made student notebooks up to 2a

Author: ericmjl

notebooks/01a-Instructor-Probability_a_simulated_introduction.ipynb renamed to notebooks/01a-instructor-probability-simulation.ipynb

@@ -110,6 +110,8 @@
     "# Solution: Calculate P(A,B)\n",
     "x_0 = np.random.binomial(2, 0.5, 10000)\n",
     "p_ab = sum(x_0==2)/len(x_0)\n",
+    "\n",
+    "# Now, plot the histogram of the results\n",
     "plt.hist(x_0);\n",
     "print(p_ab)"
    ]

notebooks/01a-student-probability-simulation.ipynb

@@ -129,16 +129,25 @@
     "def plot_posterior(p=0.6, N=0):\n",
     "    \"\"\"Plot the posterior given a uniform prior; Bernoulli trials\n",
     "    with probability p; sample size N\"\"\"\n",
+    "    # Set seed\n",
     "    np.random.seed(42)\n",
+    "\n",
     "    # Flip coins \n",
     "    n_successes = np.random.binomial(N, p)\n",
+    "    \n",
     "    # X-axis for PDF\n",
     "    x = np.linspace(0, 1, 100)\n",
-    "    # Prior\n",
+    "    \n",
+    "    # Write out equation for uniform prior\n",
     "    prior = 1\n",
-    "    # Compute posterior, given the likelihood (analytic form)\n",
-    "    posterior = x**n_successes*(1-x)**(N-n_successes)*prior\n",
-    "    posterior /= np.max(posterior)  # so that peak always at 1\n",
+    "    \n",
+    "    # Write out equation for posterior, which is likelihood * prior.\n",
+    "    posterior = (x**n_successes) * ((1-x)**(N-n_successes)) * prior\n",
+    "    \n",
+    "    # Pseudo-normalize the posterior so that we can compare them on the same scale.\n",
+    "    posterior /= np.max(posterior)  \n",
+    "    \n",
+    "    # Plot posterior\n",
     "    plt.plot(x, posterior)\n",
     "    plt.show()"
    ]
@@ -245,29 +254,37 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [],
    "source": [
-    "# Solution\n",
+    "# Write the plotting function, as above\n",
     "def plot_posteriors(p=0.6, N=0):\n",
     "    np.random.seed(42)\n",
     "    n_successes = np.random.binomial(N, p)\n",
     "    x = np.linspace(0.01, 0.99, 100)\n",
-    "    posterior1 = x**n_successes*(1-x)**(N-n_successes)  # w/ uniform prior\n",
-    "    posterior1 /= np.max(posterior1)  # so that peak always at 1\n",
-    "    plt.plot(x, posterior1, label='Uniform prior')\n",
-    "    jp = np.sqrt(x*(1-x))**(-1)  # Jeffreys prior\n",
-    "    posterior2 = posterior1*jp  # w/ Jeffreys prior\n",
-    "    posterior2 /= np.max(posterior2)  # so that peak always at 1 (not quite correct to do; see below)\n",
-    "    plt.plot(x, posterior2, label='Jeffreys prior')\n",
+    "\n",
+    "    # Write out the likelihood for the data\n",
+    "    likelihood = x**n_successes*(1-x)**(N-n_successes) \n",
+    "    \n",
+    "    # Write out equation for posterior given uniform prior\n",
+    "    prior_uniform = 1 \n",
+    "    posterior_uniform = likelihood * prior_uniform\n",
+    "    posterior_uniform /= np.max(posterior_uniform)\n",
+    "    plt.plot(x, posterior_uniform, label='Uniform prior')\n",
+    "    \n",
+    "    # Write out equation for posterior given Jeffreys prior\n",
+    "    prior_jeffreys = np.sqrt(x*(1-x))**(-1)\n",
+    "    posterior_jeffreys = likelihood * prior_jeffreys\n",
+    "    posterior_jeffreys /= np.max(posterior_jeffreys)\n",
+    "    plt.plot(x, posterior_jeffreys, label='Jeffreys prior')\n",
     "    plt.legend()\n",
     "    plt.show()"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [
     {
@@ -286,6 +303,13 @@
    "source": [
     "interact(plot_posteriors, p=(0, 1, 0.01), N=(0, 100));"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {

notebooks/01b-Instructor-Probability_a_simulated_introduction.ipynb renamed to notebooks/01b-instructor-joint-conditional-probability.ipynb

@@ -1321,7 +1321,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.3"
+   "version": "3.7.2"
   }
  },
  "nbformat": 4,