updated readme

README.md

@@ -28,8 +28,48 @@ pip install git+https://github.com/arnauqb/blackbirds
 
 Refer to the [docs](https://arnau.ai/blackbirds) for examples and specific API usage. Here is a basic example:
 
+```python
+import torch
+
+from blackbirds.models.random_walk import RandomWalk
+from blackbirds.infer.vi import VI
+from blackbirds.posterior_estimators import TrainableGaussian
+from blackbirds.simulate import simulate_and_observe_model
+
+# random walk model
+rw = RandomWalk(n_timesteps=100)
+
+# generate synthetic data to fit to
+true_p = torch.logit(torch.tensor(0.25))
+true_data = rw.observe(rw.run(torch.tensor([true_p])))
+
+# define loss to minimize
+class L2Loss:
+    def __init__(self, model):
+        self.model = model
+        self.loss_fn = torch.nn.MSELoss()
+    def __call__(self, params, data):
+        observed_outputs = simulate_and_observe_model(self.model, params)
+        return self.loss_fn(observed_outputs[0], data[0])
+
+# initialize generalized variational inference
+posterior_estimator = TrainableGaussian([0.], 1.0)
+prior = torch.distributions.Normal(true_p + 0.2, 1)
+optimizer = torch.optim.Adam(posterior_estimator.parameters(), 1e-2)
+loss = L2Loss(rw)
+
+vi = VI(loss,
+        posterior_estimator=posterior_estimator,
+        prior=prior,
+        optimizer=optimizer,
+        w = 0) # no regularization
+
+# train the estimator
+vi.run(true_data, 1000, max_epochs_without_improvement=100)
+
+```
 
 
 # 3. Citation
 
-TODO.
+TODO. add after JOSS review.