diff --git a/src/emcee/ensemble.py b/src/emcee/ensemble.py
index 45cc4ba..24faba3 100644
--- a/src/emcee/ensemble.py
+++ b/src/emcee/ensemble.py
@@ -1,9 +1,10 @@
 # -*- coding: utf-8 -*-
 
 import warnings
+from itertools import count
+from typing import Dict, List, Optional, Union
 
 import numpy as np
-from itertools import count
 
 from .backends import Backend
 from .model import Model
@@ -61,6 +62,10 @@ class EnsembleSampler(object):
             to accept a list of position vectors instead of just one. Note
             that ``pool`` will be ignored if this is ``True``.
             (default: ``False``)
+        parameter_names (Optional[Union[List[str], Dict[str, List[int]]]]):
+            names of individual parameters or groups of parameters. If
+            specified, the ``log_prob_fn`` will recieve a dictionary of
+            parameters, rather than a ``np.ndarray``.
 
     """
 
@@ -76,6 +81,7 @@ class EnsembleSampler(object):
         backend=None,
         vectorize=False,
         blobs_dtype=None,
+        parameter_names: Optional[Union[Dict[str, int], List[str]]] = None,
         # Deprecated...
         a=None,
         postargs=None,
@@ -157,6 +163,49 @@ class EnsembleSampler(object):
         # ``args`` and ``kwargs`` pickleable.
         self.log_prob_fn = _FunctionWrapper(log_prob_fn, args, kwargs)
 
+        # Save the parameter names
+        self.params_are_named: bool = parameter_names is not None
+        if self.params_are_named:
+            assert isinstance(parameter_names, (list, dict))
+
+            # Don't support vectorizing yet
+            msg = "named parameters with vectorization unsupported for now"
+            assert not self.vectorize, msg
+
+            # Check for duplicate names
+            dupes = set()
+            uniq = []
+            for name in parameter_names:
+                if name not in dupes:
+                    uniq.append(name)
+                    dupes.add(name)
+            msg = f"duplicate paramters: {dupes}"
+            assert len(uniq) == len(parameter_names), msg
+
+            if isinstance(parameter_names, list):
+                # Check for all named
+                msg = "name all parameters or set `parameter_names` to `None`"
+                assert len(parameter_names) == ndim, msg
+                # Convert a list to a dict
+                parameter_names: Dict[str, int] = {
+                    name: i for i, name in enumerate(parameter_names)
+                }
+
+            # Check not too many names
+            msg = "too many names"
+            assert len(parameter_names) <= ndim, msg
+
+            # Check all indices appear
+            values = [
+                v if isinstance(v, list) else [v]
+                for v in parameter_names.values()
+            ]
+            values = [item for sublist in values for item in sublist]
+            values = set(values)
+            msg = f"not all values appear -- set should be 0 to {ndim-1}"
+            assert values == set(np.arange(ndim)), msg
+            self.parameter_names = parameter_names
+
     @property
     def random_state(self):
         """
@@ -251,8 +300,9 @@ class EnsembleSampler(object):
             raise ValueError("'store' must be False when 'iterations' is None")
         # Interpret the input as a walker state and check the dimensions.
         state = State(initial_state, copy=True)
-        if np.shape(state.coords) != (self.nwalkers, self.ndim):
-            raise ValueError("incompatible input dimensions")
+        state_shape = np.shape(state.coords)
+        if state_shape != (self.nwalkers, self.ndim):
+            raise ValueError(f"incompatible input dimensions {state_shape}")
         if (not skip_initial_state_check) and (
             not walkers_independent(state.coords)
         ):
@@ -416,6 +466,10 @@ class EnsembleSampler(object):
         if np.any(np.isnan(p)):
             raise ValueError("At least one parameter value was NaN")
 
+        # If the parmaeters are named, then switch to dictionaries
+        if self.params_are_named:
+            p = ndarray_to_list_of_dicts(p, self.parameter_names)
+
         # Run the log-probability calculations (optionally in parallel).
         if self.vectorize:
             results = self.log_prob_fn(p)
@@ -427,9 +481,7 @@ class EnsembleSampler(object):
                 map_func = self.pool.map
             else:
                 map_func = map
-            results = list(
-                map_func(self.log_prob_fn, (p[i] for i in range(len(p))))
-            )
+            results = list(map_func(self.log_prob_fn, p))
 
         try:
             log_prob = np.array([float(l[0]) for l in results])
@@ -444,8 +496,9 @@ class EnsembleSampler(object):
             else:
                 try:
                     with warnings.catch_warnings(record=True):
-                        warnings.simplefilter("error",
-                                              np.VisibleDeprecationWarning)
+                        warnings.simplefilter(
+                            "error", np.VisibleDeprecationWarning
+                        )
                         try:
                             dt = np.atleast_1d(blob[0]).dtype
                         except Warning:
@@ -455,7 +508,8 @@ class EnsembleSampler(object):
                                 "placed in an object array. Numpy has "
                                 "deprecated this automatic detection, so "
                                 "please specify "
-                                "blobs_dtype=np.dtype('object')")
+                                "blobs_dtype=np.dtype('object')"
+                            )
                             dt = np.dtype("object")
                 except ValueError:
                     dt = np.dtype("object")
@@ -557,8 +611,8 @@ class _FunctionWrapper(object):
 
     def __init__(self, f, args, kwargs):
         self.f = f
-        self.args = [] if args is None else args
-        self.kwargs = {} if kwargs is None else kwargs
+        self.args = args or []
+        self.kwargs = kwargs or {}
 
     def __call__(self, x):
         try:
@@ -605,3 +659,22 @@ def _scaled_cond(a):
         return np.inf
     c = b / bsum
     return np.linalg.cond(c.astype(float))
+
+
+def ndarray_to_list_of_dicts(
+    x: np.ndarray,
+    key_map: Dict[str, Union[int, List[int]]],
+) -> List[Dict[str, Union[np.number, np.ndarray]]]:
+    """
+    A helper function to convert a ``np.ndarray`` into a list
+    of dictionaries of parameters. Used when parameters are named.
+
+    Args:
+      x (np.ndarray): parameter array of shape ``(N, n_dim)``, where
+        ``N`` is an integer
+      key_map (Dict[str, Union[int, List[int]]):
+
+    Returns:
+      list of dictionaries of parameters
+    """
+    return [{key: xi[val] for key, val in key_map.items()} for xi in x]

diff --git a/src/emcee/tests/unit/test_ensemble.py b/src/emcee/tests/unit/test_ensemble.py
new file mode 100644
index 0000000..f6f5ad2
--- /dev/null
+++ b/src/emcee/tests/unit/test_ensemble.py
@@ -0,0 +1,184 @@
+"""
+Unit tests of some functionality in ensemble.py when the parameters are named
+"""
+import string
+from unittest import TestCase
+
+import numpy as np
+import pytest
+
+from emcee.ensemble import EnsembleSampler, ndarray_to_list_of_dicts
+
+
+class TestNP2ListOfDicts(TestCase):
+    def test_ndarray_to_list_of_dicts(self):
+        # Try different numbers of keys
+        for n_keys in [1, 2, 10, 26]:
+            keys = list(string.ascii_lowercase[:n_keys])
+            key_set = set(keys)
+            key_dict = {key: i for i, key in enumerate(keys)}
+            # Try different number of walker/procs
+            for N in [1, 2, 3, 10, 100]:
+                x = np.random.rand(N, n_keys)
+
+                LOD = ndarray_to_list_of_dicts(x, key_dict)
+                assert len(LOD) == N, "need 1 dict per row"
+                for i, dct in enumerate(LOD):
+                    assert dct.keys() == key_set, "keys are missing"
+                    for j, key in enumerate(keys):
+                        assert dct[key] == x[i, j], f"wrong value at {(i, j)}"
+
+
+class TestNamedParameters(TestCase):
+    """
+    Test that a keyword-based log-probability function instead of
+    a positional.
+    """
+
+    # Keyword based lnpdf
+    def lnpdf(self, pars) -> np.float64:
+        mean = pars["mean"]
+        var = pars["var"]
+        if var <= 0:
+            return -np.inf
+        return (
+            -0.5 * ((mean - self.x) ** 2 / var + np.log(2 * np.pi * var)).sum()
+        )
+
+    def lnpdf_mixture(self, pars) -> np.float64:
+        mean1 = pars["mean1"]
+        var1 = pars["var1"]
+        mean2 = pars["mean2"]
+        var2 = pars["var2"]
+        if var1 <= 0 or var2 <= 0:
+            return -np.inf
+        return (
+            -0.5
+            * (
+                (mean1 - self.x) ** 2 / var1
+                + np.log(2 * np.pi * var1)
+                + (mean2 - self.x - 3) ** 2 / var2
+                + np.log(2 * np.pi * var2)
+            ).sum()
+        )
+
+    def lnpdf_mixture_grouped(self, pars) -> np.float64:
+        mean1, mean2 = pars["means"]
+        var1, var2 = pars["vars"]
+        const = pars["constant"]
+        if var1 <= 0 or var2 <= 0:
+            return -np.inf
+        return (
+            -0.5
+            * (
+                (mean1 - self.x) ** 2 / var1
+                + np.log(2 * np.pi * var1)
+                + (mean2 - self.x - 3) ** 2 / var2
+                + np.log(2 * np.pi * var2)
+            ).sum()
+            + const
+        )
+
+    def setUp(self):
+        # Draw some data from a unit Gaussian
+        self.x = np.random.randn(100)
+        self.names = ["mean", "var"]
+
+    def test_named_parameters(self):
+        sampler = EnsembleSampler(
+            nwalkers=10,
+            ndim=len(self.names),
+            log_prob_fn=self.lnpdf,
+            parameter_names=self.names,
+        )
+        assert sampler.params_are_named
+        assert list(sampler.parameter_names.keys()) == self.names
+
+    def test_asserts(self):
+        # ndim name mismatch
+        with pytest.raises(AssertionError):
+            _ = EnsembleSampler(
+                nwalkers=10,
+                ndim=len(self.names) - 1,
+                log_prob_fn=self.lnpdf,
+                parameter_names=self.names,
+            )
+
+        # duplicate names
+        with pytest.raises(AssertionError):
+            _ = EnsembleSampler(
+                nwalkers=10,
+                ndim=3,
+                log_prob_fn=self.lnpdf,
+                parameter_names=["a", "b", "a"],
+            )
+
+        # vectorize turned on
+        with pytest.raises(AssertionError):
+            _ = EnsembleSampler(
+                nwalkers=10,
+                ndim=len(self.names),
+                log_prob_fn=self.lnpdf,
+                parameter_names=self.names,
+                vectorize=True,
+            )
+
+    def test_compute_log_prob(self):
+        # Try different numbers of walkers
+        for N in [4, 8, 10]:
+            sampler = EnsembleSampler(
+                nwalkers=N,
+                ndim=len(self.names),
+                log_prob_fn=self.lnpdf,
+                parameter_names=self.names,
+            )
+            coords = np.random.rand(N, len(self.names))
+            lnps, _ = sampler.compute_log_prob(coords)
+            assert len(lnps) == N
+            assert lnps.dtype == np.float64
+
+    def test_compute_log_prob_mixture(self):
+        names = ["mean1", "var1", "mean2", "var2"]
+        # Try different numbers of walkers
+        for N in [8, 10, 20]:
+            sampler = EnsembleSampler(
+                nwalkers=N,
+                ndim=len(names),
+                log_prob_fn=self.lnpdf_mixture,
+                parameter_names=names,
+            )
+            coords = np.random.rand(N, len(names))
+            lnps, _ = sampler.compute_log_prob(coords)
+            assert len(lnps) == N
+            assert lnps.dtype == np.float64
+
+    def test_compute_log_prob_mixture_grouped(self):
+        names = {"means": [0, 1], "vars": [2, 3], "constant": 4}
+        # Try different numbers of walkers
+        for N in [8, 10, 20]:
+            sampler = EnsembleSampler(
+                nwalkers=N,
+                ndim=5,
+                log_prob_fn=self.lnpdf_mixture_grouped,
+                parameter_names=names,
+            )
+            coords = np.random.rand(N, 5)
+            lnps, _ = sampler.compute_log_prob(coords)
+            assert len(lnps) == N
+            assert lnps.dtype == np.float64
+
+    def test_run_mcmc(self):
+        # Sort of an integration test
+        n_walkers = 4
+        sampler = EnsembleSampler(
+            nwalkers=n_walkers,
+            ndim=len(self.names),
+            log_prob_fn=self.lnpdf,
+            parameter_names=self.names,
+        )
+        guess = np.random.rand(n_walkers, len(self.names))
+        n_steps = 50
+        results = sampler.run_mcmc(guess, n_steps)
+        assert results.coords.shape == (n_walkers, len(self.names))
+        chain = sampler.chain
+        assert chain.shape == (n_walkers, n_steps, len(self.names))

[ENH] support for dictionaries and/or namedtuples
## Proposal

The sampler API shares a lot of features with `scipy.optimize.minimize` -- given a model that can be typed as `Callable(List,...)` keep proposing samples to improve the model. This is fine for many problems, but one can imagine a scenario where it would be useful for model developers to handle samples with more than just a `List`. Handling parameters in a `List` means that writing a posterior *requires defining parameters positionally*. In contrast, in packages like pytorch one can refer to model parameters by name (eg. a `torch.nn.Linear` has a `weight` and `bias` named parameters).

This issue proposes enhancing the emcee API to allow for dictionary and/or namedtuple parameter constructs.  Looking at the API for the `EnsembleSampler`, this would require an additional constructor argument, since the sampler does not inspect the state of the `log_prob_fn`.

Here is a minimum proposed implementation for supporting a dictionary:

```python
class EnsembleSampler(object):
    def __init__(
        self,
        nwalkers: int,
        ndim: int,
        log_prob_fn: Callable(Union[List, Dict]),
        parameter_names: Optional[List[str]] = None,
        ...
    ):
        ...

        # Save the names
        self.parameter_names = parameter_names
        self.name_parameters: bool = parameter_names is not None
        if self.name_parameters:
            assert len(parameter_names) == ndim, f"names must match dimensions"
        ...

    def sample(...):
        ...
         with get_progress_bar(progress, total) as pbar:
            i = 0
            for _ in count() if iterations is None else range(iterations):
                for _ in range(yield_step):
                    ...

                    # If our parameters are named, return them in a named format
                    if self.name_parameters:
                        state = {key: value for key, value in zip(self.parameter_names, state)}

                    yield state
```

This allows for a lot more flexibility downstream for model developers. As a simple example, consider a model composed of two parts, that each can be updated in a way that doesn't affect the higher level model:

```python
class PartA:
    __slots__ = ["param_a"]
    param_a: float

    def __call__(self):
        ...

class PartB:
    __slots__ = ["param_b"]
    param_b: float

    def __call__(self):
        ...

class MyModel:
    def __init__(self, a = PartA(), b = PartB()):
        self.a = a
        self.b = b

    def log_likelihood_fn(self, params: Dict[str, float]):
        # Update the composed parts of the model
        for key in self.a.__slots__:
            setattr(self.a, params[key])

        for key in self.b.__slots__:
            setattr(self.b, params[key])

        # Final likelihood uses the results of A and B, but we don't
        # care how they are implemented
        return f(self.a(), self.b())
```

If this sounds like an attractive feature I would be happy to work on a PR.
src/emcee/tests/unit/test_ensemble.py::TestNP2ListOfDicts::test_ndarray_to_list_of_dicts src/emcee/tests/unit/test_ensemble.py::TestNamedParameters::test_asserts src/emcee/tests/unit/test_ensemble.py::TestNamedParameters::test_compute_log_prob src/emcee/tests/unit/test_ensemble.py::TestNamedParameters::test_compute_log_prob_mixture src/emcee/tests/unit/test_ensemble.py::TestNamedParameters::test_compute_log_prob_mixture_grouped src/emcee/tests/unit/test_ensemble.py::TestNamedParameters::test_named_parameters src/emcee/tests/unit/test_ensemble.py::TestNamedParameters::test_run_mcmc