# Quickstart¶

First ensure you have installed Python 3.5 (or greater) and ELFI. After installation you can start using 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:

```
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:

```
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):

```
# 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)
```

```
[[ 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:

```
# 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:

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

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:

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

```
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:

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