delta t$ in $\\mu$s', fontsize=15)\n", | |
"plt.ylabel(r'Relative Häufigkeit', fontsize=15)\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": {}, | |
"outputs": [], | |
"source": [] | |
} | |
], | |
"metadata": { | |
"kernelspec": { | |
"display_name": "Python 3", | |
"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": "3.7.4" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 4 | |
} |
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