diff --git a/blackjax/adaptation/mclmc_adaptation.py b/blackjax/adaptation/mclmc_adaptation.py
index b1b012c70..76a016242 100644
--- a/blackjax/adaptation/mclmc_adaptation.py
+++ b/blackjax/adaptation/mclmc_adaptation.py
@@ -200,8 +200,8 @@ def step(iteration_state, weight_and_key):
         x = ravel_pytree(state.position)[0]
         # update the running average of x, x^2
         streaming_avg = streaming_average_update(
-            expectation=jnp.array([x, jnp.square(x)]),
-            streaming_avg=streaming_avg,
+            current_value=jnp.array([x, jnp.square(x)]),
+            previous_weight_and_average=streaming_avg,
             weight=(1 - mask) * success * params.step_size,
             zero_prevention=mask,
         )
diff --git a/blackjax/util.py b/blackjax/util.py
index b9b7a250c..cdb9f4c91 100644
--- a/blackjax/util.py
+++ b/blackjax/util.py
@@ -240,31 +240,30 @@ def one_step(average_and_state, xs, return_state):
 
 
 def streaming_average_update(
-    expectation, streaming_avg, weight=1.0, zero_prevention=0.0
+    current_value, previous_weight_and_average, weight=1.0, zero_prevention=0.0
 ):
     """Compute the streaming average of a function O(x) using a weight.
     Parameters:
     ----------
-        expectation
-            the value of the expectation at the current timestep
-        streaming_avg
-            tuple of (total, average) where total is the sum of weights and average is
-            the current average
+        current_value
+            the current value of the function that we want to take average of
+        previous_weight_and_average
+            tuple of (previous_weight, previous_average) where previous_weight is the
+            sum of weights and average is the current estimated average
         weight
             weight of the current state
         zero_prevention
             small value to prevent division by zero
     Returns:
     ----------
-        new streaming average
+        new total weight and streaming average
     """
-
-    flat_expectation, unravel_fn = ravel_pytree(expectation)
-    total, average = streaming_avg
-    flat_average, _ = ravel_pytree(average)
-    average = (total * flat_average + weight * flat_expectation) / (
-        total + weight + zero_prevention
+    previous_weight, previous_average = previous_weight_and_average
+    current_weight = previous_weight + weight
+    current_average = jax.tree.map(
+        lambda x, avg: (previous_weight * avg + weight * x)
+        / (current_weight + zero_prevention),
+        current_value,
+        previous_average,
     )
-    total += weight
-    streaming_avg = (total, unravel_fn(average))
-    return streaming_avg
+    return current_weight, current_average