Merge pull request CamDavidsonPilon#149 from williamscott/master

Minor editing changes on Chapter 2

Author: CamDavidsonPilon

Chapter2_MorePyMC/MorePyMC.ipynb

@@ -470,7 +470,7 @@
       "\n",
       "1.  We started by thinking \"what is the best random variable to describe this count data?\" A Poisson random variable is a good candidate because it can represent count data. So we model the number of sms's received as sampled from a Poisson distribution.\n",
       "\n",
-      "2.  Next, we think, \"Ok, assuming sms's are Poisson-distributed, what do I need for the Poisson distribution?\" Well, the Poisson distribution has a parameters $\\lambda$. \n",
+      "2.  Next, we think, \"Ok, assuming sms's are Poisson-distributed, what do I need for the Poisson distribution?\" Well, the Poisson distribution has a parameter $\\lambda$. \n",
       "\n",
       "3.  Do we know $\\lambda$? No. In fact, we have a suspicion that there are *two* $\\lambda$ values, one for the earlier behaviour and one for the latter behaviour. We don't know when the behaviour switches though, but call the switchpoint $\\tau$.\n",
       "\n",
@@ -670,7 +670,7 @@
       "\n",
       "As this is a hacker book, we'll continue with the web-dev example. For the moment, we will focus on the analysis of site A only. Assume that there is some true $0 \\lt p_A \\lt 1$ probability that users who, upon shown site A, eventually purchase from the site. This is the true effectiveness of site A. Currently, this quantity is unknown to us. \n",
       "\n",
-      "Suppose site A was shown to $N$ people, and $n$ people purchased from the site. One might conclude hastly that $p_A = \\frac{n}{N}$. Unfortunately, the *observed frequency* $\\frac{n}{N}$ does not necessarily equal $p_A$ -- there is a difference between the *observed frequency* and the *true frequency* of an event. The true frequency can be interpreted as the probability of an event occurring. For example, the true frequency of rolling a 1 on a 6-sided die is $\\frac{1}{6}$. Knowing the true frequency of events like:\n",
+      "Suppose site A was shown to $N$ people, and $n$ people purchased from the site. One might conclude hastily that $p_A = \\frac{n}{N}$. Unfortunately, the *observed frequency* $\\frac{n}{N}$ does not necessarily equal $p_A$ -- there is a difference between the *observed frequency* and the *true frequency* of an event. The true frequency can be interpreted as the probability of an event occurring. For example, the true frequency of rolling a 1 on a 6-sided die is $\\frac{1}{6}$. Knowing the true frequency of events like:\n",
       "\n",
       "- fraction of users who make purchases, \n",
       "- frequency of social attributes, \n",
@@ -854,7 +854,7 @@
       "\n",
       "### *A* and *B* Together\n",
       "\n",
-      "A similar anaylsis can be done for site B's response data to determine the analgous $p_B$. But what we are really interested in is the *difference* between $p_A$ and $p_B$. Let's infer $p_A$, $p_B$, *and* $\\text{delta} = p_A - p_B$, all at once. We can do this using PyMC's deterministic variables. (We'll assume for this exercise that $p_B = 0.04$, so $\\text{delta} = 0.01$, $N_B = 750$ (signifcantly less than $N_A$) and we will simulate site B's data like we did for site A's data )"
+      "A similar analysis can be done for site B's response data to determine the analgous $p_B$. But what we are really interested in is the *difference* between $p_A$ and $p_B$. Let's infer $p_A$, $p_B$, *and* $\\text{delta} = p_A - p_B$, all at once. We can do this using PyMC's deterministic variables. (We'll assume for this exercise that $p_B = 0.04$, so $\\text{delta} = 0.01$, $N_B = 750$ (signifcantly less than $N_A$) and we will simulate site B's data like we did for site A's data )"
      ]
     },
     {
@@ -1074,7 +1074,7 @@
       "\n",
       "Try playing with the parameters `true_p_A`, `true_p_B`, `N_A`, and `N_B`, to see what the posterior of $\\text{delta}$ looks like. Notice in all this, the difference in sample sizes between site A and site B was never mentioned: it naturally fits into Bayesian analysis.\n",
       "\n",
-      "I hope the readers feel this style of A/B testing is more natural than hypothesis testing, which the latter has probably confused more than helped practitioners. Later in this book, we will see two extensions of this model: the first to help dynamically adjust for bad sites, and the second will improve the speed of this computation by reducing the analysis to a single equation.   "
+      "I hope the readers feel this style of A/B testing is more natural than hypothesis testing, which has probably confused more than helped practitioners. Later in this book, we will see two extensions of this model: the first to help dynamically adjust for bad sites, and the second will improve the speed of this computation by reducing the analysis to a single equation.   "
      ]
     },
     {