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@petermchale
Created March 22, 2021 19:09
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{
"cells": [
{
"cell_type": "markdown",
"id": "elegant-settlement",
"metadata": {},
"source": [
"## Changepoint detection\n",
"\n",
"Based upon https://www.tensorflow.org/probability/examples/Multiple_changepoint_detection_and_Bayesian_model_selection"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "plain-rating",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import tensorflow.compat.v2 as tf\n",
"tf.enable_v2_behavior()\n",
"import tensorflow_probability as tfp\n",
"from tensorflow_probability import distributions as tfd\n",
"\n",
"from matplotlib import pylab as plt\n",
"%matplotlib inline\n",
"import scipy.stats"
]
},
{
"cell_type": "markdown",
"id": "dirty-adapter",
"metadata": {},
"source": [
"## True data model\n",
"\n",
"Poisson events happen at a rate that changes over time, driven by sudden shifts in the (unobserved) state of some system or process generating the data:\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "diagnostic-reynolds",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'number of events per unit time')"
]
},
"execution_count": 2,
"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": [
"true_rates = [40, 3, 20, 50]\n",
"true_durations = [10, 20, 5, 35]\n",
"\n",
"observed_counts = np.concatenate([\n",
" scipy.stats.poisson(true_rate).rvs(true_duration)\n",
" for (true_rate, true_duration) in zip(true_rates, true_durations)\n",
"]).astype(np.float32)\n",
"\n",
"plt.plot(observed_counts)\n",
"plt.xlabel('time')\n",
"plt.ylabel('number of events per unit time')"
]
},
{
"cell_type": "markdown",
"id": "meaning-spice",
"metadata": {},
"source": [
"## Assumed data model: Hidden Markov Model (known number of states) "
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "arranged-volume",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Initial state logits:\n",
"[0. 0. 0. 0.]\n",
"Transition matrix:\n",
"[[0.95 0.01666667 0.01666667 0.01666667]\n",
" [0.01666667 0.95 0.01666667 0.01666667]\n",
" [0.01666667 0.01666667 0.95 0.01666667]\n",
" [0.01666667 0.01666667 0.01666667 0.95 ]]\n"
]
}
],
"source": [
"num_states = 4\n",
"daily_change_prob = 0.05\n",
"\n",
"initial_state_logits = np.zeros([num_states], dtype=np.float32) # uniform distribution\n",
"\n",
"transition_probs = daily_change_prob / (num_states-1) * np.ones(\n",
" [num_states, num_states], dtype=np.float32)\n",
"np.fill_diagonal(transition_probs,\n",
" 1-daily_change_prob)\n",
"\n",
"print(\"Initial state logits:\\n{}\".format(initial_state_logits))\n",
"print(\"Transition matrix:\\n{}\".format(transition_probs))"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "diagnostic-newsletter",
"metadata": {},
"outputs": [],
"source": [
"trainable_log_rates = tf.Variable(\n",
" np.log(np.mean(observed_counts)) + tf.random.normal([num_states]),\n",
" name='log_rates')\n",
"\n",
"hmm = tfd.HiddenMarkovModel(\n",
" initial_distribution=tfd.Categorical(\n",
" logits=initial_state_logits),\n",
" transition_distribution=tfd.Categorical(probs=transition_probs),\n",
" observation_distribution=tfd.Poisson(log_rate=trainable_log_rates),\n",
" num_steps=len(observed_counts))"
]
},
{
"cell_type": "markdown",
"id": "veterinary-photograph",
"metadata": {},
"source": [
"## MAP Training of HMM \n",
"\n",
"The model's total probability multiplied by a weakly-informative LogNormal prior on the rates yields the posterior distribution over the rates. We run an optimizer to compute the maximum a posteriori (MAP) fit to the observed count data."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "facial-electricity",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/petermchale/anaconda/envs/tf_tfp/lib/python3.8/site-packages/tensorflow_probability/python/distributions/hidden_markov_model.py:497: UserWarning: HiddenMarkovModel.log_prob in TFP versions < 0.12.0 had a bug in which the transition model was applied prior to the initial step. This bug has been fixed. You may observe a slight change in behavior.\n",
" warnings.warn(\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"step 0: log prob -373.54931640625 rates [13.759886 39.276726 48.77361 17.473715]\n",
"step 20: log prob -237.8798828125 rates [ 3.096108 42.114075 52.331783 18.199839]\n",
"step 40: log prob -239.3655242919922 rates [ 2.682757 41.753513 51.680683 18.174923]\n",
"step 60: log prob -237.8502960205078 rates [ 3.370356 41.765324 51.71199 17.981483]\n",
"step 80: log prob -237.86143493652344 rates [ 3.3711574 41.72749 51.628998 18.037527 ]\n",
"step 100: log prob -237.8477783203125 rates [ 3.277104 41.732914 51.643463 18.041698]\n",
"step 120: log prob -237.84483337402344 rates [ 3.3136847 41.736057 51.648327 18.03774 ]\n",
"step 140: log prob -237.84471130371094 rates [ 3.307979 41.732166 51.64106 18.036438]\n",
"step 160: log prob -237.84471130371094 rates [ 3.306732 41.73349 51.643238 18.037243]\n",
"step 180: log prob -237.8445281982422 rates [ 3.3080423 41.732853 51.642403 18.03724 ]\n",
"step 200: log prob -237.84466552734375 rates [ 3.3074226 41.733074 51.642574 18.03725 ]\n",
"Inferred rates: [ 3.3074226 41.733074 51.642574 18.03725 ]\n",
"True rates: [40, 3, 20, 50]\n"
]
}
],
"source": [
"rate_prior = tfd.LogNormal(5, 5)\n",
"\n",
"def log_prob():\n",
" return (tf.reduce_sum(rate_prior.log_prob(tf.math.exp(trainable_log_rates))) +\n",
" hmm.log_prob(observed_counts))\n",
"\n",
"optimizer = tf.keras.optimizers.Adam(learning_rate=0.1)\n",
"\n",
"@tf.function(autograph=False)\n",
"def train_op():\n",
" with tf.GradientTape() as tape:\n",
" neg_log_prob = -log_prob()\n",
" grads = tape.gradient(neg_log_prob, [trainable_log_rates])[0]\n",
" optimizer.apply_gradients([(grads, trainable_log_rates)])\n",
" return neg_log_prob, tf.math.exp(trainable_log_rates)\n",
"\n",
"for step in range(201):\n",
" loss, rates = [t.numpy() for t in train_op()]\n",
" if step % 20 == 0:\n",
" print(\"step {}: log prob {} rates {}\".format(step, -loss, rates))\n",
"\n",
"print(\"Inferred rates: {}\".format(rates))\n",
"print(\"True rates: {}\".format(true_rates))"
]
},
{
"cell_type": "markdown",
"id": "white-january",
"metadata": {},
"source": [
"## Inference: optimal sequence of hidden states"
]
},
{
"cell_type": "markdown",
"id": "utility-relationship",
"metadata": {},
"source": [
"Consider the probability of a hidden-state trajectory, conditioned upon the observed-count trajectory. Choose a timepoint and marginalize over hidden states at other timepoints. "
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "sapphire-bottle",
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 720x720 with 8 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Runs forward-backward algorithm to compute marginal posteriors.\n",
"posterior_dists = hmm.posterior_marginals(observed_counts)\n",
"posterior_probs = posterior_dists.probs_parameter().numpy()\n",
"\n",
"def plot_state_posterior(ax, state_posterior_probs, title):\n",
" ln1 = ax.plot(state_posterior_probs, c='blue', lw=3, label='p(state | counts)')\n",
" ax.set_ylim(0., 1.1)\n",
" ax.set_ylabel('posterior probability')\n",
" ax2 = ax.twinx()\n",
" ln2 = ax2.plot(observed_counts, c='black', alpha=0.3, label='observed counts')\n",
" ax2.set_title(title)\n",
" ax2.set_xlabel(\"time\")\n",
" lns = ln1+ln2\n",
" labs = [l.get_label() for l in lns]\n",
" ax.legend(lns, labs, loc=4)\n",
" ax.grid(True, color='white')\n",
" ax2.grid(False)\n",
"\n",
"fig = plt.figure(figsize=(10, 10))\n",
"plot_state_posterior(fig.add_subplot(2, 2, 1),\n",
" posterior_probs[:, 0],\n",
" title=\"state 0 (rate {:.2f})\".format(rates[0]))\n",
"plot_state_posterior(fig.add_subplot(2, 2, 2),\n",
" posterior_probs[:, 1],\n",
" title=\"state 1 (rate {:.2f})\".format(rates[1]))\n",
"plot_state_posterior(fig.add_subplot(2, 2, 3),\n",
" posterior_probs[:, 2],\n",
" title=\"state 2 (rate {:.2f})\".format(rates[2]))\n",
"plot_state_posterior(fig.add_subplot(2, 2, 4),\n",
" posterior_probs[:, 3],\n",
" title=\"state 3 (rate {:.2f})\".format(rates[3]))\n",
"plt.tight_layout()"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "split-linux",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x147de19d0>"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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Hjh3D6/VmfL2+YDBIV1cXHR0daS9eHM+2xDMZZWVlBIPBrNdXxQOvyTVeyTZu3IgxJqdXWvb391NeXs7KlSupqKigubmZ8fHxOR9npvquZDU1NQSDQXw+34Tt7e3tXLhwgU2bNiWykU6nMy9T2cYYOjs7qa6uxmq1TnhMW0rMjQZei9DY2Bijo6O64rtSi1S8cWoqhYWFlJSUzDjd2NHRwfnz53E6nfj9/nl9qM90bIj2iUp3iq6rqyvxoQ4kepNlu87L7/djsVimtFlIVlxcjIhMCUqyJf67N/713bZtG6Ojo7S0tMz5WPE/nuOF6NNJFaz7/X6OHj1KZWUlGzduBMjrUkNer5dQKDRhmjFOA6+50cBrEYoHXOPj43mby1dKpTY0NMTIyMi0gRdEP0j7+/tTdmAPBAK89dZblJeXs2PHDoCMBRXGGDo6OqiqqmL16tW0t7fP+jtkeHiYwcHBCR+opaWliEjWs0yBQICioqIJV4ZOZrFYKCoqmldj2kuXLs05YIq/5/jX1+PxUFtbS2tr65yDi76+PpxO57T1XXEOh4Py8vJEsB4Oh2lsbKSgoIA9e/ZMOD/5WmoofvHFihUrpjwWD7zy3epiqdDAaxFKrg2ZrU5EKZVb8Q/meFYolXgQM3lKKP6BarVa2bt3b+LDfaYr2uaiv7+foaEh6urqWL9+PeFwmLa2thmfEx9jcuBltVopLS3NWeA1m9LS0nkFp62trTQ3N8/pD9iBgQFEBI/Hk9gWv9LzxIkTc3r9vr6+WbNdcTU1Nfh8PoLBIMeOHcPv97N79+4p09nl5eXYbLacX8DR2dlJZWUlNpttymMul4tIJJKX1h9LkQZei1DyFKNONyq1uPT392O1WmesSyopKaGwsHDKh2NTUxM+n4/du3fjdDpxOBw4nc6MBV7t7e0UFBSwcuVKSkpKqKqqoq2tbcYlaTo7OykuLqawsHDC9rKyMgYHB7OWxQiHwwwNDc14HuNKSkoIhUJz/mCPX306l4W3BwYGKCkpmVDH5HK5aGho4MKFC2l/rQKBACMjI7PWd8XFpxuPHDnC+fPn2bhxI1VVVVP2s1gsrFy5kkuXLuVsqSG/308wGEyMcTJtKTE3GngtQsFgMPFXhWa8lFpc4vVdM02PQfSDtK+vL5FtuXjxIm1tbTQ0NEy4Kszj8WQk8AqHw3R2drJq1apE0LB+/XpCodC0vZ9GR0fp7+9PWbdTVlZGOBzOWm1V/I/KdDJe8dUB5jLdGAwGE+c+3QsY4kX8qbKZGzZswOFwpH21+Wz9uyZzu92UlpbS19dHeXk5mzdvnnbflStXMjY2lrMLsOJZUQ28MkMDr0UoGAxSXFyM3W7XwEupRSQeiMxU3xVXU1OTWNcuGAxy5MgRysrKEtNWcR6Ph2AwuOAC+87OTsbHx6mtrU1sq66upri4mDNnzqR8TrxjeqoP1Hjwka3pxuQ1GmdTWloKzK0WLh7MFhYWpl0P5ff7CYfDKb++BQUFbN68mf7+/rSuKuzt7cXpdE7JJM6krq4Op9PJ3r17Zwzs57rU0EJ1dnZSVlaWuPhiMg285kYDr0VoaGiIwsJC3G63Bl5KLSLxqbd0Aq/4VYIXLlygsbEREWHv3r2Jjt9x8aBiPsXjydrb23G73VOyNevXr8fn86Wcbuvq6kpkWiZzuVw4nc6sXdkYCAQQkbQCL7vdjtPpnFPg5fV6sVgsrF+/nuHh4UTripnM1J8NoutIFhcX09TUNOs032z9u1JZt24dt91227QBTtxclhpaqKGhIbxeb8qsaJzNZqOgoEA/r9KkgdciEw6HCYVCGngptQhNvuJtJvFL/y9duoTX6+Xqq69O2TYhXsS9kOnG4eFhent7qaurm5Ipqa2txW63T2ktMT4+Tk9Pz7TTR5DdRqqBQAC32z0lEJ1OSUnJnDNepaWliavw0pluHBgYwOFwTHsVooiwbds2gsHgjE1V51rfNfk10lFTU8PIyEhGvj4jIyMEg8GU/+JrQ870fQLaUmIuCvI9ADVRvO6hsLCQ8fHxxF806f4wKqWyJ9441W63p7V/TU0NbW1trF+/ftoPLrvdjsvlWlDgFe/dlTzNGGexWFi3bh3Nzc0TriLs7u4mEonMmMmIL380MjKSslnsQqRao3EmpaWl9PT0EIlEZg3WjDF4vV5qa2txuVwUFRXR3d3N+vXrZ3zeTP3Z4qqrq6mqquL48eMMDg7S0NCQqEGLm2t913zE10vs6uqa8Qrb2YRCIZ599tkZM3jxi0VmooFX+jTwWmTiGa544BWJRAiFQjM2GFRK5UZ/f3/KPkbTqays5IYbbpj1w9zj8SxoqrG9vZ2KioppMzX19fW0tLTQ2trKzp07gWjdjsPhmHFs8ccGBgZmzXjMhTGGYDA44SKD2ZSUlGCMwe/3p5waTRavmYtnE6urq2lrayMcDk/puh4Xz/qsWbNm1rHs3r2b06dPc+7cOTo6OqisrKShoYGqqipEhL6+PhwOx5wCy7kqKCigsrKSzs5Otm3bNu/jdHZ2EolE2LFjR8pWEcCE1hrTWegfD1cSDbwWmXjGy+12Jy6dHhoa0sBLqTyLL6GTzjRjsnSyHh6Ph87OTsbGxqb98JvOwMAAwWAw0d08FbvdTm1tLe3t7WzZsoWCggK6u7tZvXr1jNl0j8eDxWLJeOA1NDREJBJJq5VEXHKB/WyBVzwAiAcMVVVVtLa20t/fn7JFA6TXny3O4XCwfft2Nm3axPnz52ltbeW1116jqKiIhoaGedV3zUdNTQ1HjhzB5/NNybqlK95OpL6+fkFjcblcjI6OzhjcqigNvBaZYDCI3W7HZrMlUrtDQ0M5+SFW6kp1ceAi33zim5SsLqGwNPWUymD3IB3NHZwoPIGza+bi57kKDARoa27jqO0oRWVzy5JcaLnAYM8gp8tPY704/QdeKBji9InTvDL0Cs5CJ+ebzlMv9fxq+FczHv9MxxnkgrDeN/M03Vz4+nycbz7Pcedx3Bdn7uoeZ4yh6XQTL/lfYlXDqhn37WztpL+rn9aqVkSESDjCiZYTvBx4mZr1qadWu8520XuhlzMVZ7BY51b+HCmK4Av56G3uJdQYAmDVhlW8NP7SnI4zV+Oj45w8dZJXh19lxdr0M7GJ54+Nc/K1k1TVVfHWa28taCzxn4+TRSdxuDM7LZ1pBZYCPnXNp/L3+nl7ZZVSMBhMBFxOpxMR0SaqSmXZXd+9i8aDjSDASiBV8uAS4AMCRPfLpDBwGjgPzOVvrAhwBiiKjW02HcARwA0EAT+zX2LVDQwCF9LYN119QC/RMc8lOXIOOAbMtgrQ+dj/yeekHXgLWDfDcwzRr+9CDMWOMdf3Nl/ngaNM/75mMkj0+7oXmFtT/qmGiJ7jbiD9Dhp54Spw5TXw0qsaF5lgMJio04gvHqtXNiqVPcNjwzR2NEbv2IBOINWFYsOAk8wHXRD9gLYBoTk+L0A0+Ep3lqmMaJDnJ/rhmM4ngJNoQDJ12cn5GyX6nucamDjSGIcheh4nJyULY6+bavWgyDTPmQ83UE1ugi6IBt2jsX9zFSD6fZeJ9x2fIdflhWelGa9FJBKJMDw8POHqEW0poVR2DYQGosEI4F7v5s7SOxkaGKJ0ZSnla6L1PpFwhHPmHKWrSimvm/8VZDPpLusmFAixZvfsxd1xXSe7GK0Ype7qqW0kpnPh6AVGh0ap3lhNYfnsqYnxkXHaD7dTvrac0pXT11aNj44zNDBEcXXxrGO5ePwiYhFqtk5/RWUqvks++tr6qNtVR4Ej9cfX6NAoF7hAVUMVRZVFE7cfvUDlukqKqyfWlo0ER7goF6c8ZymIf33K6srwrPKk/bxIOMI5zlGyooSKtQsvZTERQ1tBG57VHspq51YHmWs2y9zqKDMtq4GXiLQR/dsqDIwbY/aJSDnwKFAPtAG/bYzJ7kqsS0TyFY1xbrebS5cu5WtISi17A8OXA6+68joe+fQjHD16lHPnzlG7spZdu3bR39/PK+YVrr322jldiTcXZzadoampiTvecUda7SpCoRDPhJ9hw4YNU7rhz6RrdxenTp3iwIEDaRdBP134NBUVFezZsyfl45FIhJdffpkBywDX7pv9HP07/05tbS07duxIe9wQLYB/8cUXueaaa6Yt9m9vb+ew/TC33HLLlKsKny55mrKyMvbt2zdh+9mzZznmOMZtt922JC9ker78eSwWCzfeeGPaz7lw4QJvmjc5cODAgtpRJHva/jRVVVVcffXVGTnecpWLqcZbjDFXG2Pi3+lfAJ41xmwEno3dV0zs4RXndrsZGRkhHA7na1hKLWuJjJcVylzRNRh37tzJli1b6Ojo4PXXX090fZ/rFY1zEb8CL922EhcuXMAYk7J310xWrlzJzTffPKcrz8rKymbsYH/y5EkGBgawWCyJhpvTCYVCjI+Pz6vVQvzKvZkaqQ4ODlJQUJCy71R1dTW9vb1Tur0PDAzgdDqXZNAF0asbBwYGCIXSn6vu6uqatZ3IXLndbu3llYZ81HjdDTwcu/0w8J48jGFRSm4lERe/rdONSmVHIuNlhTLn5Q+hjRs3smvXLnp7e2lpaaGoqGjOrR7mIh5UpNsLqb29nbKysqz2ioorLy9neHg45Qf7pUuXOHPmDPX19axdu5aurq7E4tSpxJfumUsriTir1UphYeGMwanX66W0tDTldGdVVRVjY2NTur2n0zh1MYs3wU1nDUkgsYboypUrM9qcO5NNVNNZ4mmpynbgZYCnRKRRRD4e27bCGBNf2bMLSHkNrIh8XEQOisjBdBc4XeqGhoYoKCiY0CFaAy+lsmtyxivZmjVruOaaa7BarVRWVmZ1HPEWMukEXgMDA/j9furq6rI6prjkRqrJQqEQhw8fpqSkhO3bt1NbW0skEuHixYvTHiv+gTrfgLG0tHTajFckEsHr9U7b8DPe4DT5M2VkZIShoaElHXgVFRVRVFTEuXPn0lq7saenh/Hx8RlXLZiPeOC10PUjT58+zS9/+ctlG3xlO/C60RizB3gX8GkRuTn5QRP96qT8ChljvmOM2WeM2Tddw7vlJrmVRFxyLy+lVOYNDA9Er2qblPGKW7FiBbfddtuCuoOny+PxpBV4tba2YrPZWL16ddbHBNFgJ95INc4YQ2NjI5FIhH379mGxWPB4PBQXF8843ej3+ykoKJh1IejplJSUMDQ0lDKrFggEiEQi0zZYtdlseDyeCes2zmX9zcVs06ZN+Hy+xPJRM+ns7MRms2W8P6TL5SISiSSaf8/H6OgoLS3RfiHZWic037IaeBljLsT+7wZ+BOwHLolIDUDs/9lXLr1CJLeSiLPb7VitVg28lMqSCRmvFIEXXP45zDaPx0MoFGJkZPqeCUNDQ3R2drJ27VoKCnJzYbrFYqG0tHTCB2FzczP9/f3s3Llzwh+MdXV1iW76qSSvFzkf8aDK7/dPeWxyx/pUqqurGRwcTAQH8dq0dJbFWcxWrVqFx+Ph5MmTM9YEG2O4dOkS1dXVaS9Qnq54jdxCphubm5sJh8NYLJasLEG0kKAwU7IWeIlIoYgUx28DtxNtffck8OHYbh8GfpytMSwlxhiGhoZSFoQWFhZq4KVUliRqvCxTpxpzLf7hP9MHztmzZwFYt24+HTPnr6ysjMHBQSKRCD09PbS0tLBmzZopWbf4MkTTZb0CgcC86rvi4rVwqeq8BgcHJ6z6kUp8BiU+3djf309JSUnGg5BcExG2b99OKBSitbV12v36+voYHR3N+DQjLDzwCgQCnDt3jrVr11JWVrag9UtTaW9v55lnnsl7Ji2b32krgBdF5AjwOvAzY8x/AF8G3ikiLcBtsftXvPi8eKpfGG63W7vXK5UlfcG+aMHDDBmvXJkpqAAYGxvj/PnzrF69et5TdfNVXl6eKMo+dOgQxcXFXHXVVVP2czqdVFVV0dHRMaXWZ2xsjFAotKCMl9PpxG63p6zzGhwcnHUdR4/Hg81mo6enh0gkwuDgYMbaKeRbeXk5NTU1tLS0TJs17erqwmKxZKUtykIDr6amJqxWK5s3b04sHB+JRDIytpaWFg4fPkx5efmCAv9MyFrgZYxpNcbsiv3bbox5ILa9zxjzDmPMRmPMbcaY6a9RvoKkaiURp01Ulcqe/mDsV1CK4vpcKygooLi4eNqM1/nz5xkfH2f9+sytm5iueA3Um2++yfj4OHv37p12+rW2tpbh4WH6+vombF9oYX1caWnplOA0Eong9/tnnTIUEaqqqujp6cHn8xGJRJZ8fVeyrVu3EolEOHny5JTHjDF0dnZSXV2dlalzm81GQUHBvAKv3t5eLl26xMaNG7Hb7ZSWlhKJRBZcYG+M4ejRo5w8eZLVq1ezf//+nE3RT2dp51aXkdkCr3A4PGPdh1Jqfvr9SYFXnjNeEA0qUgVekUiEs2fPUlFRMWtWJxvifa7C4TA7duyYMWuwcuVKbDbblOnGhbSSSFZSUoLf75+QUfP7/TMW1ierrq4mFApx7tw5YOkX1icrLCxk3bp1tLe3T6mD83q9hEKhrEwzxs1nmTtjDMePH8flciX+qEhn2n02kUiExsZG2traaGhoYPfu3YtiSjn/I1BANPCyWCwTWknEaUsJpbJnIBir91gEGS+IfuCMjIxM6ZnV2dnJ8PAwDQ0NeRpZtK5sw4YNs7axsFqtrFq1is7OTsbHxxPbA4EAFotlykVEc1VSUjIlG5JOYX1cvM6rvb19STdOnc6mTZsoKCigqalpwvbOzk5EhBUrUnZxyoj59PLq6OjA5/OxdevWRGBUWFiIzWabd+A1NjbGq6++SmdnJ9u3b2fbtm0Z7Vm2EBp4LRLxwvpU3xgaeCmVPYPBweiNRZLxmu4v/dbWVgoLC7O2ZFE6Ghoa2Lp1a1r71tbWEg6H6ezsTGzz+/3T/p6bi1Qd7OOF9ekEdU6nk+LiYowxyyrbFWez2di0aRPd3d0TepZ1dnZSWVmZ1UbAcw28wuEwJ0+exOPxsGrVqgmPpZpSTkcoFOKll15iYGCAPXv25GVqfiYaeC0SqXp4xWngpVT2DA4NRm8skoxXSUkJIjLhA6e/v5/BwUEaGhoWzV/tsykvL6ewsHDCdONCW0nEFRUVYbFYJpyjwcHBObWEiAewy6WwfrL6+nrcbjdNTU0YY/D7/QSDwWnXuMwUl8vF6Oho2svcnTlzhlAoxPbt26d8b3s8nkQdXroCgQAvvPACw8PDXHvttTnrdTcXGngtAsaYlD284qxWKw6HQwMvpTIsNB5idCTa18daYKXQNn0bglyxWq1TCuzPnDmDzWab87qM+VZXV0dfXx9DQ0NEIhGGhoYyckWZxWKhuLg4kfEKh8NpFdYnq6mpwWKxZH1FgnyxWCxs3boVn89He3t7IvOYi8ALSGvdyFAoxOnTp6mpqUkZAHs8nsRFE+lqamoiEolw4MCBRfu11cBrERgZGSESiczYe0Z7eSmVeYmu9RYod5cvmmxScoF9MBikq6uL+vr6nDRxzaR4oNjR0UEwGMQYk7G1JUtKShIZL5/PhzFmToFXWVkZ73rXuxLTlsvRqlWrKC8v5+TJk1y8eJGysrKstyGJB17pfF41NzcTiUSmnb6OXyiRbp1XJBKht7eX1atXL+qvqwZeaRgfH2dkZGTafws10xWNcS6XS3t5KZVhM63TmE8ej4fR0VGGh4dpbW3FYrHkvGFqJrhcLiorK+no6EhkLTIVeJWWljI6OkooFEoEYHO92nMxXOGWbdu2bWNkZAS/35/Vqxnj0u3l5ff7aW9vZ926dTOW2djt9rQDr76+PsLhMIt9mcH8NrNYAgKBAL/61a9mXPRzzZo17Nq1a96vkU7gVVhYyMWLF4lEIlfELwulcmFC1/pFUFgfF8/c9PT00N7ezurVq1Ne8bwU1NXVcejQIc6fPw9kLvBKLrAfHBzE4XAsu6sTM6GsrIxVq1Zx8eLFrE8zAomM2myB18mTJykoKGDjxo0z7jdde5VUenp6lsT0sQZes+jr68MYw9atW1M2XRsYGOD8+fOsWbNm3lfHDA0NISIz/tJwu90YYxgeHp4xQFNKpW+xZrziBfYnTpwgHA4vuquy5mLlypVYrVZ6enpwu90Zmy6dHHjlo7fZUrFz507WrFmTk88Oi8WC0+mcMfCKT59v2rQJu90+4/E8Hg+nT58mHA7P+r3T3d1NeXn5op+S18BrFvFLlDds2JDy8bq6Onp7ezl+/Dg33njjvF4jXlg/U31J8pWNGngplRmJjJdtcWW8LBZLooapqqpqUderzKagoIBVq1bR3t6esWwXkGgd0d/fTyAQyMk02lJls9lyOv02W0uJM2fOYLFYqK+vn/VYHo8HYww+n2/G5EYoFMLv98/aY24x0DmrWXi93hkLNuPrSg0MDHDx4sV5vcZMrSTitKWEUpk3IeO1iAIvuFyvtJSzXXHxD8NMBl4QzXp1d3fPubBeZddMgdfo6CgdHR3U1tamNX0e/zmYrZ9Xd3c3wKKv7wINvGYUiUTw+Xyz/kDX1dVRUlLCiRMn5rWgZzqBl9PpxGKxaOClVAb1D/VHr2pcZFONAGvXrqWhoSGvDVMzpby8nIaGhoxnI0pKShL1tzrVuHjEA69UtdHnzp2b0/S5y+XC4XDMWufV09OD0+lcEtlhDbxmEL9EebYfaBFh27ZtDA0Ncfbs2Tm9xujoKOPj47N2W47XgGngpVTm9Pp7ozcWYcbL4/Gwbdu2fA8jI+K/IzP9oRj/3ex0OrPeJkGlz+VyEYlEGB0dnbA9vt5odXX1nPq5zVZgb4yhp6dnSWS7QAOvGc117a/q6mpaWlqmfLPNJJ0rGuPcbrcGXkplUH8waYHsRZbxUrOLB3I6zbi4TNdS4sKFC4yMjMx5+tzj8RAIBKbthj84OMjY2NiSyQ5r4DUDr9eL3W5P+xLlbdu2MT4+zqlTp9J+jbkGXtrLS6nM6Q8kBV6LLOOlZud2u/F4PFld9FnNXXwGZ3Lg1draSklJyZwzU/EC++nqvOL1XYu9jUScBl4zmOvaX8XFxaxZs4a2tra0A6T4fuks7FpYWMjY2BhjY2Npj0kpNb2B4ED0hma8lqybbrqJNWvW5HsYKkmqjFdPTw8+n29eF4vMVmDf09NDWVnZrK0pFgsNvKYxn7W/ADZv3ozVaqWpqSmt/YPBIC6XK62mqNP9FaGUmp+BQCzwWmQNVJVaymw2G1ardcJnVWtrKw6HY16LVsdr+FLVeY2NjTE4OLhk6rtAA69ppVtYP5nD4WDDhg10dXXR19c36/5z6culLSWUyizvUOwvaM14KZVRyS0l/H4/3d3drFu3bt4rr3g8npSBV09PD8YYDbyWg7kU1k+2fv16nE4nTU1NMy41BOm1koiLB15a56VUZniDXhC0xkupDEsOvFpbW7Faraxdu3bexystLSUQCDA+Pj5he3d3Nzabbd4rx+SDBl7TiK/9NZ9LlK1WK1u3bmVwcHDGpqpjY2OMjo6mHXjZbDZsNptmvJTKgJHxEUZGR8ACVrFSZM9sc0+lrmRut5vh4WFGRkYSDVMXUoMVT4JMrvPq6emhsrJyxpVfFpsrfsmg59qe48+e+bMp233NPix2C0Xn5/fL2BiDv8WP+aWhqKEIq2Pq2lHjQ+P4W/wUNhdi96T3Dek75cNSYKHotdTjioxGCLQFcFQ4cFTMfVHdSnclf/G2v+Ca1dfM+blKLSWT12lcSr+4lVrsXC4XIyMjtLa2EolEFrwCQ3KBfUVFBRCdwgyFQkumjUTcFR94DYQGeO3CaxM3hoELQEXs//myAheBHqAWmJw88wF9QBGQ7uzhIDAKpIqpDNAODAMdQDkwj2lv74iXFz76wtyfqNQSklinUacZlcq4+JWNra2trFixYsHLRTkcDlwu14Q6r3gbiaUWeOlUYyojsf8X2gjZCawhWkPSztTgKt4VYi7ZV1vsealKx3qJBl0rgVKgH+iaZt8ZnO4/PbcnKLUETc54KaUyJx54RSIRGhoaMnLMyQX2PT09FBcXL7lVC674jNfNa2/mlY+9MmHbhXMXaD3VyrU3X4vdsfC+ICOhEY4fOs5QcIhN2zdRXRONzk8dP8VA7wDXvu3atI/V2d7J6ZOn2X/TfhzOy2mvgb4Bjr15jJWrV7Jx20YAzp05x/nW85RXlrNl5xas1qnTnXHDY8Pc+t9vBcAbmnkxUqWWA814KZU98cCrtLQ0MTW4UKWlpXR2djI2NobFYqGvr4/6+vqMHDuXsh54iYgVOAhcMMbcKSLrgEeITuQ1Ar9njEl/jZ0MK3eVc13tdRO2vdn9JiW1JdzccHPGXueGtTfwxhtv0NfVR1V5FQ0NDYTPhaGIKa8/kx5HDwW9Bewo30F5eTkAoVCI544/xzXrruGmm25KBFjX1V7HufpzHD16lMj5CNdce820xY3GGCxiIWIiDI8PMxYew2a1LfyNK7VIDYQGFu0C2UotdS6Xi6qqqgXXdiVLLrCPRCJEIpElN80IuZlqvAc4kXT/b4CvGWM2AAPAx3IwhjmZa8f6dNhsNq677jpWrVpFU1MTx48fn1MPr7jJvbyMMRw6dIhwOMzevXunZLXWrl3Lvn378Pl8vPjii9NeESkilDguL2DrG/HNaVxKLTW9/t7oNLxmvJTKOBHhuuuuy2hgFP9cHhwcpLu7G6vVmrFsWi5lNfASkVrg14F/jd0X4Fbgh7FdHgbek80xzNX4+DjBYDAri65aLBb27NnD+vXraW1tJRQKzTnwiqdv4728Wlpa6O3tZceOHdOu9r5y5Uquv/56RkdHefHFF/H5UgdVpY7LzWK9IzrdqJa33kBv9IZ2rVdqSbDZbLjdbrxeL93d3VRUVMy7IWs+ZXvEfw98nmhCH6LTi4PGmHgHtA4g5foBIvJxETkoIgd7enqyPMzL4j1CsrXavYiwfft2tm3bNq/XsVgsuFwuhoaG6O3tpbm5mdraWurq6mZ8Xnl5OQcOHEBEOHr0aMp9Sp1JgZfWeallbsIC2TrVqNSS4PF46OnpIRgMLqlu9cmyFniJyJ1AtzGmcT7PN8Z8xxizzxizL5cnN37FxFyXCpqrhoYG3vWud83rGyce8b/55psUFRWxY8eOtJ5XXFzM6tWrGRwcJBKJTHlcM17qSjIh8NKMl1JLQmlpKWNj0ZYAS7G+C7JbXH8AuEtE3k20sUIJ8HXAIyIFsaxXLQvrlJVxg4ODuN3unKxyXlAwv9Pvdrvp6+vDYrFw3XXXzek4paWlRCIRAoEAJSUlEx5LrvHSjJda7vqDmvFSaqmJzxK5XK4F9wbLl6xlvIwx9xpjao0x9cAHgF8YYz4E/BJ4X2y3DwM/ztYY5sPr9WY927VQ8bqwq666akrwNJvk4sTJJkw1asZLLXODgcHoDc14KbVkxD+fl2q2C/LTQPXPgP8sIqeJ1nw9mIcxpDQ2Npa1wvpMWrNmDXv37p3XgqOFhYXYbLbUgZdDa7zUlWNwaDB6QzNeSi0ZNpuN/fv3s2nTpnwPZd7SnqMSEbcxZl6rMxtjfgX8Kna7Fdg/n+NkW67quxbK4XCwatWqeT+/tLR01sBL20mo5c4b9Eb/9BTNeCm1lKxYsSLfQ1iQWTNeInKDiDQBJ2P3d4nIP2Z9ZHmQ7SsaFwuPx4Pf759SYK9TjepK4hvyRddTRTNeSqncSWeq8WvAHUSXc8YYcwTIXEv3RWRwcDAxFbecxQvs/X7/xO061aiuEKPhUUIjIbCCVawU21P3wFNKqUxLq8bLGNM+aVM4C2PJu8HBwUU/zZgJ0xXYa8ZLXSmS12n0OD1EezsrpVT2pRN4tYvIDYAREZuIfI6JSwAtC6OjowwPDy/7aUaItqNIVWCvfbzUlULXaVRK5Us6gdcngE8T7TB/Abga+FQWx5QX8SDkSgi8IPo+Jwde2sdLXSmSM15aWK+UyqV0Aq/NxpgPGWNWGGOqjTG/C2zN9sByLV5YfyVMNcLlAvtw+PKssU41qitF31BfNONl0YyXUiq30gm8vpnmtiVtcHCQoqKieXeTX2o8Hg/GmAkLZmtxvbpS9PpjC2RrxksplWPTRhkicj1wA1AlIv856aESEhdhLx+Dg4NUVFTkexg5E8/seb1eysqiHzzJGS/t46WWMw28lFL5MlN6xw4UxfZJvtbax+Ulf5aFkZERQqHQFVPfBdF1rhwOx4Q6r+RL6v2jfsKRMFbLsouxlaLP3xe9ocX1SqkcmzbwMsY8BzwnIt8zxpzL4Zhy7korrI+b3MHeaon2M/KPRvt7+Uf9eJye/AxOqSyasEC2ZryUUjmUTkHTkIj8HbAdcMY3GmNuzdqocszr9SIic15weqnzeDz09PQQDoexWqOZrVJnaSLw8oa8GnipZWlC4KUZL6VUDqVTXP99ossFrQO+BLQBb2RxTDnndrupq6u7Ygrr4+IF9vErOmFSSwm9slEtUwOBgegNzXgppXIsncCrwhjzIDBmjHnOGPP7wLLJdgHU1taya9eufA8j5+IF9snTjXplo7oSDAYHQdB2EkqpnEsnxTMW+79TRH4duAiUZ29IKlecTidOp3NCxkt7eakrgXfIe3mBbM14KaVyKJ3A669EpBT4E6L9u0qAP87qqFTOTC6wT854aUsJtVz5hnyXAy/NeCmlcmjGwEtErMBGY8xPAS9wS05GpXLG4/Fw6dIlxsfHKSgo0KlGdUXwDfkShRaa8VJK5dKMNV7GmDDwOzkai8qDeAuNxJJJOtWolrmx8BihkRBYwSIWih3Fsz9JKaUyJJ2pxpdE5FvAo0AwvtEY82bWRqVyJrmDfUVFhWa81LI3ELq8QLbH6cEi6VxjpJRSmZFO4HV17P+/TNpmWGZXNl6pHA4HLpcrUeelGS+13A0MXw68dJpRKZVrswZexhit61rmkgvstY+XWu56/D3RG9o8VSmVB5pjV3g8HoLBIGNjYzrVqJa9Hl9S4KUZL6VUjmngpSYU2OtUo1ruegO90Rua8VJK5cGsgZeIONLZppau5A722sdLLXd9/r7oDYtmvJRSuZdOxuuVNLepJcput+N2u6dmvHSqUS1DfYFY4KVTjUqpPJi2uF5EVgKrAZeI7Ca6shlEO9e7ZzuwiDiB5wFH7HV+aIz5CxFZBzwCVACNwO8ZY0YX9C7Ugnk8HgYHB6l31Ce26VSjWo76A/3RGzrVqJTKg5muarwD+AhQC3w1absf+GIaxx4BbjXGBETEBrwoIv8O/Gfga8aYR0Tk28DHgH+az+BV5pSWlnLx4kWc4kxs8434MMYgIjM8U6mlZXBoMHpDM15KqTyYNvAyxjwMPCwi/5cx5vG5HtgYY4BA7K4t9i/e/+uDse0PA/ejgVfexQvshwJDuApcDI8PEzERAqMB7eytlpWB4EC0yEI046WUyr10Gqj+VEQ+CNQn72+M+ctpnxETW+uxEdgA/ANwBhg0xozHdukgOp2Z6rkfBz4OsGbNmjSGqRZiQoG9s5ThwDAQnW7UwEstJ96g9/IC2ZrxUkrlWDrF9T8G7gbGiS4ZFP83K2NM2BhzNdHpyv3AlnQHZoz5jjFmnzFmX1VVVbpPU/Nks9koLCyccmWjFtir5cY7lBR4acZLKZVj6WS8ao0xv7aQFzHGDIrIL4HrAY+IFMSyXrXAhYUcW2WOx+Ohv79/wpWN2lJCLTe+IZ9mvJRSeZNOxutlEdkx1wOLSJWIeGK3XcA7gRPAL4H3xXb7MNGMmloESktLGR4epth6eWpRr2xUy41/2K8ZL6VU3qST8boR+IiInCV6paIQrZ3fOcvzaogW51uJBniPGWN+KiJNwCMi8lfAIeDB+Q9fZZLL5QKgyFKU2KZTjWo5GQuPEQqFwAmCTFibVCmlciGdwOtd8zmwMeYtYHeK7a1E673UIuNwRBckKLImBV6a8VLLSP9Qf/Taait4nB4soqumKaVya9bfOsaYc0Ad0Z5c54ChdJ6nlp544OWWy/1xNeOllpNuX3f0hjZPVUrlSTprNf4F8GfAvbFNNuDfsjkolR92ux0Al7gS2zTjpZaTHl9P9Iau06iUypN0MlfvBe4i1kLCGHMR0MZOy5DNZkNEcFs046WWpx5/LPDSjJdSKk/SCbxGY13oDYCIFGZ3SCpfRAS73T5h2SDNeKnlRBfIVkrlWzqB12Mi8s9E+2/9IfAM8K/ZHZbKF4fDMWGqUft4qeVEAy+lVL7NelWjMeYrIvJOwAdsBv7cGPN01kem8sLhcGDHnrivGS+1nPQH+qM3dKpRKZUnswZeIvI3xpg/A55OsU0tM3a7HbtJCry0xkstIwOBgWgnQi2uV0rlSTpTje9MsW1evb3U4qcZL7WcDQYHtWu9Uiqvps14icgngU8B60XkraSHioGXsj0wlR92ux2HOCACWDTjpZaXwaFBXadRKZVXM001/gD4d+C/AV9I2u43xvRndVQqbxwOB267G8JEA68RL8YYRCTfQ1NqwbxDXs14KaXyatqpRmOM1xjTZoz5nVjH+mGiLSWKRGRNzkaocsrhcGC32rEZGwDjkXGGx4fzPCqlMsMX9GnGSymVV+l0rv8NEWkBzgLPAW1EM2FqGYp3ry+xXl48WFtKqOXCH/InfutpxksplQ/pFNf/FXAdcMoYsw54B/BqVkel8iaxUHZB0kLZWuellgFjDIHhgGa8lFJ5lU7gNWaM6QMsImIxxvwS2Jflcak8SQRelqTAS69sVMtAaDTE8NgwWEEQSp2l+R6SUuoKNGsfL2BQRIqA54Hvi0g3sXUb1fJjtVqxWq0UWgqjBfZoxkstD92+7ugNK5Q6S7FIOn93KqVUZqXzm+duooX1fwz8B3AG+I1sDkrll8PhmLhQtma81DLQ40taIFunGZVSeZLOkkHJ2a2HszgWtUjY7XbckhR4acZLLQM9/qTASwvrlVJ5MlMDVT/R9hFTHgKMMaYkxWNqGXA4HDjFmbivGS+1HPT5dYFspVT+TRt4GWOKczkQtXg4HA5c4krc14yXWg76AkmBl2a8lFJ5otWlagq73Y4DR+K+9vFSy0F/ILbghi6QrZTKIw281BQOhwO3zX35qkadalQ5dOzYMV566SXC4XBGjzsQHIj28BINvJRS+aOBl5oiEXiNR+9r4KVyZXBwkLNnz9Lf38/x48czeuzegV6ILsygU41KqbzRwEtNYbfbKbRpHy+Ve8ePH8dut7Nu3TrOnTvHhQsXMnJcYwx9g33EZ9A146WUyhcNvNQUDocDl82lU40qp7q6uujv72fLli1s27aN8vJy3nrrLYLBhfdrHh4ejq7TGA+8NOOllMqTrAVeIlInIr8UkSYROS4i98S2l4vI0yLSEvtffwMuMprxUrkWiURoamqiqKiINWvWYLFY2LNnDyJCY2MjkUhkQcf3er0ERgKa8VJK5V02M17jwJ8YY7YRXWT70yKyDfgC8KwxZiPwbOy+WkTsdjtuu9Z4qdw5d+4cwWCQbdu2ISIAuFwudu/ejdfrpampaUHH9/l8BMYCmvFSSuVd1gIvY0ynMebN2G0/cAJYTXQJongH/IeB92RrDGp+LBYLHpcnkfHSdhIqm8bGxmhubqayspIVK1ZMeGzFihWsX7+es2fP0tnZOe/X8Pl8DDGU+I2nGS+lVL7kpMZLROqB3cBrwApjTPw3aBewYprnfFxEDorIwZ6enlwMUyUpKSzBEol+e4TGQ4yGR/M8IrVctbS0MDY2xvbt21M+vnXrVjweD0eOHGFoaGher+H1eglYAon7mvFSSuVL1gMvESkCHgc+a4yZkDoxxhhSL0uEMeY7xph9xph9VVVV2R6mmsTpdFJoKUzc1zovlQ1DQ0OcPXuWuro6SkpSr0JmsVjYu3cvwLzqvcbGxggEAwTlcpF+qaN0/oNWSqkFyGrgJSI2okHX940x/zu2+ZKI1MQerwG6szkGNT92u31i4KV1XioLTpw4gYiwZcuWGfdzu93s2rWLwcFBTpw4MafX8Pl8BMeCifquUkcpVot1vkNWSqkFyeZVjQI8CJwwxnw16aEngQ/Hbn8Y+HG2xqDmz+Fw4LLoeo0qewYGBrh48SINDQ04nc5Z96+pqaG+vp7W1lb8fn/ar+P1egmMBiD2EjrNqJTKp2xmvA4AvwfcKiKHY//eDXwZeKeItAC3xe6rRcbhcOC2uBMTwZrxUpl2/PhxHA4HDQ0NaT9nw4YNAMyl7tPn8zHKKBRE72thvVIqnwqydWBjzIuATPPwO7L1uioz7HY77oLYeo0FmvFSmXN24Cz3PnEvLcdaKF5TzNd6vjan5/cd66PgUAGlDenVafWf6CcQ1oyXUmpxyFrgpZY2h8NBob0w2surQDNeKnP+9Ok/5fFfPR7NtxcDg3M8wCDQDkSY/k+7uAhwFigjEXiVu8rn+IJKKZU5umSQSimxULb28lIZ9mrbqzAGlDJ74JSKi2hANZLGvqNEp8sdlzf95pbfnMeLKqVUZmjGS6WUWDYo1vpIpxpVJgRHg1zoiy58bXVaefKDTyJzjL5GQiMcfvkwazeuZWXdyhn37e3q5UzTGXbs34G7yE1DeQObKjbNe/xKKbVQGniplBIZL102SGXQqb5T0WwXsK5qHe/e+O55Hae4u5jSklL2bdw3437HR49TXlvOu69+d2IpIqWUyiedalQp2Wy2aI2XLpStMqi5rzk6/QdsqZm5d9dMKioq6OvrI9qDeXo+n4+SkhINupRSi4YGXmpapYWllwMvzXipDEhkvGywpXJhgdfo6CiBQGDG/eKBl1JKLRYaeKlplRaW6lSjyqhExssGmys3z/s4FRUVAPT19U27TygUYnR0VAMvpdSiooGXmpan0KNTjSqjmnuboxkvOwsqcne73bhcLnp7e6fdx+uNfs+Wluq6jEqpxUMDLzWt8uJybSehMsYYw8lLJ6OtIGywuWL+GS+4XOc1HZ8v+j2rGS+l1GKigZeaVllhmU41qozpCnQRDAYBKC4qprqwekHHi9d5Tbduo9frxe12U1CgF28rpRYPDbzUtCpKKqLNJyM61agWrrmvOdFKYlPNpgVfaVhZWQlMX+fl8/l0mlEpteho4KWmVV4UW1plHIJjQcYj4/kdkFrSmnsz00oizu1243Q6UwZe4+PjBINBnWZUSi06GnipaTkdTlw2l9Z5qYxIZLwKYEvVwgMvmL7OKz79qIGXUmqx0cBLTcvhcESXDdIrG1UGnOo7Fc142RdeWB9XWVnJyMjIlH5eekWjUmqx0sBLTUuXDVKZlMh4LbCHV7Lp+nn5fD5sNhsulysjr6OUUpmigZeaVmKhbM14qQUaDY/S2tsa/V6ywYbyDRk5bmFhYco6L+1Yr5RarDTwUtOyWq0UOgu1xkst2Jn+M0RGIwCsrlgdzaRmyOQ6L2OMXtGolFq0NPBSMyp2FetUo1qw5MWxN9XMv2N9KhUVFYRCoUSPsGAwSDgc1oyXUmpR0sBLzajEXaJTjWrBEotjA1trtmb02JPrvOId6zXjpZRajDTwUjMqKUwKvDTjpeYpsUajFbauyGzgVVRUhMPhSKzb6PV6ERGKiooy+jpKKZUJGnipGZUWlmrGSy1YYqpxgYtjTye5zsvn81FcXIzFor/elFKLj/5mUjPyFHqiNV5GM15q/ia0kshQD69klZWViTovvaJRKbWYaeClZlRWVBa9EdHAS81P/3A/vYFeGAeHy0FdaV3GXyNe59XZ2UkoFNL6LqXUoqWBl5pR8nqN2k5CzUdyYf36FeuxSOZ/7cTrvM6ePQvoUkFKqcUra4GXiDwkIt0icixpW7mIPC0iLbH/y7L1+iozEoFXWGu81PwkL469ceXGrL1OvK0EaOCllFq8spnx+h7wa5O2fQF41hizEXg2dl8tYhXF0SkcwjrVqOYnUd8FbFu1LWuvE59udDqd2O32rL2OUkotRNYCL2PM80D/pM13Aw/Hbj8MvCdbr68yo7KkMnpjXDNean4SU40W2LYi+4GX1ncppRazXNd4rTDGdMZudwErpttRRD4uIgdF5GBPT09uRqemqCyOBV6a8VLzlNxKIlOLY6dSXFxMaWkp1dXVWXsNpZRaqLwV1xtjDGBmePw7xph9xph9VVVVORyZSlbqLAUrEAb/iJ+IieR7SGoJCUfCtPS1JFpJZKOHV7Kbb76Z+vr6rL6GUkotREGOX++SiNQYYzpFpAbozvHrqzkqsBTgdDgJjYcwGPwj/mgwplQaznvPMzI2AmNQvqIcj9OT7yEplRdjY2N0dHQkLgBRy4PT6aS2thabzZb2c3IdeD0JfBj4cuz/H+f49dU8FLmKCA1Ff1l4R7waeKm0Nfc1JxZZ37BiQ34Ho1QedXR0UFxcTH19PSKS7+GoDDDG0NfXR0dHB+vWrUv7edlsJ/E/gVeAzSLSISIfIxpwvVNEWoDbYvfVIlfkLkosG6S9vNRcnOo7lWglsWlldqcZlVrMQqEQFRUVGnQtIyIyoY1NurKW8TLG/M40D70jW6+psqPEXZLIWuiVjWouEotjA9tXb8/vYJTKMw26lp/5fE21c72aVYm7BCLoskFXmHA4zKuvvkpbW9u8j5Ho4SWwrSZ7rSSUUmqp0MBLzaq0KFbTpd3rryg9PT309PRw9OhRTpw4Ma9jTGglkYXFsZVS6bvhhhtm3eeFF15g+/btXH311QwPD2d1PPfffz9f+cpX5v38w4cP8/Of/zyDI8oNDbzUrEpdSYGXZryuGJ2dndhsNtauXcvp06c5dOgQkUj67USCo0E6fB0wBlaHlfVl67M4WqXUbF5++eVZ9/n+97/Pvffey+HDh3G5XLPub4yZ8Hth8v2FGh8fn/axpRp45fqqRrUEeYo80Rua8bpiRCIRLl26xIoVK9i5cycul4uTJ08yOjrK3r17KSiY/VdHS39LtFPfGNHLra3pX26t1HImX8perZf5i2nbY1JUVEQgEOBXv/oV999/P5WVlRw7doy9e/fyb//2bzz44IM89thj/J//83/493//d77//e/zd3/3dzz22GOMjIzw3ve+ly996Uu0tbVxxx13cO2119LY2Mg//uM/8vGPfzxx/+c//zmPPfbYlOcBPPDAAzz88MNUV1dTV1fH3r17p4zzIx/5CE6nk0OHDnHgwAE+8IEPcM899xAKhXC5XHz3u99l3bp1/Pmf/znDw8O8+OKL3Hvvvdx555185jOf4dixY4yNjXH//fdz9913Z+1cz5cGXmpWExbK1ozXFaGvr4+xsTFqamoA2LhxIw6Hg7feeotXXnmF/fv343A4ZjxGc2+slYTRVhJKLTaHDh3i+PHjrFq1igMHDvDSSy/xB3/wB7z44ovceeedvO997+Opp56ipaWF119/HWMMd911F88//zxr1qyhpaWFhx9+mOuuu462trYJ96d7XmFhIY888giHDx9mfHycPXv2pAy8INp+4+WXX8ZqteLz+XjhhRcoKCjgmWee4Ytf/CKPP/44f/mXf8nBgwf51re+BcAXv/hFbr31Vh566CEGBwfZv38/t912G4WFhbk8tbPSwEvNqrw4FniNazuJK0VXVxdWq5XkVSPWrFmDw+GgsbGRl156iWuvvXbGX2iJ+i60lYRSi83+/fupra0F4Oqrr6atrY0bb7xxwj5PPfUUTz31FLt37wYgEAjQ0tLCmjVrWLt2Ldddd11i3+T70z3P7/fz3ve+F7fbDcBdd9017fh+67d+C6vVCoDX6+XDH/4wLS0tiAhjY2Mpn/PUU0/x5JNPJurGQqEQ58+fZ+vWrXM+P9mkgZeaVXlhOQiLLuMVDofx+XyUlZXleyjLijGGrq4uqqurE7/44lasWMH111/P66+/ngi+pluUOrE4NrB9lbaSUCpupunAXEnOWFut1pS1VMYY7r33Xv7Tf/pPE7a3tbVN+aMr+f50z/v7v//7tMeXfLz77ruPW265hR/96Ee0tbXx9re/PeVzjDE8/vjjbN68uC/k0eJ6Navk9RoXQ43XyMgIzc3NPPPMM7z44ou0trbme0jLyuDgIKFQKDHNOFlZWRkHDhzAYrHw+uuvEw6HU+6XyHgJXLX6qiyOWCmVDXfccQcPPfQQgUAAgAsXLtDdPftKf9M97+abb+aJJ55geHgYv9/PT37yk7TG4fV6Wb16NQDf+973EtuLi4vx+/0TXveb3/wm0aWgo9Opi5EGXmpWpY5Y4DWe34xXIBDgyJEjPPPMM5w6dYqysjKqqqo4ceIEg4ODeRvXctPZ2YmIUF1dPe0+RUVF7Nmzh1AoxJkzZ6Y8boy53DzVBpsrF/dfoEqpqW6//XY++MEPcv3117Njxw7e9773TQh05vq8PXv28P73v59du3bxrne9i2uuuSatcXz+85/n3nvvZffu3RMyc7fccgtNTU1cffXVPProo9x3332MjY2xc+dOtm/fzn333Tfv955NEo8MF7N9+/aZgwcP5nsYV6zGi43s+/N9EIFd+3dx+BOHM/4aM30f9vX1cebMGbq7u7FYLNTV1bF+/XqKiooYGxvjueeeQ0S4+eab57RQqUrtF7/4BW63e0L9xnQOHjxId3c3t956K06nM7G909/Jqq+ugjYodBfi/5Zfu3arK9qJEycWXa2RyoxUX1sRaTTG7Eu1v9Z4qVmVOkuj3ynDmc94jYyM8NJLLxEMBmfcz+FwsHnzZurr67Hb7YntNpuNvXv38tJLL3HkyBH27Uv5fa7S5PP5CAaDNDQ0pLX/1q1buXTpEs3NzezatSuxvbmvOXpjFNbVr9OgSymlYjTwUrOaMNWYwRovYwxvvvkmoVCITZs2Tfvh7Ha7WbVqFRZL6pnxsrIytm7dSlNTE21tbdTX12dsjFearq4uAFauXJnW/oWFhdTX13P27FnWr19PcXExkFRYb2DDSm0loZRScRp4qVkliusNeIe9GGMyksFoaWmht7eXXbt2sWbNmgUda/369fT29nL8+HHKysqmvdJOzayzs5Py8vJZe3Ql27RpE+3t7Rw/fjwxPZm8OPaWmi3ZGKpSSi1JGnipWdmtdhwOByOMEBmLMDQ2RKF9YQ3p+vr6OHXqFKtXr15w0AXRFeJ3797Nc889R2NjIzfffHNa3dUzrbOzk97eXrZu3Tqn1zfG0NzcPONFAoWFhWzfvn3azN9CBYNBfD4f27fPrfWDzWZj06ZNHD9+nJ6eHqqqqi4vjg1srdG6FqWUitPAS6WlpLCEHnogDK90vEKVu2r2J01jbHSMg68cxGq1UlNdw5GuIxkbp6PWwZGDR+j+RTdbd+b2A7/jXAdnmqNX+B08c5Crdl+F3WGf5VnRfmQnjp6gr7uPouKilIGVMQa/z8+p/lNs2Jydqbv2tnbODpyliir8XbNfuZQs4ozQGerkxy/8mH3X7+N4z/FE89Qdq3dkYbRKKbU0aeCl0lLivhx4vfN/vHP+BzLABWAIWAMcz8z4JugDeoEVgCcLx5/MAD3AAFAEFANdwI+AWmCm2CtM9HwMA9XATL1gLwH/AayKvUamnQciwNl5Pt8PXAReIHre460kqrSVhFJKxWkfL5WW9VXrozf8RAOMVP8CRIOQmfQDQaAKcM6y73yVA26gm2iAl00RoJPo+/cQDYpKiAZcYaLBTGia544lPb6KmYMuiJ4zB9GgLvWKGakNzzCG5LEMEw0c56sYcBENesPRY66tWovb5l7AQZVS2dTW1sZVVy2+Bsdvf/vbyUcbqSeeeIKmpqasvoZmvFRa/vr2v6b/RD99gb7EFNIUo2AZt2CvtGMrsyGWiQX448FxhrqHKFhbgHttdj+MIxURgqeDGL/BaqzYK+0UFBdktK2BCRuGzg0RtoZxbHHgqJ5YkB6uCTN0dgjjN7jL3RQUX/5xCw+HGWobgmJwrXVRUJTej2KkPEKgJYA1ZMW9yj3lHE82OjBKqDsadblKXdg8qfucjfaNEvKEKGwoxOq0ptwnHeNF4wydGcJuseMoc/DZ2z4772MppZam8fHxvNTYZsITTzzBnXfeybZt27L2GkvzzKic27d6H69/+fWU63nF9fT0cObMGbxeL3a7nfr6eurr63E4HJcbnV6du0anY2NjnD9/ntbWVkKhEEVFRaxfv57a2topaxDO1cjICK+99hq+tT527dpFXV1dyv1CoRCvvfYafr+f3bt3s3r1avr6+nj99dcpuKqAa6+9lpKSkjm99sWLF2lsbGTDhg0zNmQ8c+YMTU1NVLytAmMM/f39XHXVVaxbt27Kvq+++ipDQ0PceuutcxpLKo2NjXR1dRGJRNi+SddoVGqy48eP4/VmtidiaWnprBfGfPWrX+Whhx4C4A/+4A/47Gc/C0QDpQ996EO8+eabbN++nf/+3/87brebL3zhCzz55JMUFBRw++2385WvfIWenh4+8YlPcP78eSC6/uKBAwe4//77OXPmDK2traxZs4azZ8/y4IMPJsb09re/na985Sts3bqVz3zmMxw7doyxsTHuv/9+7r77boaHh/noRz/KkSNH2LJlC8PDwynfwxtvvME999xDMBjE4XDw7LPPYrPZ+OQnP8nBgwcpKCjgq1/9Krfccgvf+973OHjwIN/61rcAuPPOO/nc5z7H29/+doqKirjnnnv46U9/isvl4sc//jFnzpzhySef5LnnnuOv/uqvePzxx/nZz37Gt7/9bQoKCti2bRuPPPLIgr9WGniptFkslgnNSydbvXp1IrBobW3l1KlTnD59mtraWkKhECMjIxw4cCBn3eVtNhsNDQ2sW7eOzs5Ozpw5w1tvvcXJkycnBIVzFQwGefXVVxkZGWH//v0zLq3jdDq54YYbeOONN3jzzTfp6enhwoULic7wLpdrzq+/atUqent7OX36NBUVFVNe3xhDU1MTra2trFq1it27dyd6ph07doxQKDQhYBsbG6O3tzftpqmz2bp1a6If2OSFdJVS+dHY2Mh3v/tdXnvtNYwxXHvttbztbW+jrKyM5uZmHnzwQQ4cOMDv//7v84//+I989KMf5Uc/+hEnT55ERBJXXN9zzz388R//MTfeeCPnz5/njjvu4MSJEwA0NTXx4osv4nK5+NrXvsZjjz3Gl770JTo7O+ns7GTfvn188Ytf5NZbb+Whhx5icHCQ/fv3c9ttt/HP//zPuN1uTpw4wVtvvcWePXumvIfR0VHe//738+ijj3LNNdfg8/lwuVx8/etfR0Q4evQoJ0+e5Pbbb+fUqVMzno9gMMh1113HAw88wOc//3n+5V/+hf/yX/4Ld911F3feeSfve9/7APjyl7/M2bNncTgcGVuaTgMvlXEVFRVUVFQQDAY5c+YMHR0dhMNhtm/fjsfjyfl4LBbLhKDwzJkzE4LChoYGiopmL24KBAK0trbS0dGB1WrlhhtuSOv92Gw2rrvuOg4dOkR7ezvl5eXs379/QQHo9u3bGRgY4NChQ7ztbW9LLNcTiUQ4dOgQFy9eZP369Wzbti0xvbpv3z6OHj3K6dOnCYVC7Nq1C4vFwqVLlzDGTLso9ly53W7WrVvHmTNn0jqvSl1p5tqyJRNefPFF3vve9yb+GPrN3/xNXnjhBe666y7q6uo4cOAAAL/7u7/LN77xDT772c/idDr52Mc+xp133smdd94JwDPPPDOhBsrn8yUWw77rrrsSf0z+9m//Nrfffjtf+tKXeOyxxxKBzFNPPcWTTz7JV77yFSA6K3D+/Hmef/55/uiP/giAnTt3snPnzinvobm5mZqamsQaj/HZghdffJHPfOYzAGzZsoW1a9fOGnjZ7fbEe9q7dy9PP/10yv127tzJhz70Id7znvfwnve8Z8ZjpksDL5U1hYWF7Ny5ky1btuD1eqmqmn8LikyJB4XxIKq9vZ3z589TXV1NQ0MDlZWVU54TD9YuXbqExWKhtraWjRs34nanX6dmsVjYs2cPa9asoby8fMFTnVarlb179/L888/T2NjIDTfcwPj4OG+88QZ9fX1s27ZtSgZLRNi5cydOp5Pm5mZGRkbYt28fnZ2dOJ3OjDad3bJlC9XV1ZrxUmoJmFz7KiIUFBTw+uuv8+yzz/LDH/6Qb33rW/ziF78gEonw6quvTlibNS7553316tVUVFTw1ltv8eijj/Ltb38biGbkH3/8cTZvzv7VzgUFBUQikcT9UOjyVUY2my3xvq1W67RlND/72c94/vnn+clPfsIDDzzA0aNHF1y/plc1qqyz2+2LIuhKVlRUxM6dO3nnO9/J5s2b8Xq9vPLKKzz33HOJDN2FCxd4/vnnefnllxkYGGDTpk3cdttt7Nq1a05BV5yIUFVVteCga/J76O/v59ixY7z88sv09/eze/fuGacNN23axK5du+jt7eWVV16hu7ubmpqajF54YLFYUgaxSqn8uOmmm3jiiScYGhoiGAzyox/9iJtuugmA8+fP88orrwDwgx/8gBtvvJFAIIDX6+Xd7343X/va1zhyJNpv8fbbb+eb3/xm4riHDx+e9jXf//7387d/+7d4vd5EBuuOO+7gm9/8JsZEL4E/dOgQADfffDM/+MEPADh27BhvvfXWlONt3ryZzs5O3njjDQD8fj/j4+PcdNNNfP/73wfg1KlTnD9/PrG27+HDh4lEIrS3t/P666/Pep6Ki4vx+6N9DOPPu+WWW/ibv/kbvF5vIru3EJrxUlc0u93Opk2b2LBhAx0dHbS2tnLo0CEOHz6MMSaRtctEQX421NbW0tfXR1tbGwUF0WL9dILcNWvW4HA4aGxsJBKJpL02o1JqadqzZw8f+chH2L9/PxAtrt+9ezdtbW1s3ryZf/iHf+D3f//32bZtG5/85Cfxer3cfffdhEIhjDF89atfBeAb3/gGn/70p9m5cyfj4+PcfPPNiWzWZO973/u45557uO+++xLb7rvvPj772c+yc+dOIpEI69at46c//Smf/OQn+ehHP8rWrVvZunUre/funXI8u93Oo48+ymc+8xmGh4dxuVw888wzfOpTn+KTn/wkO3bsoKCggO9973s4HA4OHDjAunXr2LZtG1u3bk1ZNzbZBz7wAf7wD/+Qb3zjGzzyyCN87GMfw+uNLpX3R3/0Rxkpl5F41JlLIvJrwNeJrgD4r8aYL8+0/759+0w++nmoK1N3dzeXLl2iurqa6urqjGaCsiEcDtPc3Mzq1avnPF04ODjIpUuXZlykXCm1cCdOnJjxKmS1dKX62opIozFmX6r9c57xEhEr8A/AO4EO4A0RedIYk92OZUqlKR5wLRVWq3XePWc8Hk9eLnhQSqkrVT5qvPYDp40xrcaYUeAR4O48jEMppZRSKqfyEXitBtqT7nfEtk0gIh8XkYMicrCnpydng1NKKaWyIR+lPSq75vM1XbRXNRpjvmOM2WeM2bfYrohTSiml5sLpdNLX16fB1zJijKGvry9la42Z5OOqxgtA8voqtbFtSiml1LJUW1tLR0cHOoOzvDidTmpra+f0nHwEXm8AG0VkHdGA6wPAB/MwDqWUUionbDZbynVS1ZUn54GXMWZcRP4f4P8QbSfxkDHmeK7HoZRSSimVa3lpoGqM+Tnw83y8tlJKKaVUviza4nqllFJKqeUmL53r50pEeoBzWX6ZSqA3y6+xHOh5mp2eo/ToeZqdnqP06HmanZ6j9GTqPK01xqRsybAkAq9cEJGD07X3V5fpeZqdnqP06HmanZ6j9Oh5mp2eo/Tk4jzpVKNSSimlVI5o4KWUUkoplSMaeF32nXwPYInQ8zQ7PUfp0fM0Oz1H6dHzNDs9R+nJ+nnSGi+llFJKqRzRjJdSSimlVI5o4KWUUkoplSMaeAEi8msi0iwip0XkC/kez2IhIg+JSLeIHEvaVi4iT4tIS+z/snyOMd9EpE5EfikiTSJyXETuiW3X8xQjIk4ReV1EjsTO0Zdi29eJyGuxn7tHRcSe77Hmm4hYReSQiPw0dl/P0SQi0iYiR0XksIgcjG3Tn7dJRMQjIj8UkZMickJErtfzdJmIbI59D8X/+UTks7k4R1d84CUiVuAfgHcB24DfEZFt+R3VovE94NcmbfsC8KwxZiPwbOz+lWwc+BNjzDbgOuDTse8fPU+XjQC3GmN2AVcDvyYi1wF/A3zNGLMBGAA+lr8hLhr3ACeS7us5Su0WY8zVSf2W9Odtqq8D/2GM2QLsIvp9pecpxhjTHPseuhrYCwwBPyIH5+iKD7yA/cBpY0yrMWYUeAS4O89jWhSMMc8D/ZM23w08HLv9MPCeXI5psTHGdBpj3ozd9hP95bYaPU8JJioQu2uL/TPArcAPY9uv6HMEICK1wK8D/xq7L+g5Spf+vCURkVLgZuBBAGPMqDFmED1P03kHcMYYc44cnCMNvKIfku1J9zti21RqK4wxnbHbXcCKfA5mMRGRemA38Bp6niaITaEdBrqBp4EzwKAxZjy2i/7cwd8DnwcisfsV6DlKxQBPiUijiHw8tk1/3iZaB/QA341NXf+riBSi52k6HwD+Z+x21s+RBl5q3ky0F4n2IwFEpAh4HPisMcaX/JieJzDGhGMp/VqiWeYt+R3R4iIidwLdxpjGfI9lCbjRGLOHaHnIp0Xk5uQH9ecNgAJgD/BPxpjdQJBJU2Z6nqJidZN3Af9r8mPZOkcaeMEFoC7pfm1sm0rtkojUAMT+787zePJORGxEg67vG2P+d2yznqcUYtMdvwSuBzwiUhB76Er/uTsA3CUibUTLHW4lWqOj52gSY8yF2P/dRGty9qM/b5N1AB3GmNdi939INBDT8zTVu4A3jTGXYvezfo408II3gI2xq4fsRFOOT+Z5TIvZk8CHY7c/DPw4j2PJu1gdzoPACWPMV5Me0vMUIyJVIuKJ3XYB7yRaC/dL4H2x3a7oc2SMudcYU2uMqSf6O+gXxpgPoedoAhEpFJHi+G3gduAY+vM2gTGmC2gXkc2xTe8AmtDzlMrvcHmaEXJwjrRzPSAi7yZaX2EFHjLGPJDfES0OIvI/gbcDlcAl4C+AJ4DHgDXAOeC3jTGTC/CvGCJyI/ACcJTLtTlfJFrnpecJEJGdRItUrUT/2HvMGPOXIrKeaHanHDgE/K4xZiR/I10cROTtwOeMMXfqOZoodj5+FLtbAPzAGPOAiFSgP28TiMjVRC/UsAOtwEeJ/fyh5wlIBO/ngfXGGG9sW9a/lzTwUkoppZTKEZ1qVEoppZTKEQ28lFJKKaVyRAMvpZRSSqkc0cBLKaWUUipHNPBSSimllMoRDbyUUsuKiHhE5FOx26tE5IezPUcppXJF20kopZaV2JqZPzXGXJXvsSil1GQFs++ilFJLypeBhtii3C3AVmPMVSLyEeA9QCGwEfgK0eaSvweMAO82xvSLSAPwD0AVMAT8oTHmZK7fhFJqedKpRqXUcvMF4ExsUe4/nfTYVcBvAtcADwBDsUWEXwH+79g+3wE+Y4zZC3wO+MdcDFopdWXQjJdS6kryS2OMH/CLiBf4SWz7UWCniBQBNwD/K7oMJwCO3A9TKbVcaeCllLqSJK9zGEm6HyH6+9ACDMayZUoplXE61aiUWm78QPF8nmiM8QFnReS3ACRqVyYHp5S6smngpZRaVowxfcBLInIM+Lt5HOJDwMdE5AhwHLg7k+NTSl3ZtJ2EUkoppVSOaMZLKaWUUipHNPBSSimllMoRDbyUUkoppXJEAy+llFJKqRzRwEsppZRSKkc08FJKKaWUyhENvJRSSimlcuT/B8Pd9jY3GpgaAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 720x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"most_probable_states = np.argmax(posterior_probs, axis=1)\n",
"most_probable_rates = rates[most_probable_states]\n",
"\n",
"fig = plt.figure(figsize=(10, 4))\n",
"ax = fig.add_subplot(1, 1, 1)\n",
"ax.plot(most_probable_rates, c='green', lw=3, label='inferred rate')\n",
"ax.plot(observed_counts, c='black', alpha=0.3, label='observed counts')\n",
"ax.set_ylabel(\"latent rate\")\n",
"ax.set_xlabel(\"time\")\n",
"ax.set_title(\"Inferred latent rate over time\")\n",
"ax.legend(loc=4)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "center-plane",
"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": "3.8.8"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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