diff --git a/BayesianKDEy/bayesian_kdey.py b/BayesianKDEy/bayesian_kdey.py
index 11aba80..573b86b 100644
--- a/BayesianKDEy/bayesian_kdey.py
+++ b/BayesianKDEy/bayesian_kdey.py
@@ -11,7 +11,7 @@ from tqdm import tqdm
 from scipy.stats import dirichlet
 
 
-def bayesian(kdes, data, probabilistic_classifier, init=None, MAX_ITER=100_000, warmup=3_000):
+def bayesian(kdey, data, probabilistic_classifier, init=None, MAX_ITER=100_000, warmup=3_000):
     """
     Bayes:
         P(prev|data) = P(data|prev) P(prev) / P(data)
@@ -26,6 +26,7 @@ def bayesian(kdes, data, probabilistic_classifier, init=None, MAX_ITER=100_000,
         return np.exp(kde.score_samples(X))
 
     X = probabilistic_classifier.predict_proba(data)
+    kdes = kdey.mix_densities
     test_densities = np.asarray([pdf(kde_i, X) for kde_i in kdes])
 
     def log_likelihood(prev, epsilon=1e-10):
@@ -44,9 +45,9 @@ def bayesian(kdes, data, probabilistic_classifier, init=None, MAX_ITER=100_000,
     def log_prior(prev):
         return 0
 
-    def sample_neighbour(prev):
-        dir_noise = np.random.normal(scale=0.05, size=len(prev))
-        # neighbour = F.normalize_prevalence(prev + dir_noise, method='clip')
+    def sample_neighbour(prev, step_size=0.05):
+        # random-walk Metropolis-Hastings
+        dir_noise = np.random.normal(scale=step_size, size=len(prev))
         neighbour = F.normalize_prevalence(prev + dir_noise, method='mapsimplex')
         return neighbour
 
@@ -54,22 +55,33 @@ def bayesian(kdes, data, probabilistic_classifier, init=None, MAX_ITER=100_000,
     current_prev = F.uniform_prevalence(n_classes) if init is None else init
     current_likelihood = log_likelihood(current_prev) + log_prior(current_prev)
 
-    # Metropolis-Hastings
+    # Metropolis-Hastings with adaptive rate
+    step_size = 0.05
+    target_acceptance = 0.3
+    adapt_rate = 0.01
+    acceptance_history = []
+
     samples = []
-    for _ in tqdm(range(MAX_ITER), total=MAX_ITER):
-        proposed_prev = sample_neighbour(current_prev)
+    for i in tqdm(range(MAX_ITER), total=MAX_ITER):
+        proposed_prev = sample_neighbour(current_prev, step_size)
 
         # probability of acceptance
         proposed_likelihood = log_likelihood(proposed_prev) + log_prior(proposed_prev)
         acceptance = proposed_likelihood - current_likelihood
 
         # decide acceptance
-        if np.log(np.random.rand()) < acceptance:
-            # accept
+        accepted = np.log(np.random.rand()) < acceptance
+        if accepted:
             current_prev = proposed_prev
             current_likelihood = proposed_likelihood
 
         samples.append(current_prev)
+        acceptance_history.append(1. if accepted else 0.)
+
+        if i < warmup and i%10==0 and len(acceptance_history)>=100:
+            recent_accept_rate = np.mean(acceptance_history[-100:])
+            # print(f'{i=} recent_accept_rate={recent_accept_rate:.4f} (current step_size={step_size:.4f})')
+            step_size *= np.exp(adapt_rate * (recent_accept_rate - target_acceptance))
 
     # remove "warmup" initial iterations
     samples = np.asarray(samples[warmup:])
@@ -81,31 +93,34 @@ if __name__ == '__main__':
     cls = LogisticRegression()
     kdey = KDEyML(cls)
 
-    train, test = qp.datasets.fetch_UCIMulticlassDataset('dry-bean', standardize=True).train_test
+    train, test = qp.datasets.fetch_UCIMulticlassDataset('academic-success', standardize=True).train_test
 
     with qp.util.temp_seed(2):
         print('fitting KDEy')
         kdey.fit(*train.Xy)
 
         # shifted = test.sampling(500, *[0.7, 0.1, 0.2])
-        shifted = test.sampling(500, *test.prevalence()[::-1])
+        # shifted = test.sampling(500, *test.prevalence()[::-1])
+        shifted = test.sampling(500, *F.uniform_prevalence_sampling(train.n_classes))
         prev_hat = kdey.predict(shifted.X)
         mae = qp.error.mae(shifted.prevalence(), prev_hat)
-        print(f'true_prev={strprev(shifted.prevalence())}, prev_hat={strprev(prev_hat)}, {mae=:.4f}')
+        print(f'true_prev={strprev(shifted.prevalence())}')
+        print(f'prev_hat={strprev(prev_hat)}, {mae=:.4f}')
 
-        kdes = kdey.mix_densities
         h = kdey.classifier
-        samples = bayesian(kdes, shifted.X, h, init=None, MAX_ITER=5_000, warmup=1_000)
+        samples = bayesian(kdey, shifted.X, h, init=None, MAX_ITER=5_000, warmup=3_000)
 
-        print(f'mean posterior {strprev(samples.mean(axis=0))}')
         conf_interval = ConfidenceIntervals(samples, confidence_level=0.95)
-        print()
+        mae = qp.error.mae(shifted.prevalence(), conf_interval.point_estimate())
+        print(f'mean posterior {strprev(samples.mean(axis=0))}, {mae=:.4f}')
+        print(f'CI={conf_interval}')
+        print(f'\tcontains true={conf_interval.coverage(true_value=shifted.prevalence())==1}')
+        print(f'\tamplitude={conf_interval.montecarlo_proportion(50_000)*100.:.20f}%')
 
         if train.n_classes == 3:
             plot_prev_points(samples, true_prev=shifted.prevalence(), point_estim=prev_hat, train_prev=train.prevalence())
             # plot_prev_points_matplot(samples)
 
-
         # report = qp.evaluation.evaluation_report(kdey, protocol=UPP(test), verbose=True)
         # print(report.mean(numeric_only=True))
 
diff --git a/BayesianKDEy/plot_simplex.py b/BayesianKDEy/plot_simplex.py
index 4d3044b..515db3f 100644
--- a/BayesianKDEy/plot_simplex.py
+++ b/BayesianKDEy/plot_simplex.py
@@ -27,7 +27,7 @@ def plot_prev_points(prevs, true_prev, point_estim, train_prev):
 
     # Plot
     fig, ax = plt.subplots(figsize=(6, 6))
-    ax.scatter(*cartesian(prevs), s=50, alpha=0.05, edgecolors='none', label='samples')
+    ax.scatter(*cartesian(prevs), s=10, alpha=0.5, edgecolors='none', label='samples')
     ax.scatter(*cartesian(prevs.mean(axis=0)), s=10, alpha=1, label='sample-mean', edgecolors='black')
     ax.scatter(*cartesian(true_prev), s=10, alpha=1, label='true-prev', edgecolors='black')
     ax.scatter(*cartesian(point_estim), s=10, alpha=1, label='KDEy-estim', edgecolors='black')