Merge pull request #9 from barentsen/fix-typos

Fix intro tutorial typos

docs/_static/notebooks/intro-to-pymc3.ipynb

@@ -355,7 +355,7 @@
     "$$\n",
     "\n",
     "for the eccentric anomaly $E$ given some mean anomaly $M$ and eccentricity $e$.\n",
-    "There are commonly accepted methods of solving this equartion using [Newton's method](https://en.wikipedia.org/wiki/Newton%27s_method), but if we want to expose that to PyMC3, we have to define a [custom Theano operation](http://deeplearning.net/software/theano/extending/extending_theano.html) with a custom gradient.\n",
+    "There are commonly accepted methods of solving this equation using [Newton's method](https://en.wikipedia.org/wiki/Newton%27s_method), but if we want to expose that to PyMC3, we have to define a [custom Theano operation](http://deeplearning.net/software/theano/extending/extending_theano.html) with a custom gradient.\n",
     "I won't go into the details of the math (because [I blogged about it](https://dfm.io/posts/stan-c++/)) and I won't go into the details of the implementation (because [you can take a look at it on GitHub](https://github.com/dfm/exoplanet/tree/master/exoplanet/theano_ops/kepler)).\n",
     "So, for this tutorial, we'll use the custom Kepler solver that is implemented as part of *exoplanet* and fit the publicly available radial velocity observations of the famous exoplanetary system 51 Peg using PyMC3.\n",
     "\n",
@@ -422,11 +422,11 @@
     "Take a minute to take a look through this and see if you can follow it.\n",
     "There's a lot going on, so I want to point out a few things to pay attention to:\n",
     "\n",
-    "1. All of the mathemtical operations (for example `exp` and `sqrt`) are being performed using Theano instead of NumPy.\n",
+    "1. All of the mathematical operations (for example `exp` and `sqrt`) are being performed using Theano instead of NumPy.\n",
     "2. All of the parameters have initial guesses provided. This is an example where this makes a big difference because some of the parameters (like period) are very tightly constrained.\n",
     "3. Some of the lines are wrapped in `Deterministic` distributions. This can be useful because it allows us to track values as the chain progresses even if they're not parameters. For example, after sampling, we will have a sample for `bkg` (the background RV trend) for each step in the chain. This can be especially useful for making plots of the results.\n",
     "4. Similarly, at the end of the model definition, we compute the RV curve for a single orbit on a fine grid. This can be very useful for diagnosing fits gone wrong.\n",
-    "5. For parameters that specify angles (like $\\omega$, called `w` in the model below), it can be inefficient to sample in the angle directly because of the fact that the value wraps around at $2\\pi$. Instead, it can be better to sample the unit vector specified by the angle. In practice, this can be acheived by sampling a 2-vector from an isotropic Gaussian and normalizing the components by the norm. This is implemented as part of *exoplanet* in the :class:`exoplanet.distributions.Angle` class."
+    "5. For parameters that specify angles (like $\\omega$, called `w` in the model below), it can be inefficient to sample in the angle directly because of the fact that the value wraps around at $2\\pi$. Instead, it can be better to sample the unit vector specified by the angle. In practice, this can be achieved by sampling a 2-vector from an isotropic Gaussian and normalizing the components by the norm. This is implemented as part of *exoplanet* in the :class:`exoplanet.distributions.Angle` class."
    ]
   },
   {