ch2 edits + 1 style change to h4

Author: CamDavidsonPilon

Chapter2_MorePyMC/MorePyMC.ipynb

@@ -45,7 +45,7 @@
       "\n",
       "*  *child variable* are variables that are affected by other variables, i.e. are the subject of parent variables. \n",
       "\n",
-      "Variables can be both parents and children. For example, consider the PyMC code below"
+      "Variables can be both parents and children. For example, consider the PyMC code below."
      ]
     },
     {
@@ -63,7 +63,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 9
+     "prompt_number": 4
     },
     {
      "cell_type": "markdown",
@@ -73,7 +73,7 @@
       "\n",
       "Likewise, `data_generator` is a parent to the variable `output` (hence making `data_generator` both a parent and child variable). Although it does not look like one, `output` should be treated as a PyMC variable as it is a function of another PyMC variable. \n",
       "\n",
-      "This nomenclature is introduced to help us describe relationships in PyMC modeling. You can access a variables children and parent variables using the `children` and `parents` methods attached to variables."
+      "This nomenclature is introduced to help us describe relationships in PyMC modeling. You can access a variables children and parent variables using the `children` and `parents` attributes attached to variables."
      ]
     },
     {
@@ -119,7 +119,7 @@
      "cell_type": "markdown",
      "metadata": {},
      "source": [
-      "Of course a child can  have more than one parent, and parent can have many children."
+      "Of course a child can  have more than one parent, and a parent can have many children."
      ]
     },
     {
@@ -1149,9 +1149,7 @@
       "plt.subplot(212)\n",
       "plt.hist( alpha_samples, histtype='stepfilled', bins = 45, alpha = 0.85, \\\n",
       "        label = r\"positerior of $\\alpha$\", color = \"#A60628\",normed = True )\n",
-      "plt.legend()\n",
-      "\n",
-      "\n"
+      "plt.legend()\n"
      ],
      "language": "python",
      "metadata": {},
@@ -1335,25 +1333,47 @@
      "cell_type": "markdown",
      "metadata": {},
      "source": [
-      "### More PyMC tricks: \n",
+      "### More PyMC Tricks\n",
+      "\n",
+      "#### Protip: *Lighter* deterministic variables with `Lambda` class\n",
+      "\n",
+      "Sometimes writing a deterministic function using the `@mc.deterministic` dectorator can seem like a chore, especially for small function. I have already mentioned that simple elementary math operations *can* produce deterministic variables implicitly, but what about operations like indexing or slicing? Built-in `Lambda` functions can achieve the elegance desired plus that simplicity required. For example,  \n",
+      "\n",
+      "    beta = mc.Normal( \"coefficients\", 0, size=(N,1) )\n",
+      "    x = np.random.randn( (N,1) )\n",
+      "    linear_combination = mc.Lambda( lambda x=x, beta = beta, np.dot( x.T, beta ) )\n",
       "\n",
       "\n",
-      "##TO DO\n",
-      "- lambda function\n",
-      "- potential functions\n",
-      "- containers?"
+      "#### Protip: Arrays of PyMC variables\n",
+      "There is no reason why we cannot store multiple heterogeneous PyMC variables in a Numpy array. Just remember to set the `dtype` of the array to `object` upon initialization. For example:\n",
+      "\n",
+      "\n"
      ]
     },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "N = 10\n",
+      "x = np.empty( N , dtype=object )\n",
+      "for i in range(0, N):\n",
+      "        x[i] = mc.Exponential('x_%i' % i, (i+1)**2)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 13
+    },
     {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
-      "### Returning to the Challenger data\n",
+      "### Bonus: Returning to the Challenger data\n",
       "#####Is there really a relationship between failure and temperature?\n",
       "\n",
       "An critism of our above analysis is that *assumed* that the relationship followed a logistic model, this we implictly assumed that the probabilities change over temperature. Let's look at the data again. (Top figure)\n",
       "\n",
-      "Could it be that infact this pattern occured by chance? This might explain the large overlap in temperatures. After all, I can produce similar plots. (Bottom figure)"
+      "Could it be that infact this particular sequence of defects occured by chance?  After all, I can produce similar plots. (Bottom figure) This might explain the large overlap in temperatures."
      ]
     },
     {
@@ -1505,7 +1525,6 @@
      "cell_type": "code",
      "collapsed": false,
      "input": [
-      "\n",
       "beta = 0\n",
       "alpha = mc.Normal( \"alpha\", 0, 0.001, value = 0 )\n",
       "\n",
@@ -1609,12 +1628,7 @@
      "source": [
       "Is this good? Below is a chart that can be used to compare the computed Bayes factors to a degree of confidence in M1. \n",
       "\n",
-      "-  <1:1  Negative (supports M2)\n",
-      "-  1:1 to 3:1 Barely worth mentioning\n",
-      "-  3:1 to 10:1 Substantial\n",
-      "-  10:1 to 30:1 Strong\n",
-      "-  30:1 to 100:1 Very strong\n",
-      "-  \\> 100:1\t Decisive\n",
+      "<table><tbody><tr><th>Bayes factor</th><th>Supporting M1</th></tr><tr><td>&lt;1:1  </td><td>Negative (supports M2)</td></tr><tr><td>  1:1 to 3:1 </td><td>Barely worth mentioning</td></tr><tr><td>  3:1 to 10:1 </td><td>Substantial</td></tr><tr><td>  10:1 to 30:1 </td><td>Strong</td></tr><tr><td>  30:1 to 100:1</td><td> Very strong</td></tr><tr><td>  &gt; 100:1</td><td> Decisive</td></tr></tbody></table>\n",
       "\n",
       "We are not done yet. If you recall, we selected only one model, but recall we actually have a distribution of possible models (sequential pairs of ($\\beta, \\alpha$) from the posterior disitributions). So to be correct we need to average over samples from the posterior:"
      ]
@@ -1623,17 +1637,6 @@
      "cell_type": "code",
      "collapsed": false,
      "input": [
-      "\"\"\"\n",
-      "linear_combination= np.dot( beta_samples[:,None], \n",
-      "                            observed_temperatures[None,:]) \\\n",
-      "                    + alpha_samples[:,None]\n",
-      "    \n",
-      "p_model_1 = 1.0/(1.0 + np.exp( linear_combination ) )\n",
-      "product = p_model_1**( D )*(1-p_model_1)**(1-D)\n",
-      "model_1_product = product.prod(axis=1).mean()\n",
-      "print model_1_product\n",
-      "\"\"\"\n",
-      "\n",
       "p = logistic( temperature[None,:], beta_samples, alpha_samples )\n",
       "_product = p**( D )*(1-p)**(1-D)\n",
       "prob_given_model_1 = _product.prod(axis=1).mean()\n",
@@ -1750,6 +1753,10 @@
         "    h1 {\n",
         "        font-family: \"Charis SIL\", Palatino, serif;\n",
         "    }\n",
+        "    h4{\n",
+        "        margin-top:12px;\n",
+        "        margin-bottom: 3px;\n",
+        "       }\n",
         "    div.text_cell_render{\n",
         "        font-family: Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n",
         "        line-height: 145%;\n",
@@ -1797,7 +1804,7 @@
        "output_type": "pyout",
        "prompt_number": 1,
        "text": [
-        "<IPython.core.display.HTML at 0x8293dd8>"
+        "<IPython.core.display.HTML at 0x57da050>"
        ]
       }
      ],

styles/custom.css

@@ -11,6 +11,10 @@
     h1 {
         font-family: "Charis SIL", Palatino, serif;
     }
+    h4{
+        margin-top:12px;
+        margin-bottom: 3px;
+       }
     div.text_cell_render{
         font-family: Computer Modern, "Helvetica Neue", Arial, Helvetica, Geneva, sans-serif;
         line-height: 145%;