From cd91bac8900b8e9c3714c46178c865f3795d9027 Mon Sep 17 00:00:00 2001
From: "Aaron J. Maxwell, PhDI only answer queries on the fifth Wednesday of
 each month" <ajmax.85@gmail.com>
Date: Thu, 17 May 2018 12:53:58 -0400
Subject: [PATCH] Correction to Nomenclature in Volatility Model

This small correction is in response to issue Stochastic Volatility Example #2566.  It concerns the
two different examples of the Volatility Model used in the PyMC3 notebooks to introduce users to the
wonder that is Bayesian modeling.  In getting_started.ipynb, under:
--Case Study 1: Stochastic volatility
---The Model
the model specification uses `y_i` to represent the daily precentage returns.  However, later on in
the `with pm.Model() as sp500_model:` block the dummy variable `r` is used to represent the daily
returns as well as the tensor variable name.

The second correction also concerns the useage of `s_i` to represent the volatility process in daily
returns.  In both Volatility Process walkthroughs (there is a stand-alone notebook dedicated to it)
the model specs treat `s_i` as the standard deviation of the StudentT distribution used to model the
log-returns.  In the PyMC3 API docs on the StudentT, the distribution is defined with `lambda`
representing the precision.  This is why the `volatility_process` variable is mapped from
`pm.math.exp(-2 * s)` in the `pm.Model()` block.  However, when the returns were defined in the
model block the **kwarg was `lambda=1/volatility_process`.  This has been fixed.

Thanks to @twiecki and the OP for highlighting this error.
---
 docs/source/notebooks/getting_started.ipynb | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/docs/source/notebooks/getting_started.ipynb b/docs/source/notebooks/getting_started.ipynb
index 86a4ba70d7..560941fce2 100644
--- a/docs/source/notebooks/getting_started.ipynb
+++ b/docs/source/notebooks/getting_started.ipynb
@@ -820,11 +820,11 @@
     "  \\sigma &\\sim exp(50) \\\\\n",
     "  \\nu &\\sim exp(.1) \\\\\n",
     "  s_i &\\sim \\mathcal{N}(s_{i-1}, \\sigma^{-2}) \\\\\n",
-    "  log(y_i) &\\sim t(\\nu, 0, exp(-2 s_i))\n",
+    "  log(r_i) &\\sim t(\\nu, 0, exp(-2 s_i))\n",
     "\\end{aligned}\n",
     "$$\n",
     "\n",
-    "Here, $y$ is the daily return series which is modeled with a Student-t distribution with an unknown degrees of freedom parameter, and a scale parameter determined by a latent process $s$. The individual $s_i$ are the individual daily log volatilities in the latent log volatility process. "
+    "Here, $r$ is the daily return series which is modeled with a Student-t distribution with an unknown degrees of freedom parameter, and a scale parameter determined by a latent process $s$. The individual $s_i$ are the individual daily log volatilities in the latent log volatility process. "
    ]
   },
   {
@@ -933,7 +933,7 @@
     "    s = pm.GaussianRandomWalk('s', sigma**-2, shape=len(returns))\n",
     "    volatility_process = pm.Deterministic('volatility_process', pm.math.exp(-2*s))\n",
     "\n",
-    "    r = pm.StudentT('r', nu, lam=1/volatility_process, observed=returns)"
+    "    r = pm.StudentT('r', nu, lam=volatility_process, observed=returns)"
    ]
   },
   {