Chapter 3 typo correction

1.  replace "that is does" with "that this does"
2.  add "a" to "using loss function"
3. replace "parameter of interested" with "parameter of interest"

Author: williamscott

Chapter3_MCMC/IntroMCMC.ipynb

@@ -417,7 +417,7 @@
       "\n",
       "    taus = 1.0/mc.Uniform( \"stds\", 0, 100, size= 2)**2 \n",
       "\n",
-      "Notice that we specified `size=2`: we are modeling both $\\tau$s as a single PyMC variable. Note that is does not induce a necessary relationship between the two $\\tau$s, it is simply for succinctness.\n",
+      "Notice that we specified `size=2`: we are modeling both $\\tau$s as a single PyMC variable. Note that this does not induce a necessary relationship between the two $\\tau$s, it is simply for succinctness.\n",
       "\n",
       "We also need to specify priors on the centers of the clusters. The centers are really the $\\mu$ parameters in this Normal distributions. Their priors can be modeled by a Normal distribution. Looking at the data, I have an idea where the two centers might be — I would guess somewhere around 120 and 190 respectively, though I am not very confident in these eyeballed estimates. Hence I will set $\\mu_0 = 120, \\mu_1 = 190$ and $\\sigma_{0,1} = 10$ (recall we enter the $\\tau$ parameter, so enter $1/\\sigma^2 = 0.01$ in the PyMC variable.)"
      ]
@@ -917,7 +917,7 @@
       "\n",
       "    L = 1 if prob > 0.5 else 0\n",
       "\n",
-      "we can optimize our guesses using *loss function*, of which the entire fifth chapter is devoted to.  \n",
+      "we can optimize our guesses using a *loss function*, which the entire fifth chapter is devoted to.  \n",
       "\n",
       "\n",
       "### Using `MAP` to improve convergence\n",
@@ -1177,7 +1177,7 @@
      "cell_type": "markdown",
      "metadata": {},
      "source": [
-      "The largest plot on the right-hand side is the histograms of the samples, plus a few extra features. The thickest vertical line represents the posterior mean, which is a good summary of posterior distribution. The interval between the two  dashed vertical lines in each the posterior distributions represent the *95% credible interval*, not to be confused with a *95% confidence interval*. I won't get into the latter, but the former can be interpreted as \"there is a 95% chance the parameter of interested lies in this interval\". (Changing default parameters in the call to `mcplot` provides alternatives to 95%.) When communicating your results to others, it is incredibly important to state this interval. One of our purposes for studying Bayesian methods is to have a clear understanding of our uncertainty in unknowns. Combined with the posterior mean, the 95% credible interval provides a reliable interval to communicate the likely location of the unknown (provided by the mean) *and* the uncertainty (represented by the width of the interval)."
+      "The largest plot on the right-hand side is the histograms of the samples, plus a few extra features. The thickest vertical line represents the posterior mean, which is a good summary of posterior distribution. The interval between the two  dashed vertical lines in each the posterior distributions represent the *95% credible interval*, not to be confused with a *95% confidence interval*. I won't get into the latter, but the former can be interpreted as \"there is a 95% chance the parameter of interest lies in this interval\". (Changing default parameters in the call to `mcplot` provides alternatives to 95%.) When communicating your results to others, it is incredibly important to state this interval. One of our purposes for studying Bayesian methods is to have a clear understanding of our uncertainty in unknowns. Combined with the posterior mean, the 95% credible interval provides a reliable interval to communicate the likely location of the unknown (provided by the mean) *and* the uncertainty (represented by the width of the interval)."
      ]
     },
     {