Simulating datasets MCMC.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",
    "import theano.tensor as tt\n",
    "\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": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Ornstein_Uhlenbeck(pm.Continuous):\n",
    "    \"\"\"\n",
    "    Ornstein-Uhlenbeck Process\n",
    "    Parameters\n",
    "    ----------\n",
    "    B : tensor\n",
    "        B > 0, B = exp(-(D/A)*delta_t)\n",
    "    A : tensor\n",
    "        A > 0, amplitude of fluctuation <x**2>=A\n",
    "    delta_t: scalar\n",
    "        delta_t > 0, time step\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self, A=None, B=None,\n",
    "                 *args, **kwargs):\n",
    "        super(Ornstein_Uhlenbeck, self).__init__(*args, **kwargs)\n",
    "        self.A = A\n",
    "        self.B = B\n",
    "        self.mean = 0.\n",
    "\n",
    "    def logp(self, x):\n",
    "        A = self.A\n",
    "        B = self.B\n",
    "\n",
    "        x_im1 = x[:-1]\n",
    "        x_i = x[1:]\n",
    "\n",
    "        ou_like = pm.Normal.dist(mu=x_im1*B, tau=1.0/A/(1-B**2)).logp(x_i)\n",
    "        return pm.Normal.dist(mu=0.0,tau=1.0/A).logp(x[0]) + tt.sum(ou_like)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "A,D = 1.0,1.0\n",
    "delta_t_list=np.linspace(0.01,4,50)\n",
    "#M=1000 # number of data sets\n",
    "N=100000 # length of data set\n",
    "#print(np.exp(-delta_t*D/A))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x109b49f28>]"
      ]
     },
     "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[3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c1d6eec88>]"
      ]
     },
     "execution_count": 8,
     "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": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5800000000000001\n"
     ]
    }
   ],
   "source": [
    "AA,DD = 1.0,1.0\n",
    "tau_real = AA/DD\n",
    "delta_t_list=np.linspace(0.01,4,50)\n",
    "#M=1000 # number of data sets\n",
    "N=100000 # 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=AA, D=DD, delta_t=delta_t_list[pick_delta], N=N)"
   ]
  },
  {
   "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 (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:39<00:00, 1208.89draws/s]\n",
      "/Users/hstrey/anaconda3/lib/python3.6/site-packages/mkl_fft/_numpy_fft.py:1044: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  output = mkl_fft.rfftn_numpy(a, s, axes)\n"
     ]
    }
   ],
   "source": [
    "d_bound=20\n",
    "a_bound=20\n",
    "delta_t=delta_t_list[pick_delta]\n",
    "# compile model for reuse\n",
    "with pm.Model() as model:\n",
    "    D = pm.Uniform('D', lower=0, upper=d_bound)\n",
    "    A = pm.Uniform('A', lower=0, upper=a_bound)\n",
    "\n",
    "    B = pm.Deterministic('B', pm.math.exp(-delta_t * D / A))\n",
    "\n",
    "    path = Ornstein_Uhlenbeck('path',A=A, B=B, observed=data)\n",
    "    \n",
    "    trace = pm.sample(20000,tune=10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x1c2a070c50>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x1c2a295358>],\n",
       "       [<matplotlib.axes._subplots.AxesSubplot object at 0x1c2a2c6a20>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x1c2a2f1128>],\n",
       "       [<matplotlib.axes._subplots.AxesSubplot object at 0x1c2a0a5828>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x1c2a0c8eb8>]],\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 (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:59<00:00, 1004.11draws/s]\n",
      "/Users/hstrey/anaconda3/lib/python3.6/site-packages/mkl_fft/_numpy_fft.py:1044: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  output = mkl_fft.rfftn_numpy(a, s, axes)\n",
      "The acceptance probability does not match the target. It is 0.6707121158890552, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.09142857142857143\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:40<00:00, 1188.48draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.17285714285714288\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:38<00:00, 1212.38draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.2542857142857143\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:38<00:00, 1219.46draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.33571428571428574\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:40<00:00, 429.15draws/s] \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.41714285714285715\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:42<00:00, 1166.13draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.4985714285714286\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:37<00:00, 1228.13draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5800000000000001\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:37<00:00, 1227.40draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6614285714285715\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:43<00:00, 1160.79draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7428571428571429\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:44<00:00, 1152.83draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8242857142857143\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:43<00:00, 1160.17draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9057142857142858\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:38<00:00, 1213.21draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9871428571428572\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:49<00:00, 1091.07draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0685714285714287\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:49<00:00, 1100.07draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.1500000000000001\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:53<00:00, 1057.39draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.2314285714285715\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:48<00:00, 1109.77draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.312857142857143\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:52<00:00, 1070.93draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3942857142857144\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:52<00:00, 1061.97draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.4757142857142858\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [02:07<00:00, 938.59draws/s] \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.5571428571428572\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [02:02<00:00, 976.93draws/s] \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.6385714285714286\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [02:24<00:00, 831.93draws/s] \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.7200000000000002\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [02:23<00:00, 837.44draws/s] \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.8014285714285716\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [02:24<00:00, 828.31draws/s] \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.882857142857143\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [02:24<00:00, 828.63draws/s] \n",
      "The acceptance probability does not match the target. It is 0.7211230460996797, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.9642857142857144\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [02:10<00:00, 918.02draws/s] \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.045714285714286\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [02:25<00:00, 822.19draws/s] \n",
      "The acceptance probability does not match the target. It is 0.7018979069548527, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.1271428571428572\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [02:13<00:00, 896.42draws/s] \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.2085714285714286\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:49<00:00, 1099.60draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.29\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [02:12<00:00, 907.59draws/s] \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.3714285714285714\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:58<00:00, 1014.83draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.452857142857143\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:46<00:00, 1121.68draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.5342857142857143\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:56<00:00, 1026.88draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.6157142857142857\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:58<00:00, 1015.53draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.697142857142857\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [02:00<00:00, 997.23draws/s] \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.7785714285714285\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [02:09<00:00, 929.76draws/s] \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.86\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [02:09<00:00, 368.59draws/s] \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.9414285714285713\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [02:04<00:00, 962.99draws/s] \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.0228571428571427\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [02:03<00:00, 975.40draws/s] \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.104285714285714\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:47<00:00, 1114.47draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.1857142857142855\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [02:06<00:00, 947.32draws/s] \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.267142857142857\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [02:13<00:00, 898.83draws/s] \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.3485714285714288\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [02:16<00:00, 879.91draws/s] \n",
      "The acceptance probability does not match the target. It is 0.6615696348006885, 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 0.7139275217757943, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.43\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [02:11<00:00, 910.37draws/s] \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.5114285714285716\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [02:19<00:00, 862.04draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.592857142857143\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [02:46<00:00, 719.54draws/s]\n",
      "The acceptance probability does not match the target. It is 0.6303915595261954, 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 0.8817741970464621, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.6742857142857144\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [02:44<00:00, 730.14draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.755714285714286\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [02:54<00:00, 688.02draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.837142857142857\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [02:50<00:00, 705.65draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.9185714285714286\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [02:51<00:00, 700.28draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [03:00<00:00, 664.41draws/s]\n",
      "The number of effective samples is smaller than 10% for some parameters.\n"
     ]
    }
   ],
   "source": [
    "result_array = None\n",
    "for delta_t in delta_t_list:\n",
    "    print(delta_t)\n",
    "    data = langevin.time_series(A=AA, D=DD, delta_t=delta_t, N=N)\n",
    "    with pm.Model() as model:\n",
    "        D = pm.Uniform('D', lower=0, upper=d_bound)\n",
    "        A = pm.Uniform('A', lower=0, upper=a_bound)\n",
    "\n",
    "        B = pm.Deterministic('B', pm.math.exp(-delta_t * D / A))\n",
    "\n",
    "        path = Ornstein_Uhlenbeck('path',A=A, B=B, observed=data)\n",
    "    \n",
    "        trace = pm.sample(20000,tune=10000)\n",
    "        \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 0x1c2a4c2f28>]"
      ]
     },
     "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 0x1c2bddf0b8>]"
      ]
     },
     "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 0x1c29c21c18>]"
      ]
     },
     "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+result_array.T[3]**2)\n",
    "plt.semilogy(delta_t_list,dtau,\"o\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c306c26a0>]"
      ]
     },
     "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],\"o\",label=r\"$dD/D$\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# function to calculate A and B from the dataset\n",
    "def OUlargeN(N,A,B):\n",
    "    data1sq = A\n",
    "    dataNsq = A\n",
    "    datasq = (N-2)*A\n",
    "    datacorr = (N-1)*A*B\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 dA,dB\n",
    "\n",
    "def OUlargeN2(deltat,N,A,tau):\n",
    "    dA,dB = OUlargeN(N,A,np.exp(-deltat/tau))\n",
    "    dtau = np.exp(deltat/tau)*tau/deltat*dB\n",
    "    return dA,dtau\n",
    "\n",
    "def OUlargeNdtau(deltat,N,A,tau):\n",
    "    dA,dB = OUlargeN(N,A,np.exp(-deltat/tau))\n",
    "    dtau = np.exp(deltat/tau)*tau/deltat*dB\n",
    "    return dtau\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "dAt,dtaut = OUlargeN2(delta_t_list,100000,1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1c263cd908>"
      ]
     },
     "execution_count": 17,
     "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],\"o\",label=r\"$dD/D$\")\n",
    "plt.semilogy(delta_t_list,result_array.T[1],\"o\",label=r'$dA/A$')\n",
    "plt.semilogy(delta_t_list,dtau,\"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": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00448436, 0.00469024, 0.00483756, 0.0050082 , 0.00519471,\n",
       "       0.00548525, 0.00570548, 0.00581807, 0.00610982, 0.00625748,\n",
       "       0.00648739, 0.00678642, 0.00696807, 0.00737972, 0.00759159,\n",
       "       0.00789547, 0.0082585 , 0.00854288, 0.00898338, 0.0094004 ,\n",
       "       0.00956691, 0.00992503, 0.01058945, 0.01118118, 0.01124841,\n",
       "       0.01156248, 0.01209093, 0.01285228, 0.01396464, 0.01494869,\n",
       "       0.01407299, 0.0153801 , 0.01685775, 0.0177234 , 0.01960731,\n",
       "       0.02023764, 0.02108697, 0.02112391, 0.02357771, 0.02390514,\n",
       "       0.02387387, 0.03091935, 0.02800515, 0.02827125, 0.03741653,\n",
       "       0.03596699, 0.03689829, 0.04060072, 0.0345806 ])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result_array.T[3][:-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "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[:-1],result_array.T[3][:-1]/DD,\"ko\",markersize=8,fillstyle=\"none\",markeredgewidth=1,markeredgecolor=\"k\",label=r\"$dD/D$\")\n",
    "plt.semilogy(delta_t_list[:-1],result_array.T[1][:-1]/AA,\"kv\",markersize=8,fillstyle=\"none\",markeredgewidth=1,markeredgecolor=\"k\",label=r'$dA/A$')\n",
    "plt.semilogy(delta_t_list[:-1],dtau[:-1]/tau_real,\"ks\",markersize=8,fillstyle=\"none\",markeredgewidth=1,markeredgecolor=\"k\",label=r'$d\\tau/\\tau$')\n",
    "plt.semilogy(delta_t_list[:-1],dtaut[:-1],\"k-\",label=r\"$d\\tau/\\tau$ ind\",linewidth=2)\n",
    "plt.semilogy(delta_t_list[:-1],result_Bayes_array.T[1][:-1]/AA,\"k--\",label=r\"$dA/A$ ind\",linewidth=2)\n",
    "plt.xlabel(r'$\\Delta t/\\tau$')\n",
    "plt.ylabel(\"relative error\")\n",
    "plt.legend(ncol=2)\n",
    "plt.savefig(\"optimaldt_1_1.png\",format='png',dpi=300,bbox_inches='tight',facecolor=\"white\",backgroundcolor=\"white\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_label = \"1_1\"\n",
    "np.save(\"dtnorm_\"+data_label,delta_t_list/tau_real)\n",
    "np.save(\"dD_D_\"+data_label,result_array.T[3]/DD)\n",
    "np.save(\"dA_A_\"+data_label,result_array.T[1]/AA)\n",
    "np.save(\"dtau_tau_\"+data_label,dtau/tau_real)\n",
    "np.save(\"dtau_tau_ind_\"+data_label,result_Bayes_array.T[3]/tau_real)\n",
    "np.save(\"dA_A_ind_\"+data_label,result_Bayes_array.T[1]/AA)\n"
   ]
  },
  {
   "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": "3.6.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}