diff --git a/examples/hmm.py b/examples/hmm.py
index 4972f1642..1953080fe 100644
--- a/examples/hmm.py
+++ b/examples/hmm.py
@@ -8,11 +8,9 @@
 from jax.scipy.special import logsumexp
 
 import numpyro.distributions as dist
-from numpyro.diagnostics import summary
 from numpyro.handlers import sample
 from numpyro.hmc_util import initialize_model
-from numpyro.mcmc import hmc
-from numpyro.util import fori_collect
+from numpyro.mcmc import mcmc
 
 
 """
@@ -117,21 +115,6 @@ def semi_supervised_hmm(transition_prior, emission_prior,
     return sample('forward_log_prob', dist.Multinomial(logits=-log_prob), obs=0)
 
 
-def run_inference(transition_prior, emission_prior, supervised_categories, supervised_words,
-                  unsupervised_words, rng, args):
-    init_params, potential_fn, constrain_fn = initialize_model(
-        rng,
-        semi_supervised_hmm,
-        transition_prior, emission_prior, supervised_categories,
-        supervised_words, unsupervised_words,
-    )
-    init_kernel, sample_kernel = hmc(potential_fn, algo='NUTS')
-    hmc_state = init_kernel(init_params, args.num_warmup)
-    hmc_states = fori_collect(args.num_samples, sample_kernel, hmc_state,
-                              transform=lambda state: constrain_fn(state.z))
-    return hmc_states
-
-
 def print_results(posterior, transition_prob, emission_prob):
     header = semi_supervised_hmm.__name__ + ' - TRAIN'
     columns = ['', 'ActualProb', 'Pred(p25)', 'Pred(p50)', 'Pred(p75)']
@@ -165,11 +148,15 @@ def main(args):
         num_unsupervised_data=args.num_unsupervised,
     )
     print('Starting inference...')
-    zs = run_inference(transition_prior, emission_prior,
-                       supervised_categories, supervised_words, unsupervised_words,
-                       random.PRNGKey(2), args)
-    summary(zs)
-    print_results(zs, transition_prob, emission_prob)
+    init_params, potential_fn, constrain_fn = initialize_model(
+        random.PRNGKey(2),
+        semi_supervised_hmm,
+        transition_prior, emission_prior, supervised_categories,
+        supervised_words, unsupervised_words,
+    )
+    samples = mcmc(args.num_warmup, args.num_samples, init_params,
+                   potential_fn=potential_fn, constrain_fn=constrain_fn)
+    print_results(samples, transition_prob, emission_prob)
 
 
 if __name__ == '__main__':
diff --git a/examples/ucbadmit.py b/examples/ucbadmit.py
index bf31964e1..bb4d8885a 100644
--- a/examples/ucbadmit.py
+++ b/examples/ucbadmit.py
@@ -3,7 +3,7 @@
 import numpy as onp
 
 import jax.numpy as np
-import jax.random as random
+from jax import random, vmap
 from jax.config import config as jax_config
 
 import numpyro.distributions as dist
@@ -52,20 +52,18 @@
 """
 
 
-# TODO: Remove broadcasting logic when support for `pyro.plate` is available.
 def glmm(dept, male, applications, admit):
     v_mu = sample('v_mu', dist.Normal(0, np.array([4., 1.])))
 
     sigma = sample('sigma', dist.HalfNormal(np.ones(2)))
     L_Rho = sample('L_Rho', dist.LKJCholesky(2))
-    scale_tril = np.expand_dims(sigma, axis=-1) * L_Rho
+    scale_tril = sigma[..., np.newaxis] * L_Rho
     # non-centered parameterization
     num_dept = len(onp.unique(dept))
     z = sample('z', dist.Normal(np.zeros((num_dept, 2)), 1))
-    v = np.squeeze(np.matmul(np.expand_dims(scale_tril, axis=-3), np.expand_dims(z, axis=-1)),
-                   axis=-1)
+    v = np.dot(scale_tril, z.T).T
 
-    logits = v_mu[..., :1] + v[..., dept, 0] + (v_mu[..., 1:] + v[..., dept, 1]) * male
+    logits = v_mu[0] + v[dept, 0] + (v_mu[1] + v[dept, 1]) * male
     sample('admit', dist.Binomial(applications, logits=logits), obs=admit)
 
 
@@ -79,13 +77,10 @@ def run_inference(dept, male, applications, admit, rng, args):
     return hmc_states
 
 
-def predict(dept, male, applications, admit, z, rng):
-    header = glmm.__name__ + ' - TRAIN'
+def predict(dept, male, applications, z, rng):
     model = substitute(seed(glmm, rng), z)
     model_trace = trace(model).get_trace(dept, male, applications, admit=None)
-    predictions = model_trace['admit']['fn'].probs
-    probs = admit / applications
-    print_results('=' * 30 + header + '=' * 30, predictions, dept, male, probs)
+    return model_trace['admit']['fn'].probs
 
 
 def print_results(header, preds, dept, male, probs):
@@ -105,7 +100,10 @@ def main(args):
     dept, male, applications, admit = fetch_train()
     rng, rng_predict = random.split(random.PRNGKey(1))
     zs = run_inference(dept, male, applications, admit, rng, args)
-    predict(dept, male, applications, admit, zs, rng_predict)
+    rngs = random.split(rng_predict, args.num_samples)
+    pred_probs = vmap(lambda z, rng: predict(dept, male, applications, z, rng))(zs, rngs)
+    header = '=' * 30 + 'glmm - TRAIN' + '=' * 30
+    print_results(header, pred_probs, dept, male, admit / applications)
 
 
 if __name__ == '__main__':