Simulating datasets MCMC-D larger.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['seaborn-dark', 'seaborn-darkgrid', 'seaborn-ticks', 'fivethirtyeight', 'seaborn-whitegrid', 'classic', '_classic_test', 'fast', 'seaborn-talk', 'seaborn-dark-palette', 'seaborn-bright', 'seaborn-pastel', 'grayscale', 'seaborn-notebook', 'ggplot', 'seaborn-colorblind', 'seaborn-muted', 'seaborn', 'Solarize_Light2', 'seaborn-paper', 'bmh', 'tableau-colorblind10', 'seaborn-white', 'dark_background', 'seaborn-poster', 'seaborn-deep']\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import pymc3 as pm\n",
    "import langevin\n",
    "import langevin_cached_model as lcm\n",
    "import lmfit as lm\n",
    "from lmfit.models import ExponentialModel\n",
    "from scipy.stats import pearsonr\n",
    "from scipy.optimize import minimize_scalar\n",
    "\n",
    "SMALL_SIZE = 16\n",
    "MEDIUM_SIZE = 18\n",
    "BIGGER_SIZE = 20\n",
    "\n",
    "plt.rc('font', size=SMALL_SIZE)          # controls default text sizes\n",
    "plt.rc('axes', titlesize=SMALL_SIZE)     # fontsize of the axes title\n",
    "plt.rc('axes', labelsize=MEDIUM_SIZE)    # fontsize of the x and y labels\n",
    "plt.rc('xtick', labelsize=SMALL_SIZE)    # fontsize of the tick labels\n",
    "plt.rc('ytick', labelsize=SMALL_SIZE)    # fontsize of the tick labels\n",
    "plt.rc('legend', fontsize=SMALL_SIZE)    # legend fontsize\n",
    "plt.rc('figure', titlesize=BIGGER_SIZE)  # fontsize of the figure title\n",
    "\n",
    "SEED = 35010732 # from random.org\n",
    "np.random.seed(SEED)\n",
    "\n",
    "print(plt.style.available)\n",
    "plt.style.use('seaborn-white')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# function to calculate A and B from the dataset\n",
    "def OUanalytic1(data):\n",
    "    N = data.size\n",
    "    data1sq = data[0]**2\n",
    "    dataNsq = data[-1]**2\n",
    "    datasq = np.sum(data[1:-1]**2)\n",
    "    datacorr = np.sum(data[0:-1]*data[1:])\n",
    "    coef = [(N-1)*datasq,\n",
    "       (2.0-N)*datacorr,\n",
    "       -data1sq-(N+1)*datasq-dataNsq,\n",
    "       N*datacorr]\n",
    "    B=np.roots(coef)[-1]\n",
    "    Q=(data1sq+dataNsq)/(1-B**2)\n",
    "    Q=Q+datasq*(1+B**2)/(1-B**2)\n",
    "    Q=Q-datacorr*2*B/(1-B**2)\n",
    "    A = Q/N\n",
    "    P2A = -N/2/A**2\n",
    "    Btmp = (N-1)*(1+B**2)/(1-B**2)**2\n",
    "    tmp = (2+6*B**2)*(data1sq+dataNsq) + (4+12*B**2)*datasq - (12*B+4*B**3)*datacorr\n",
    "    P2B = Btmp - tmp/A/2/(1-B**2)**3\n",
    "    PAB = (N-1)*B/A/(1-B**2)\n",
    "    dA = np.sqrt(-P2B/(P2A*P2B-PAB**2))\n",
    "    dB = np.sqrt(-P2A/(P2A*P2B-PAB**2))\n",
    "    return A,dA,B,dB\n",
    "\n",
    "def OUresult1(data,deltat):\n",
    "    A, dA, B ,dB = OUanalytic1(data)\n",
    "    tau = -deltat/np.log(B)\n",
    "    dtau = deltat*dB/B/np.log(B)**2\n",
    "    return A,dA,tau,dtau"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# function to calculate A and B from the dataset\n",
    "def OUanalytic2(data):\n",
    "    N = data.size\n",
    "    data1sq = data[0]**2\n",
    "    dataNsq = data[-1]**2\n",
    "    datasq = np.sum(data[1:-1]**2)\n",
    "    datacorr = np.sum(data[0:-1]*data[1:])\n",
    "    coef = [(N-1)*datasq,\n",
    "       (2.0-N)*datacorr,\n",
    "       -data1sq-(N+1)*datasq-dataNsq,\n",
    "       N*datacorr]\n",
    "    B=np.roots(coef)[-1]\n",
    "    Q=(data1sq+dataNsq)/(1-B**2)\n",
    "    Q=Q+datasq*(1+B**2)/(1-B**2)\n",
    "    Q=Q-datacorr*2*B/(1-B**2)\n",
    "    A = Q/N\n",
    "    P2A = -N/A**2/2\n",
    "    Btmp = B**2*(1+2*N)\n",
    "    tmp = (1+Btmp)*(data1sq+dataNsq) + (2*Btmp + N + 1 -B**4*(N-1))*datasq - 2*B*(1+B**2+2*N)*datacorr\n",
    "    P2B = -tmp/((1-B**2)**2*(data1sq+dataNsq + (1+B**2)*datasq - 2*B*datacorr))\n",
    "    PAB = (N-1)*B/A/(1-B**2)\n",
    "    dA = np.sqrt(-P2B/(P2A*P2B-PAB**2))\n",
    "    dB = np.sqrt(-P2A/(P2A*P2B-PAB**2))\n",
    "    return A,dA,B,dB\n",
    "\n",
    "def OUresult2(data,deltat):\n",
    "    A, dA, B ,dB = OUanalytic2(data)\n",
    "    tau = -deltat/np.log(B)\n",
    "    dtau = deltat*dB/B/np.log(B)**2\n",
    "    return A,dA,tau,dtau"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "A,D = 1.0,2.0\n",
    "tau_real = A/D\n",
    "delta_t_list=np.linspace(0.01,1,50)\n",
    "#M=1000 # number of data sets\n",
    "N=50000 # length of data set\n",
    "#print(np.exp(-delta_t*D/A))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# let us first calculate the standard deviation for each point of the acf\n",
    "# all acfs are stored in acf_all for later analysis\n",
    "\n",
    "result_Bayes_array = None\n",
    "for delta_t in delta_t_list:\n",
    "    data = langevin.time_series(A=A, D=D, delta_t=delta_t, N=N)\n",
    "    \n",
    "    results = OUresult1(data,delta_t)\n",
    "    if result_Bayes_array is None:\n",
    "        result_Bayes_array = results\n",
    "    else:\n",
    "        result_Bayes_array = np.vstack((result_Bayes_array, results))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c24a70b70>]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogy(delta_t_list/tau_real,result_Bayes_array.T[3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10bf14470>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogy(delta_t_list,result_Bayes_array.T[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.15142857142857144\n"
     ]
    }
   ],
   "source": [
    "A,D = 1.0,2.0\n",
    "tau_real = D/A\n",
    "delta_t_list=np.linspace(0.01,1,50)\n",
    "#M=1000 # number of data sets\n",
    "N=50000 # length of data set\n",
    "#print(np.exp(-delta_t*D/A))\n",
    "pick_delta = 7\n",
    "print(delta_t_list[pick_delta])\n",
    "data = langevin.time_series(A=A, D=D, delta_t=delta_t_list[pick_delta], N=N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# compile model for reuse\n",
    "sm = lcm.OU_DA()\n",
    "sm.samples=20000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:14<00:00, 550.53draws/s]\n"
     ]
    }
   ],
   "source": [
    "trace = sm.run(x=data,\n",
    "                d_bound=5,\n",
    "                a_bound=5,\n",
    "                delta_t=delta_t_list[pick_delta],\n",
    "                N=50000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x1c21ff58d0>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x1c2225ad68>],\n",
       "       [<matplotlib.axes._subplots.AxesSubplot object at 0x1c1f093b00>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x1c21a529b0>],\n",
       "       [<matplotlib.axes._subplots.AxesSubplot object at 0x1c21a22b38>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x1c219c5828>]],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(trace)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.01\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:16<00:00, 532.83draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8878604257688776, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.030204081632653063\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:23<00:00, 493.94draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8868184718100317, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.05040816326530612\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:23<00:00, 488.25draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8791559189586702, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.07061224489795918\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:20<00:00, 511.86draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.09081632653061224\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:19<00:00, 512.64draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8829859959508816, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.11102040816326529\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:21<00:00, 503.57draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.13122448979591836\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:19<00:00, 514.45draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.15142857142857144\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:20<00:00, 510.15draws/s]\n",
      "The acceptance probability does not match the target. It is 0.880306026754848, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1716326530612245\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:19<00:00, 512.68draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.19183673469387755\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:24<00:00, 487.01draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8888854596046103, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.2120408163265306\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:22<00:00, 499.76draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.23224489795918368\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:29<00:00, 460.40draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8875879071170303, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.2524489795918367\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:24<00:00, 486.85draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8894288401090014, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.2726530612244898\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:22<00:00, 495.28draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8853580556975372, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.29285714285714287\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:21<00:00, 501.59draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.3130612244897959\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:26<00:00, 475.58draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.333265306122449\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:21<00:00, 506.16draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8822559980542907, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.35346938775510206\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:36<00:00, 425.09draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.3736734693877551\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:16<00:00, 535.78draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8800161163178807, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.39387755102040817\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:26<00:00, 474.55draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8883022134237737, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.4140816326530612\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:24<00:00, 485.36draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8843442308631161, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.4342857142857143\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:25<00:00, 479.51draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8935157428436903, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The acceptance probability does not match the target. It is 0.8813899399811538, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.45448979591836736\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:22<00:00, 499.36draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.4746938775510204\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:23<00:00, 491.90draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.49489795918367346\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:24<00:00, 485.37draws/s]\n",
      "The acceptance probability does not match the target. It is 0.88855611001427, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5151020408163265\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:26<00:00, 472.84draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8848652565096765, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5353061224489796\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:28<00:00, 461.43draws/s]\n",
      "The acceptance probability does not match the target. It is 0.892366966902241, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The acceptance probability does not match the target. It is 0.8838645413341726, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5555102040816327\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:25<00:00, 480.58draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8866519163050983, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5757142857142857\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:27<00:00, 466.71draws/s]\n",
      "The acceptance probability does not match the target. It is 0.884164015791079, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5959183673469388\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:23<00:00, 491.49draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6161224489795918\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:32<00:00, 440.95draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8981678365337469, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6363265306122449\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:34<00:00, 431.96draws/s]\n",
      "The acceptance probability does not match the target. It is 0.9013641250654368, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.656530612244898\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:21<00:00, 500.10draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.676734693877551\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:19<00:00, 513.87draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6969387755102041\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:14<00:00, 546.72draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7171428571428571\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:21<00:00, 502.27draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8894336739125621, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7373469387755102\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:18<00:00, 519.92draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8823516829621367, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7575510204081632\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:19<00:00, 517.44draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7777551020408163\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:18<00:00, 524.94draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8819524152329018, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The acceptance probability does not match the target. It is 0.8807839589183974, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7979591836734694\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:21<00:00, 503.33draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8869368109936824, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8181632653061224\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:16<00:00, 533.64draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8383673469387755\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:16<00:00, 534.24draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8585714285714285\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:22<00:00, 496.74draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8942676538453224, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8787755102040816\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:17<00:00, 530.14draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8989795918367347\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:16<00:00, 538.60draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9191836734693878\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:18<00:00, 521.25draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8809301409715896, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The acceptance probability does not match the target. It is 0.881752326158024, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9393877551020408\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:20<00:00, 506.87draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8851168392193605, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9595918367346938\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:28<00:00, 465.44draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8989670204494812, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9797959183673469\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:16<00:00, 536.86draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:16<00:00, 537.94draws/s]\n"
     ]
    }
   ],
   "source": [
    "result_array = None\n",
    "for delta_t in delta_t_list:\n",
    "    print(delta_t)\n",
    "    data = langevin.time_series(A=A, D=D, delta_t=delta_t, N=N)\n",
    "    trace = sm.run(x=data,\n",
    "                d_bound=5,\n",
    "                a_bound=5,\n",
    "                delta_t=delta_t,\n",
    "                N=50000)\n",
    "    a_mean = trace['A'].mean()\n",
    "    d_mean = trace['D'].mean()\n",
    "    a_std = trace['A'].std()\n",
    "    d_std = trace['D'].std()\n",
    "    results = [a_mean,a_std,d_mean,d_std]\n",
    "    if result_array is None:\n",
    "        result_array = results\n",
    "    else:\n",
    "        result_array = np.vstack((result_array, results))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c21840a58>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogy(delta_t_list,result_array.T[3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c21553f98>]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogy(delta_t_list,result_array.T[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c22056860>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dtau = np.sqrt(result_array.T[1]**2/D**2+A**2/D**4*result_array.T[3]**2)\n",
    "plt.semilogy(delta_t_list,dtau/tau_real,\"o\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1c24a6f9e8>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogy(delta_t_list,result_array.T[3]/D,\"o\",label=r\"$dD/D$\")\n",
    "plt.semilogy(delta_t_list,result_array.T[1]/A,\"o\",label=r'$dA/A$')\n",
    "plt.semilogy(delta_t_list,dtau/tau_real,\"o\",label=r'$d\\tau/\\tau$')\n",
    "plt.xlabel(r'$\\Delta t/\\tau$')\n",
    "plt.ylabel(\"relative error\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogy(delta_t_list/tau_real,result_array.T[3]/D,\"o\",label=r\"$dD/D$\")\n",
    "plt.semilogy(delta_t_list/tau_real,result_array.T[1]/A,\"o\",label=r'$dA/A$')\n",
    "plt.semilogy(delta_t_list/tau_real,dtau/tau_real,\"o\",label=r'$d\\tau/\\tau$')\n",
    "plt.semilogy(delta_t_list/tau_real,result_Bayes_array.T[3]/tau_real,color=\"k\",label=r\"$d\\tau/\\tau$ ind\")\n",
    "plt.semilogy(delta_t_list/tau_real,result_Bayes_array.T[1]/A,\"-.\",color=\"k\",label=r\"$dA/A$ ind\")\n",
    "plt.xlabel(r'$\\Delta t/\\tau$')\n",
    "plt.ylabel(\"relative error\")\n",
    "plt.legend(ncol=2)\n",
    "plt.savefig(\"optimaldt_1_2.png\",format='png',dpi=300,bbox_inches='tight',facecolor=\"white\",backgroundcolor=\"white\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}