diff --git a/pyro/nn/module.py b/pyro/nn/module.py
index 05190e24d7..298fd859e5 100644
--- a/pyro/nn/module.py
+++ b/pyro/nn/module.py
@@ -138,7 +138,7 @@ def __get__(
         if name not in obj.__dict__["_pyro_params"]:
             init_value, constraint, event_dim = self
             # bind method's self arg
-            init_value = functools.partial(init_value, obj)  # type: ignore[arg-type,misc,operator]
+            init_value = functools.partial(init_value, obj)  # type: ignore[arg-type,call-arg,misc,operator]
             setattr(obj, name, PyroParam(init_value, constraint, event_dim))
         value: PyroParam = obj.__getattr__(name)
         return value
diff --git a/pyro/poutine/indep_messenger.py b/pyro/poutine/indep_messenger.py
index 69d41756f6..19ad050b32 100644
--- a/pyro/poutine/indep_messenger.py
+++ b/pyro/poutine/indep_messenger.py
@@ -1,8 +1,7 @@
 # Copyright (c) 2017-2019 Uber Technologies, Inc.
 # SPDX-License-Identifier: Apache-2.0
 
-import numbers
-from typing import Iterator, NamedTuple, Optional, Tuple
+from typing import Iterator, NamedTuple, Optional, Tuple, Union
 
 import torch
 from typing_extensions import Self
@@ -108,7 +107,7 @@ def __exit__(self, *args) -> None:
             _DIM_ALLOCATOR.free(self.name, self.dim)
         return super().__exit__(*args)
 
-    def __iter__(self) -> Iterator[int]:
+    def __iter__(self) -> Iterator[Union[int, float]]:
         if self._vectorized is True or self.dim is not None:
             raise ValueError(
                 "cannot use plate {} as both vectorized and non-vectorized"
@@ -121,7 +120,14 @@ def __iter__(self) -> Iterator[int]:
             for i in self.indices:
                 self.next_context()
                 with self:
-                    yield i if isinstance(i, numbers.Number) else i.item()
+                    if isinstance(i, (int, float)):
+                        yield i
+                    elif isinstance(i, torch.Tensor):
+                        yield i.item()
+                    else:
+                        raise ValueError(
+                            f"Expected int, float or torch.Tensor, but got {type(i)}"
+                        )
 
     def _reset(self) -> None:
         if self._vectorized: