Quickstart
==========

First ensure you have
`installed <http://elfi.readthedocs.io/en/stable/installation.html>`__
Python 3.9 (or greater) and ELFI. After installation you can start using
ELFI:

.. code:: ipython3

    import elfi

ELFI includes an easy to use generative modeling syntax, where the
generative model is specified as a directed acyclic graph (DAG). Let’s
create two prior nodes:

.. code:: ipython3

    mu = elfi.Prior('uniform', -2, 4)
    sigma = elfi.Prior('uniform', 1, 4)

The above would create two prior nodes, a uniform distribution from -2
to 2 for the mean ``mu`` and another uniform distribution from 1 to 5
for the standard deviation ``sigma``. All distributions from
``scipy.stats`` are available.

For likelihood-free models we typically need to define a simulator and
summary statistics for the data. As an example, lets define the
simulator as 30 draws from a Gaussian distribution with a given mean and
standard deviation. Let’s use mean and variance as our summaries:

.. code:: ipython3

    import scipy.stats as ss
    import numpy as np
    
    def simulator(mu, sigma, batch_size=1, random_state=None):
        mu, sigma = np.atleast_1d(mu, sigma)
        return ss.norm.rvs(mu[:, None], sigma[:, None], size=(batch_size, 30), random_state=random_state)
    
    def mean(y):
        return np.mean(y, axis=1)
    
    def var(y):
        return np.var(y, axis=1)

Let’s now assume we have some observed data ``y0`` (here we just create
some with the simulator):

.. code:: ipython3

    # Set the generating parameters that we will try to infer
    mean0 = 1
    std0 = 3
    
    # Generate some data (using a fixed seed here)
    np.random.seed(20170525) 
    y0 = simulator(mean0, std0)
    print(y0)


.. parsed-literal::

    [[ 3.7990926   1.49411834  0.90999905  2.46088006 -0.10696721  0.80490023
       0.7413415  -5.07258261  0.89397268  3.55462229  0.45888389 -3.31930036
      -0.55378741  3.00865492  1.59394854 -3.37065996  5.03883749 -2.73279084
       6.10128027  5.09388631  1.90079255 -1.7161259   3.86821266  0.4963219
       1.64594033 -2.51620566 -0.83601666  2.68225112  2.75598375 -6.02538356]]


Now we have all the components needed. Let’s complete our model by
adding the simulator, the observed data, summaries and a distance to our
model:

.. code:: ipython3

    # Add the simulator node and observed data to the model
    sim = elfi.Simulator(simulator, mu, sigma, observed=y0)
    
    # Add summary statistics to the model
    S1 = elfi.Summary(mean, sim)
    S2 = elfi.Summary(var, sim)
    
    # Specify distance as euclidean between summary vectors (S1, S2) from simulated and
    # observed data
    d = elfi.Distance('euclidean', S1, S2)

If you have ``graphviz`` installed to your system, you can also
visualize the model:

.. code:: ipython3

    # Plot the complete model (requires graphviz)
    elfi.draw(d)




.. image:: https://raw.githubusercontent.com/elfi-dev/notebooks/dev/figures/quickstart_files/quickstart_11_0.svg



.. Note:: The automatic naming of nodes may not work in all environments e.g. in interactive Python shells. You can alternatively provide a name argument for the nodes, e.g. ``S1 = elfi.Summary(mean, sim, name='S1')``.

We can try to infer the true generating parameters ``mean0`` and
``std0`` above with any of ELFI’s inference methods. Let’s use ABC
Rejection sampling and sample 1000 samples from the approximate
posterior using threshold value 0.5:

.. code:: ipython3

    rej = elfi.Rejection(d, batch_size=10000, seed=30052017)
    res = rej.sample(1000, threshold=.5)
    print(res)


.. parsed-literal::

    Method: Rejection
    Number of samples: 1000
    Number of simulations: 120000
    Threshold: 0.492
    Sample means: mu: 0.748, sigma: 3.1
    


Let’s plot also the marginal distributions for the parameters:

.. code:: ipython3

    import matplotlib.pyplot as plt
    res.plot_marginals()
    plt.show()



.. image:: https://raw.githubusercontent.com/elfi-dev/notebooks/dev/figures/quickstart_files/quickstart_16_0.png