.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "tutorials/02_probability.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_tutorials_02_probability.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_tutorials_02_probability.py:


Probabilities under changing assumptions
============================================
Rain or a sprinkler makes the ground wet:
``W = R ∨ S``. Given wet ground, what is the probability of rain?
We build the events once, then evaluate them under two sets of independent
priors. A third variable, wind, is unconstrained by these events.

.. GENERATED FROM PYTHON SOURCE LINES 11-20

.. code-block:: Python

    from fractions import Fraction
    from tididi import Vtree, literal

    vtree = Vtree.balanced(3)
    rain = literal(vtree, 1)
    sprinkler = literal(vtree, 2)
    wet = rain.copy() | sprinkler
    rain_and_wet = rain & wet.copy()








.. GENERATED FROM PYTHON SOURCE LINES 21-29

Exact fractions
-------------------
``Fraction`` comes from Python's standard library. Each variable has a pair
of weights: false first, true second. For independent probabilities these
sum to one. In particular, the free wind variable contributes one.

In both scenarios below the evidence has positive probability, so
``P(R | W) = P(R ∧ W) / P(W)`` is defined.

.. GENERATED FROM PYTHON SOURCE LINES 29-37

.. code-block:: Python

    for rain_probability in [Fraction(1, 5), Fraction(3, 5)]:
        priors = {1: rain_probability, 2: Fraction(1, 10), 3: Fraction(2, 5)}
        weights = {variable: (1 - p, p) for variable, p in priors.items()}
        wet_probability = wet.weighted_count(weights)
        conditional = rain_and_wet.weighted_count(weights) / wet_probability
        print(f"P(rain) = {rain_probability}, P(wet) = {wet_probability}")
        print("P(rain | wet) =", conditional)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    P(rain) = 1/5, P(wet) = 7/25
    P(rain | wet) = 5/7
    P(rain) = 3/5, P(wet) = 16/25
    P(rain | wet) = 15/16




.. GENERATED FROM PYTHON SOURCE LINES 38-41

Both evaluations borrowed their circuits. No rebuilding or copying was
needed when the priors changed. More generally, weights need not sum to
one: unit weights recover the model count.

.. GENERATED FROM PYTHON SOURCE LINES 41-45

.. code-block:: Python

    unit_weights = {variable: (1, 1) for variable in vtree.variables}
    print("Models of wet:", wet.weighted_count(unit_weights))






.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Models of wet: 6




.. GENERATED FROM PYTHON SOURCE LINES 46-51

Change observations
-------------------
An evaluator caches values so changing an observation refreshes only affected
branches. It consumes ``wet``; ``finish()`` returns the circuit when we are done.
The value with no rain is the joint probability ``P(W ∧ ¬R)``, without normalization.

.. GENERATED FROM PYTHON SOURCE LINES 51-57

.. code-block:: Python

    evaluator = wet.evaluator(weights)
    evaluator.observe([-1])
    print("P(wet and no rain) =", evaluator.value())
    evaluator.clear_observations()
    print("P(wet) =", evaluator.value())
    wet = evaluator.finish()




.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    P(wet and no rain) = 1/25
    P(wet) = 16/25





.. _sphx_glr_download_tutorials_02_probability.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: 02_probability.ipynb <02_probability.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: 02_probability.py <02_probability.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: 02_probability.zip <02_probability.zip>`