.. _posterior_predictive_checks:

Posterior Predictive Checks
===========================

Introduction
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[Content for Posterior Predictive Checks will go here]

Key Concepts
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* Concept 1
* Concept 2
* Concept 3

Mathematical Framework
----------------------

.. math::

   \text{Placeholder equation}

Python Implementation
---------------------

.. code-block:: python

   # Python code example will go here
   import numpy as np
   import pandas as pd

Examples
--------

**Example 1:** 

[Example content]

Summary
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[Section summary]