.gitattributes

+.git/objects/pack/pack-e4d8eb24c8980fa83f56e5f1721afdf30e1511f0.pack filter=lfs diff=lfs merge=lfs -text
+notebooks/Normal filter=lfs diff=lfs merge=lfs -text
+and filter=lfs diff=lfs merge=lfs -text
+t-Distribution/students.csv filter=lfs diff=lfs merge=lfs -text
+.git/objects/pack/pack-503b0d3875a89d392191586b9f3094e805e9d648.pack filter=lfs diff=lfs merge=lfs -text
+.git/objects/pack/pack-7d220d49f09763a29a52292682de638409708007.pack filter=lfs diff=lfs merge=lfs -text
+.git/objects/pack/pack-78227f007957049b16a096f6f700f2945d6a0428.pack filter=lfs diff=lfs merge=lfs -text
+notebooks/problems_demo.pdf filter=lfs diff=lfs merge=lfs -text

Untitled.ipynb

+%% Cell type:code id:727a1945-aba9-4e43-8419-738f886f8f51 tags:
+
+``` python
+```

notebooks/Beta Distribution/hdi.ipynb

@@ -73,7 +73,11 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
+<<<<<<< HEAD
+   "version": "3.9.7"
+=======
    "version": "3.9.12"
+>>>>>>> 74c736b4bd250d513a4c3e1aa0d9d4e67c1d31f3
   }
  },
  "nbformat": 4,

notebooks/Beta Distribution/hdi_BACKUP_1043.ipynb

+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Bestimmung 95%-HDI für die Betaverteilung\n",
+    "\n",
+    "Die folgende Prozedur definiert, das HDI für die Beta-Verteilung:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from scipy.stats import beta\n",
+    "import numpy as np\n",
+    "\n",
+    "def hdi(a,b, prob = 0.95):\n",
+    "    k = 0\n",
+    "    x = np.linspace(0,1,1000)\n",
+    "    y = beta.pdf(x,a,b)\n",
+    "    while True:\n",
+    "       k = k+0.0001\n",
+    "       if np.sum(y[y > k])/np.size(x) < prob:\n",
+    "        break\n",
+    "    return x[np.argwhere(y > k)][0] ,x[np.argwhere(y > k)][np.argwhere(y > k).size-1]      "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In hdi(...) müssen nur noch die Parameter $a$ und $b$ eingegeben werden. Wenn die Prozentzahl noch geändert soll, fügen Sie ein zusätzliches prob=... ein. prob=0.5 würde dann bedeuten, dass 50% der glaubwürdigsten Parameter im HDI enthalten sind. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(array([0.21221221]), array([0.78778779]))"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "hdi(5,5)  "
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+<<<<<<< HEAD
+   "version": "3.9.7"
+=======
+   "version": "3.9.12"
+>>>>>>> 74c736b4bd250d513a4c3e1aa0d9d4e67c1d31f3
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}

notebooks/Beta Distribution/hdi_BACKUP_727.ipynb

+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Bestimmung 95%-HDI für die Betaverteilung\n",
+    "\n",
+    "Die folgende Prozedur definiert, das HDI für die Beta-Verteilung:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from scipy.stats import beta\n",
+    "import numpy as np\n",
+    "\n",
+    "def hdi(a,b, prob = 0.95):\n",
+    "    k = 0\n",
+    "    x = np.linspace(0,1,1000)\n",
+    "    y = beta.pdf(x,a,b)\n",
+    "    while True:\n",
+    "       k = k+0.0001\n",
+    "       if np.sum(y[y > k])/np.size(x) < prob:\n",
+    "        break\n",
+    "    return x[np.argwhere(y > k)][0] ,x[np.argwhere(y > k)][np.argwhere(y > k).size-1]      "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In hdi(...) müssen nur noch die Parameter $a$ und $b$ eingegeben werden. Wenn die Prozentzahl noch geändert soll, fügen Sie ein zusätzliches prob=... ein. prob=0.5 würde dann bedeuten, dass 50% der glaubwürdigsten Parameter im HDI enthalten sind. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(array([0.21221221]), array([0.78778779]))"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "hdi(5,5)  "
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+<<<<<<< HEAD
+   "version": "3.9.7"
+=======
+   "version": "3.9.12"
+>>>>>>> 74c736b4bd250d513a4c3e1aa0d9d4e67c1d31f3
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}

notebooks/Beta Distribution/hdi_BASE_1043.ipynb

+%% Cell type:markdown id: tags:
+
+# Bestimmung 95%-HDI für die Betaverteilung
+
+Die folgende Prozedur definiert, das HDI für die Beta-Verteilung:
+
+%% Cell type:code id: tags:
+
+``` python
+from scipy.stats import beta
+import numpy as np
+
+def hdi(a,b, prob = 0.95):
+    k = 0
+    x = np.linspace(0,1,1000)
+    y = beta.pdf(x,a,b)
+    while True:
+       k = k+0.0001
+       if np.sum(y[y > k])/np.size(x) < prob:
+        break
+    return x[np.argwhere(y > k)][0] ,x[np.argwhere(y > k)][np.argwhere(y > k).size-1]
+```
+
+%% Cell type:markdown id: tags:
+
+In hdi(...) müssen nur noch die Parameter $a$ und $b$ eingegeben werden. Wenn die Prozentzahl noch geändert soll, fügen Sie ein zusätzliches prob=... ein. prob=0.5 würde dann bedeuten, dass 50% der glaubwürdigsten Parameter im HDI enthalten sind.
+
+%% Cell type:code id: tags:
+
+``` python
+hdi(5,5)
+```
+
+%% Output
+
+    (array([0.21201212]), array([0.78798788]))

notebooks/Beta Distribution/hdi_BASE_727.ipynb

+%% Cell type:markdown id: tags:
+
+# Bestimmung 95%-HDI für die Betaverteilung
+
+Die folgende Prozedur definiert, das HDI für die Beta-Verteilung:
+
+%% Cell type:code id: tags:
+
+``` python
+from scipy.stats import beta
+import numpy as np
+
+def hdi(a,b, prob = 0.95):
+    k = 0
+    x = np.linspace(0,1,1000)
+    y = beta.pdf(x,a,b)
+    while True:
+       k = k+0.0001
+       if np.sum(y[y > k])/np.size(x) < prob:
+        break
+    return x[np.argwhere(y > k)][0] ,x[np.argwhere(y > k)][np.argwhere(y > k).size-1]
+```
+
+%% Cell type:markdown id: tags:
+
+In hdi(...) müssen nur noch die Parameter $a$ und $b$ eingegeben werden. Wenn die Prozentzahl noch geändert soll, fügen Sie ein zusätzliches prob=... ein. prob=0.5 würde dann bedeuten, dass 50% der glaubwürdigsten Parameter im HDI enthalten sind.
+
+%% Cell type:code id: tags:
+
+``` python
+hdi(5,5)
+```
+
+%% Output
+
+    (array([0.21201212]), array([0.78798788]))

notebooks/Beta Distribution/hdi_LOCAL_1043.ipynb

+%% Cell type:markdown id: tags:
+
+# Bestimmung 95%-HDI für die Betaverteilung
+
+Die folgende Prozedur definiert, das HDI für die Beta-Verteilung:
+
+%% Cell type:code id: tags:
+
+``` python
+from scipy.stats import beta
+import numpy as np
+
+def hdi(a,b, prob = 0.95):
+    k = 0
+    x = np.linspace(0,1,1000)
+    y = beta.pdf(x,a,b)
+    while True:
+       k = k+0.0001
+       if np.sum(y[y > k])/np.size(x) < prob:
+        break
+    return x[np.argwhere(y > k)][0] ,x[np.argwhere(y > k)][np.argwhere(y > k).size-1]
+```
+
+%% Cell type:markdown id: tags:
+
+In hdi(...) müssen nur noch die Parameter $a$ und $b$ eingegeben werden. Wenn die Prozentzahl noch geändert soll, fügen Sie ein zusätzliches prob=... ein. prob=0.5 würde dann bedeuten, dass 50% der glaubwürdigsten Parameter im HDI enthalten sind.
+
+%% Cell type:code id: tags:
+
+``` python
+hdi(5,5)
+```
+
+%% Output
+
+    (array([0.21201212]), array([0.78798788]))

notebooks/Beta Distribution/hdi_LOCAL_727.ipynb

+%% Cell type:markdown id: tags:
+
+# Bestimmung 95%-HDI für die Betaverteilung
+
+Die folgende Prozedur definiert, das HDI für die Beta-Verteilung:
+
+%% Cell type:code id: tags:
+
+``` python
+from scipy.stats import beta
+import numpy as np
+
+def hdi(a,b, prob = 0.95):
+    k = 0
+    x = np.linspace(0,1,1000)
+    y = beta.pdf(x,a,b)
+    while True:
+       k = k+0.0001
+       if np.sum(y[y > k])/np.size(x) < prob:
+        break
+    return x[np.argwhere(y > k)][0] ,x[np.argwhere(y > k)][np.argwhere(y > k).size-1]
+```
+
+%% Cell type:markdown id: tags:
+
+In hdi(...) müssen nur noch die Parameter $a$ und $b$ eingegeben werden. Wenn die Prozentzahl noch geändert soll, fügen Sie ein zusätzliches prob=... ein. prob=0.5 würde dann bedeuten, dass 50% der glaubwürdigsten Parameter im HDI enthalten sind.
+
+%% Cell type:code id: tags:
+
+``` python
+hdi(5,5)
+```
+
+%% Output
+
+    (array([0.21201212]), array([0.78798788]))

notebooks/Beta Distribution/hdi_REMOTE_1043.ipynb

+%% Cell type:markdown id: tags:
+
+# Bestimmung 95%-HDI für die Betaverteilung
+
+Die folgende Prozedur definiert, das HDI für die Beta-Verteilung:
+
+%% Cell type:code id: tags:
+
+``` python
+from scipy.stats import beta
+import numpy as np
+
+def hdi(a,b, prob = 0.95):
+    k = 0
+    x = np.linspace(0,1,1000)
+    y = beta.pdf(x,a,b)
+    while True:
+       k = k+0.0001
+       if np.sum(y[y > k])/np.size(x) < prob:
+        break
+    return x[np.argwhere(y > k)][0] ,x[np.argwhere(y > k)][np.argwhere(y > k).size-1]
+```
+
+%% Cell type:markdown id: tags:
+
+In hdi(...) müssen nur noch die Parameter $a$ und $b$ eingegeben werden. Wenn die Prozentzahl noch geändert soll, fügen Sie ein zusätzliches prob=... ein. prob=0.5 würde dann bedeuten, dass 50% der glaubwürdigsten Parameter im HDI enthalten sind.
+
+%% Cell type:code id: tags:
+
+``` python
+hdi(5,5)
+```
+
+%% Output
+
+    (array([0.21221221]), array([0.78778779]))

notebooks/Beta Distribution/hdi_REMOTE_727.ipynb

+%% Cell type:markdown id: tags:
+
+# Bestimmung 95%-HDI für die Betaverteilung
+
+Die folgende Prozedur definiert, das HDI für die Beta-Verteilung:
+
+%% Cell type:code id: tags:
+
+``` python
+from scipy.stats import beta
+import numpy as np
+
+def hdi(a,b, prob = 0.95):
+    k = 0
+    x = np.linspace(0,1,1000)
+    y = beta.pdf(x,a,b)
+    while True:
+       k = k+0.0001
+       if np.sum(y[y > k])/np.size(x) < prob:
+        break
+    return x[np.argwhere(y > k)][0] ,x[np.argwhere(y > k)][np.argwhere(y > k).size-1]
+```
+
+%% Cell type:markdown id: tags:
+
+In hdi(...) müssen nur noch die Parameter $a$ und $b$ eingegeben werden. Wenn die Prozentzahl noch geändert soll, fügen Sie ein zusätzliches prob=... ein. prob=0.5 würde dann bedeuten, dass 50% der glaubwürdigsten Parameter im HDI enthalten sind.
+
+%% Cell type:code id: tags:
+
+``` python
+hdi(5,5)
+```
+
+%% Output
+
+    (array([0.21221221]), array([0.78778779]))

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notebooks/MCMC/metro_beta_walk_hist.ipynb

@@ -59,7 +59,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.6"
+   "version": "3.9.7"
   }
  },
  "nbformat": 4,

notebooks/MCMC/potato.csv

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notebooks/MCMC/pymc3_beta.ipynb

 %% Cell type:code id: tags:
 
 ``` python
 %matplotlib inline
 import pymc3 as pm
 import matplotlib.pyplot as plt
 import scipy.stats as st
 import arviz as az
 
 import numpy as np
 import warnings
 warnings.filterwarnings("ignore")
 ```
 
 %% Output
 
     WARNING (theano.tensor.blas): Using NumPy C-API based implementation for BLAS functions.
 
 %% Cell type:code id: tags:
 
 ``` python
 # Wird später gebraucht
 def hdi(a,b, prob = 0.95):
     k = 0
     x = np.linspace(0,1,100000)
     y = st.beta.pdf(x,a,b)
     while True:
        k = k+0.0001
        if np.sum(y[y > k])/np.size(x) < prob:
         break
     hdi_l, hdi_r = x[np.argwhere(y > k)][0][0] ,x[np.argwhere(y > k)][np.argwhere(y > k).size-1][0]
     return hdi_l, hdi_r
 
 def plot_beta(a,b):
     x = np.linspace(0,1,1000)
     y = st.beta.pdf(x,a,b)
     hdi_l, hdi_r = hdi(a,b)
     omega = (a-1)/(a+b-2)
     plt.plot(x,y)
 
     plt.plot([hdi_l, hdi_r],[.1,.1])
     plt.text((hdi_l+hdi_r)/2, .5, "95  HDI", ha="center")
     plt.text(hdi_l, .2, str(np.round(hdi_l,3)), ha="right")
     plt.text(hdi_r,.2, str(np.round(hdi_r,3)), ha="left")
 
     plt.text(0.2, st.beta.pdf(omega,a,b)-.5, "om="+str(np.round(omega,3)), ha="right")
 ```
 
 %% Cell type:code id: tags:
 
 ``` python
 trials = 20
 head = 4
 
 # unknown value in a real experiment
 
 data = np.zeros(trials)
 data[np.arange(head)]  = 1
 ```
 
 %% Cell type:code id: tags:
 
 ``` python
 alph = 1
 bet = 1
 
 with pm.Model() as our_first_model:
    theta = pm.Beta('theta', alpha=alph, beta=bet)
    y = pm.Bernoulli('y', p=theta, observed=data)
    trace = pm.sample(100)
 
 ```
 
 %% Output
 
     Only 100 samples in chain.
     Auto-assigning NUTS sampler...
     Initializing NUTS using jitter+adapt_diag...
     Multiprocess sampling (4 chains in 4 jobs)
     NUTS: [theta]
 
 
-    Sampling 4 chains for 1_000 tune and 100 draw iterations (4_000 + 400 draws total) took 2 seconds.
+
+    Sampling 4 chains for 1_000 tune and 100 draw iterations (4_000 + 400 draws total) took 4 seconds.
+    The acceptance probability does not match the target. It is 0.8820701017088629, but should be close to 0.8. Try to increase the number of tuning steps.
 
 %% Cell type:code id: tags:
 
 ``` python
 az.plot_trace(trace)
 ```
 
 %% Output
 
     Got error No model on context stack. trying to find log_likelihood in translation.
     Got error No model on context stack. trying to find log_likelihood in translation.
 
     array([[<AxesSubplot:title={'center':'theta'}>,
             <AxesSubplot:title={'center':'theta'}>]], dtype=object)
 
 
 %% Cell type:code id: tags:
 
 ``` python
 az.summary(trace, hdi_prob=.95)
 ```
 
 %% Output
 
     Got error No model on context stack. trying to find log_likelihood in translation.
 
             mean     sd  hdi_2.5%  hdi_97.5%  mcse_mean  mcse_sd  ess_bulk  \
     theta  0.224  0.086     0.068      0.384      0.007    0.005     155.0
     
            ess_tail  r_hat
     theta     171.0   1.02
 
 %% Cell type:code id: tags:
 
 ``` python
 az.plot_posterior(trace, hdi_prob=.95, point_estimate="mode")
 ```
 
 %% Output
 
     Got error No model on context stack. trying to find log_likelihood in translation.
 
     <AxesSubplot:title={'center':'theta'}>
 
 
 %% Cell type:code id: tags:
 
 ``` python
 plot_beta(a=alph+head, b=bet+trials-head)
 ```
 
 %% Output