Independence test
========================

The goal of the independence test is to compute the edge strength using a statistical test of independence based using the model structure (DAG) and the data. For the pairs in the DAG (either by structure learning or user-defined), an statistical test is performed. Any two variables are associated if the test’s p-value < significance_level.

Lets compute the DAG for **asia data set** and examine the edge strength.


.. code-block:: python
    
	# Import library
	import bnlearn as bn

	# Load example data set
	df = bn.import_example(data='asia')

	# Structure learning of sampled dataset
	model = bn.structure_learning.fit(df)

	# Plot without independence test
	G = bn.plot(model)

	# Compute edge strength with chi square test
	model = bn.independence_test(model, df, test='chi_square')

	# Show the results of the independence test
	print(model['independence_test'])

	#    source  target  stat_test        p_value   chi_square  dof
	# 0     tub  either       True   0.000000e+00  1509.729663    1
	# 1   smoke    lung       True   8.542258e-81   362.378980    1
	# 2    lung  either       True   0.000000e+00  8340.061758    1
	# 3   bronc    dysp       True   0.000000e+00  4619.926593    1
	# 4   bronc   smoke       True  1.075377e-197   899.817192    1
	# 5  either    xray       True   0.000000e+00  5455.522990    1
	# 6  either    dysp       True   8.726744e-73   325.601286    1

	# The results from the independence test are automatically used in the plot.
	# We will use the same layout as in the previous plot to make the comparison easier.
	bn.plot(model, pos=G['pos'])


.. |K1| image:: ../figs/asia_no_indeptest.png
.. |K2| image:: ../figs/asia_with_indeptest.png

.. table:: Independence test
   :align: center

   +---------+---------+
   | |K1|    | |K2|    |
   +---------+---------+





.. include:: add_bottom.add