diff --git a/CHANGELOG.md b/CHANGELOG.md
index 80171eb746..e8956ad4d6 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -7,6 +7,7 @@
 * Added confidence interval band to auto-correlation plot ([1535](https://github.com/arviz-devs/arviz/pull/1535)) 
 
 ### Maintenance and fixes
+* Updated `from_cmdstan` and `from_numpyro` converter to follow schema convention ([1541](https://github.com/arviz-devs/arviz/pull/1541) and [1525](https://github.com/arviz-devs/arviz/pull/1525))
 
 ### Deprecation
 * Removed Geweke diagnostic ([1545](https://github.com/arviz-devs/arviz/pull/1545)) 
diff --git a/arviz/data/io_cmdstan.py b/arviz/data/io_cmdstan.py
index 9b9a350d14..368e3ccf71 100644
--- a/arviz/data/io_cmdstan.py
+++ b/arviz/data/io_cmdstan.py
@@ -203,22 +203,24 @@ def posterior_to_xarray(self):
     def sample_stats_to_xarray(self):
         """Extract sample_stats from fit."""
         dtypes = {"divergent__": bool, "n_leapfrog__": np.int64, "treedepth__": np.int64}
+        rename_dict = {
+            "divergent": "diverging",
+            "n_leapfrog": "n_steps",
+            "treedepth": "tree_depth",
+            "stepsize": "step_size",
+            "accept_stat": "acceptance_rate",
+        }
 
         sampler_params, sampler_params_warmup = self.sample_stats
 
         for j, s_params in enumerate(sampler_params):
-            rename_dict = {}
             for key in s_params:
-                key_, *end = key.split(".")
-                name = re.sub("__$", "", key_)
-                name = "diverging" if name == "divergent" else name
-                rename_dict[key] = ".".join((name, *end))
-                sampler_params[j][key] = s_params[key].astype(dtypes.get(key_))
-                sampler_params_warmup[j][key] = sampler_params_warmup[j][key].astype(
-                    dtypes.get(key_)
+                name = re.sub("__$", "", key)
+                name = rename_dict.get(name, name)
+                sampler_params[j][name] = s_params[key].astype(dtypes.get(key))
+                sampler_params_warmup[j][name] = sampler_params_warmup[j][key].astype(
+                    dtypes.get(key)
                 )
-            sampler_params[j] = sampler_params[j].rename(columns=rename_dict)
-            sampler_params_warmup[j] = sampler_params_warmup[j].rename(columns=rename_dict)
         data = _unpack_dataframes(sampler_params)
         data_warmup = _unpack_dataframes(sampler_params_warmup)
         return (