[DOC] Trying to fix theory of the second prob tutorial

Author: Leguark

docs/source/_static/Thickness_example.svg

@@ -1,4 +1,13 @@
+"""
+2.2 - Including GemPy
+=====================
+
+Complex probabilistic model
+---------------------------
+
+"""
 from pyro.infer.autoguide import init_to_mean
+
 from pyro.infer.inspect import get_dependencies
 
 import gempy as gp

docs/source/_static/correlation.pdf

@@ -13,48 +13,18 @@ Lucky for us, after we perform the first inference on the thickness, :math:`\til
 
 .. math::
    :nowrap:
-
    \pi(\theta_{thickness}) = \pi(\theta_{top})  - \pi(\theta_{bottom}) 
 
 or,
 
 .. math::
    :nowrap:
-
    \pi(\theta_{bottom})  = \pi(\theta_{top})  - \pi(\theta_{thickness})
 
 now the question is which probabilistic model design is more suitable. In the end this relates directly to the question the model is trying to answer---and possible limitations on the algorithms used---since joint probability follows the commutative and associative properties.
 
-.. figure:: Thickness_example.eps
+.. figure:: ../_static/Thickness_example.svg
    :align: center
    :width: 80%
 
    Prior (in blue) and posterior distributions (in red) of all the parameters of the probabilistic model :math:`\theta` (the full list of values of the simulation can be found in Appendix X). Case A) correspond to the subtraction equation while Case B) has been generated with the summation equation. Both cases yield the exact same posterior for the random variables---within the Monte Carlo error---as expected.
-
-**Correlations**
-
-Furthermore, keep in mind that the inference happens in a multidimensional manifold---although for obvious visualization reasons we display each parameter independently. This means that although in the previous figures the posterior distributions seem independent, a closer examination---e.g. joint plots---uncovers correlation in the parameters.
-
-.. figure:: correlation.eps
-   :align: center
-   :width: 80%
-
-   Correlations between parameters can be uncovered with joint plots.
-
-.. list-table::
-   :widths: 10 30
-   :header-rows: 0
-
-   * - 
-     - Here we are showing how to combine geometric data but with the same pattern we could encapsulate geological knowledge in form of geometrical rules
-
-License
--------
-The code in this case study is copyrighted by Miguel de la Varga and licensed under the new BSD (3-clause) license:
-
-https://opensource.org/licenses/BSD-3-Clause
-
-The text and figures in this case study are copyrighted by Miguel de la Varga and licensed under the CC BY-NC 4.0 license:
-
-https://creativecommons.org/licenses/by-nc/4.0/
-Make sure to replace the links with actual hyperlinks if you're using a platform that supports it (e.g., Markdown or HTML). Otherwise, the plain URLs work fine for plain text.

docs/source/_static/correlation.png

@@ -0,0 +1,28 @@
+Correlations
+````````````
+
+Furthermore, keep in mind that the inference happens in a multidimensional manifold---although for obvious visualization reasons we display each parameter independently. This means that although in the previous figures the posterior distributions seem independent, a closer examination---e.g. joint plots---uncovers correlation in the parameters.
+
+.. figure::../_static/correlation.png
+   :align: center
+   :width: 80%
+
+   Correlations between parameters can be uncovered with joint plots.
+
+.. list-table::
+   :widths: 10 30
+   :header-rows: 0
+
+   * - 
+     - Here we are showing how to combine geometric data but with the same pattern we could encapsulate geological knowledge in form of geometrical rules
+
+License
+-------
+The code in this case study is copyrighted by Miguel de la Varga and licensed under the new BSD (3-clause) license:
+
+https://opensource.org/licenses/BSD-3-Clause
+
+The text and figures in this case study are copyrighted by Miguel de la Varga and licensed under the CC BY-NC 4.0 license:
+
+https://creativecommons.org/licenses/by-nc/4.0/
+Make sure to replace the links with actual hyperlinks if you're using a platform that supports it (e.g., Markdown or HTML). Otherwise, the plain URLs work fine for plain text.