Explained JointProbDist

reachtarunhere · reachtarunhere · commit e6100d48a89b · 2016-06-30T22:36:41.000+05:30
diff --git a/probability.ipynb b/probability.ipynb
@@ -156,6 +156,113 @@
    "source": [
     "p.show_approx()"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Joint Probability Distribution\n",
+    "\n",
+    "The helper function **event_values** returns a tuple of the values of variables in event. An event is specified by a dict where the keys are the names of variables and the corresponding values are the value of the variable. Variables are specified with a list. The ordering of the returned tuple is same as those of the variables.\n",
+    "\n",
+    "\n",
+    "Alternatively if the event is specified by a list or tuple of equal length of the variables. Then the events tuple is returned as it is."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "event = {'A': 10, 'B': 9, 'C': 8}\n",
+    "variables = ['C', 'A']\n",
+    "event_values (event, variables)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "collapsed": true
+   },
+   "source": [
+    "_A probability model is completely determined by the joint distribution for all of the random variables._ (**Section 13.3**) The probability module implements these as the class **JointProbDist** which inherits from the **ProbDist** class. This class specifies a discrete probability distribute over a set of variables. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "%psource JointProbDist"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Values for a Joint Distribution is a an ordered tuple in which each item corresponds to the value associate with a particular variable. For Joint Distribution of X, Y where X, Y take integer values this can be something like (18, 19).\n",
+    "\n",
+    "To specify a Joint distribution we first need an ordered list of variables."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "variables = ['X', 'Y']\n",
+    "j = JointProbDist(variables)\n",
+    "j"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Like the **ProbDist** class **JointProbDist** also employes magic methods to assign probability to different values.\n",
+    "The probability can be assigned in either of the two formats for all possible values of the distribution. The **event_values** call inside  **_ _getitem_ _**  and **_ _setitem_ _** does the required processing to make this work."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "j[1,1] = 0.2\n",
+    "j[dict(X=0, Y=1)] = 0.5\n",
+    "\n",
+    "(j[1,1], j[0,1])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "It is also possible to list all the values for a particular variable using the **values** method."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "j.values('X')"
+   ]
   }
  ],
  "metadata": {
