def sample_posterior_predictive(model, posterior_samples, baseball_dataset):
"""
Generate samples from posterior predictive distribution.
"""
train, test, player_names = train_test_split(baseball_dataset)
at_bats = train[:, 0]
at_bats_season = test[:, 0]
logging.Formatter("%(message)s")
logging.info("\nPosterior Predictive:")
logging.info("Hit Rate - Initial 45 At Bats")
logging.info("-----------------------------")
# set hits=None to convert it from observation node to sample node
with ignore_experimental_warning():
train_predict = predictive(model, posterior_samples, at_bats, None)
train_summary = summary(train_predict,
sites=["obs"],
player_names=player_names)["obs"]
train_summary = train_summary.assign(ActualHits=baseball_dataset[["Hits"]].values)
logging.info(train_summary)
logging.info("\nHit Rate - Season Predictions")
logging.info("-----------------------------")
with ignore_experimental_warning():
test_predict = predictive(model, posterior_samples, at_bats_season, None)
test_summary = summary(test_predict,
sites=["obs"],
player_names=player_names)["obs"]
test_summary = test_summary.assign(ActualHits=baseball_dataset[["SeasonHits"]].values)
logging.info(test_summary)
def test_predictive(num_samples, parallel):
model, data, true_probs = beta_bernoulli()
init_params, potential_fn, transforms, _ = initialize_model(
model, model_args=(data, ))
nuts_kernel = NUTS(potential_fn=potential_fn, transforms=transforms)
mcmc = MCMC(nuts_kernel, 100, initial_params=init_params, warmup_steps=100)
mcmc.run(data)
samples = mcmc.get_samples()
with ignore_experimental_warning():
with optional(pytest.warns(UserWarning), num_samples
not in (None, 100)):
predictive_samples = predictive(model,
samples,
num_samples=num_samples,
return_sites=["beta", "obs"],
parallel=parallel)
# check shapes
assert predictive_samples["beta"].shape == (100, 5)
assert predictive_samples["obs"].shape == (100, 1000, 5)
# check sample mean
assert_close(predictive_samples["obs"].reshape([-1, 5]).mean(0),
true_probs,
rtol=0.1)
def evaluate_log_posterior_density(model, posterior_samples, baseball_dataset):
"""
Evaluate the log probability density of observing the unseen data (season hits)
given a model and posterior distribution over the parameters.
"""
_, test, player_names = train_test_split(baseball_dataset)
at_bats_season, hits_season = test[:, 0], test[:, 1]
with ignore_experimental_warning():
trace = predictive(model, posterior_samples, at_bats_season, hits_season,
parallel=True, return_trace=True)
# Use LogSumExp trick to evaluate $log(1/num_samples \sum_i p(new_data | \theta^{i})) $,
# where $\theta^{i}$ are parameter samples from the model's posterior.
trace.compute_log_prob()
log_joint = 0.
for name, site in trace.nodes.items():
if site["type"] == "sample" and not site_is_subsample(site):
# We use `sum_rightmost(x, -1)` to take the sum of all rightmost dimensions of `x`
# except the first dimension (which corresponding to the number of posterior samples)
site_log_prob_sum = sum_rightmost(site['log_prob'], -1)
log_joint += site_log_prob_sum
posterior_pred_density = torch.logsumexp(log_joint, dim=0) - math.log(log_joint.shape[0])
logging.info("\nLog posterior predictive density")
logging.info("--------------------------------")
logging.info("{:.4f}\n".format(posterior_pred_density))
def sample_posterior_predictive(model, posterior_samples, *args):
with ignore_experimental_warning():
predict = predictive(model, posterior_samples, *args)
return predict