diff --git a/numpyro/optim.py b/numpyro/optim.py
index eab3f594a..8d1717b16 100644
--- a/numpyro/optim.py
+++ b/numpyro/optim.py
@@ -9,7 +9,7 @@
 
 from collections import namedtuple
 from collections.abc import Callable
-from typing import Any, TypeVar
+from typing import Any
 
 import jax
 from jax import jacfwd, lax, value_and_grad
@@ -18,6 +18,7 @@
 import jax.numpy as jnp
 from jax.scipy.optimize import minimize
 from jax.tree_util import register_pytree_node
+from jax.typing import ArrayLike
 
 __all__ = [
     "Adam",
@@ -31,12 +32,12 @@
     "SM3",
 ]
 
-_Params = TypeVar("_Params")
-_OptState = TypeVar("_OptState")
-_IterOptState = tuple[int, _OptState]
+_Params = Any
+_OptState = Any
+_IterOptState = tuple[ArrayLike, _OptState]
 
 
-def _value_and_grad(f, x, forward_mode_differentiation=False):
+def _value_and_grad(f, x, forward_mode_differentiation=False) -> tuple:
     if forward_mode_differentiation:
 
         def _wrapper(x):
@@ -51,6 +52,9 @@ def _wrapper(x):
 
 class _NumPyroOptim(object):
     def __init__(self, optim_fn: Callable, *args, **kwargs) -> None:
+        self.init_fn: Callable[[_Params], _IterOptState]
+        self.update_fn: Callable[[ArrayLike, _Params, _OptState], _OptState]
+        self.get_params_fn: Callable[[_OptState], _Params]
         self.init_fn, self.update_fn, self.get_params_fn = optim_fn(*args, **kwargs)
 
     def init(self, params: _Params) -> _IterOptState:
@@ -80,7 +84,7 @@ def eval_and_update(
         fn: Callable[[Any], tuple],
         state: _IterOptState,
         forward_mode_differentiation: bool = False,
-    ):
+    ) -> tuple[tuple[Any, Any], _IterOptState]:
         """
         Performs an optimization step for the objective function `fn`.
         For most optimizers, the update is performed based on the gradient
@@ -96,7 +100,7 @@ def eval_and_update(
         :param forward_mode_differentiation: boolean flag indicating whether to use forward mode differentiation.
         :return: a pair of the output of objective function and the new optimizer state.
         """
-        params = self.get_params(state)
+        params: _Params = self.get_params(state)
         (out, aux), grads = _value_and_grad(
             fn, x=params, forward_mode_differentiation=forward_mode_differentiation
         )
@@ -107,7 +111,7 @@ def eval_and_stable_update(
         fn: Callable[[Any], tuple],
         state: _IterOptState,
         forward_mode_differentiation: bool = False,
-    ):
+    ) -> tuple[tuple[Any, Any], _IterOptState]:
         """
         Like :meth:`eval_and_update` but when the value of the objective function
         or the gradients are not finite, we will not update the input `state`
@@ -118,7 +122,7 @@ def eval_and_stable_update(
         :param forward_mode_differentiation: boolean flag indicating whether to use forward mode differentiation.
         :return: a pair of the output of objective function and the new optimizer state.
         """
-        params = self.get_params(state)
+        params: _Params = self.get_params(state)
         (out, aux), grads = _value_and_grad(
             fn, x=params, forward_mode_differentiation=forward_mode_differentiation
         )
@@ -141,7 +145,7 @@ def get_params(self, state: _IterOptState) -> _Params:
         return self.get_params_fn(opt_state)
 
 
-def _add_doc(fn):
+def _add_doc(fn) -> Callable[[Any], Any]:
     def _wrapped(cls):
         cls.__doc__ = "Wrapper class for the JAX optimizer: :func:`~jax.example_libraries.optimizers.{}`".format(
             fn.__name__
@@ -153,7 +157,7 @@ def _wrapped(cls):
 
 @_add_doc(optimizers.adam)
 class Adam(_NumPyroOptim):
-    def __init__(self, *args, **kwargs):
+    def __init__(self, *args, **kwargs) -> None:
         super(Adam, self).__init__(optimizers.adam, *args, **kwargs)
 
 
@@ -170,11 +174,11 @@ class ClippedAdam(_NumPyroOptim):
     https://arxiv.org/abs/1412.6980
     """
 
-    def __init__(self, *args, clip_norm=10.0, **kwargs):
+    def __init__(self, *args, clip_norm: float = 10.0, **kwargs) -> None:
         self.clip_norm = clip_norm
         super(ClippedAdam, self).__init__(optimizers.adam, *args, **kwargs)
 
-    def update(self, g, state):
+    def update(self, g: _Params, state: _IterOptState) -> _IterOptState:
         i, opt_state = state
         # clip norm
         g = jax.tree.map(lambda g_: jnp.clip(g_, -self.clip_norm, self.clip_norm), g)
@@ -184,25 +188,25 @@ def update(self, g, state):
 
 @_add_doc(optimizers.adagrad)
 class Adagrad(_NumPyroOptim):
-    def __init__(self, *args, **kwargs):
+    def __init__(self, *args, **kwargs) -> None:
         super(Adagrad, self).__init__(optimizers.adagrad, *args, **kwargs)
 
 
 @_add_doc(optimizers.momentum)
 class Momentum(_NumPyroOptim):
-    def __init__(self, *args, **kwargs):
+    def __init__(self, *args, **kwargs) -> None:
         super(Momentum, self).__init__(optimizers.momentum, *args, **kwargs)
 
 
 @_add_doc(optimizers.rmsprop)
 class RMSProp(_NumPyroOptim):
-    def __init__(self, *args, **kwargs):
+    def __init__(self, *args, **kwargs) -> None:
         super(RMSProp, self).__init__(optimizers.rmsprop, *args, **kwargs)
 
 
 @_add_doc(optimizers.rmsprop_momentum)
 class RMSPropMomentum(_NumPyroOptim):
-    def __init__(self, *args, **kwargs):
+    def __init__(self, *args, **kwargs) -> None:
         super(RMSPropMomentum, self).__init__(
             optimizers.rmsprop_momentum, *args, **kwargs
         )
@@ -210,13 +214,13 @@ def __init__(self, *args, **kwargs):
 
 @_add_doc(optimizers.sgd)
 class SGD(_NumPyroOptim):
-    def __init__(self, *args, **kwargs):
+    def __init__(self, *args, **kwargs) -> None:
         super(SGD, self).__init__(optimizers.sgd, *args, **kwargs)
 
 
 @_add_doc(optimizers.sm3)
 class SM3(_NumPyroOptim):
-    def __init__(self, *args, **kwargs):
+    def __init__(self, *args, **kwargs) -> None:
         super(SM3, self).__init__(optimizers.sm3, *args, **kwargs)
 
 
@@ -225,7 +229,11 @@ def __init__(self, *args, **kwargs):
 # and pass `unravel_fn` around.
 # When arbitrary pytree is supported in JAX, we can just simply use
 # identity functions for `init_fn` and `get_params`.
-_MinimizeState = namedtuple("MinimizeState", ["flat_params", "unravel_fn"])
+class _MinimizeState(namedtuple("_MinimizeState", ["flat_params", "unravel_fn"])):
+    flat_params: ArrayLike
+    unravel_fn: Callable[[ArrayLike], _Params]
+
+
 register_pytree_node(
     _MinimizeState,
     lambda state: ((state.flat_params,), (state.unravel_fn,)),
@@ -233,16 +241,24 @@ def __init__(self, *args, **kwargs):
 )
 
 
-def _minimize_wrapper():
-    def init_fn(params):
+def _minimize_wrapper() -> (
+    tuple[
+        Callable[[_Params], _MinimizeState],
+        Callable[[Any, Any, _MinimizeState], _MinimizeState],
+        Callable[[_MinimizeState], _Params],
+    ]
+):
+    def init_fn(params: _Params) -> _MinimizeState:
         flat_params, unravel_fn = ravel_pytree(params)
         return _MinimizeState(flat_params, unravel_fn)
 
-    def update_fn(i, grad_tree, opt_state):
+    def update_fn(
+        i: ArrayLike, grad_tree: ArrayLike, opt_state: _MinimizeState
+    ) -> _MinimizeState:
         # we don't use update_fn in Minimize, so let it do nothing
         return opt_state
 
-    def get_params(opt_state):
+    def get_params(opt_state: _MinimizeState) -> _Params:
         flat_params, unravel_fn = opt_state
         return unravel_fn(flat_params)
 
@@ -289,7 +305,7 @@ class Minimize(_NumPyroOptim):
         >>> assert_allclose(quantiles["b"], 3., atol=1e-3)
     """
 
-    def __init__(self, method="BFGS", **kwargs):
+    def __init__(self, method="BFGS", **kwargs) -> None:
         super().__init__(_minimize_wrapper)
         self._method = method
         self._kwargs = kwargs
@@ -298,8 +314,8 @@ def eval_and_update(
         self,
         fn: Callable[[Any], tuple],
         state: _IterOptState,
-        forward_mode_differentiation=False,
-    ):
+        forward_mode_differentiation: bool = False,
+    ) -> tuple[tuple[Any, None], _IterOptState]:
         i, (flat_params, unravel_fn) = state
 
         def loss_fn(x):
@@ -333,17 +349,19 @@ def optax_to_numpyro(transformation) -> _NumPyroOptim:
     """
     import optax
 
-    def init_fn(params):
+    def init_fn(params: _Params) -> tuple[_Params, Any]:
         opt_state = transformation.init(params)
         return params, opt_state
 
-    def update_fn(step, grads, state):
+    def update_fn(
+        step: ArrayLike, grads: ArrayLike, state: tuple[_Params, Any]
+    ) -> tuple[_Params, Any]:
         params, opt_state = state
         updates, opt_state = transformation.update(grads, opt_state, params)
         updated_params = optax.apply_updates(params, updates)
         return updated_params, opt_state
 
-    def get_params_fn(state):
+    def get_params_fn(state: tuple[_Params, Any]) -> _Params:
         params, _ = state
         return params
 
diff --git a/pyproject.toml b/pyproject.toml
index 660eb5e0e..28947c4ad 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -116,6 +116,7 @@ module = [
     "numpyro.contrib.stochastic_support.*",
     "numpyro.diagnostics.*",
     "numpyro.handlers.*",
+    "numpyro.optim.*",
     "numpyro.primitives.*",
     "numpyro.patch.*",
     "numpyro.util.*",