We are currently solving the following issue within our repository. Here is the issue text:
--- BEGIN ISSUE ---
Documentation: meaning of value for return_fitted_val=True
# Description

In this code snippet from the documentation 

```python
>>> pyhf.infer.mle.fixed_poi_fit(test_poi, data, model, return_fitted_val=True)
(array([1.        , 0.97224597, 0.87553894]), array([28.92218013]))
```

it isn't clear what the meaning of `array([28.92218013])` is. Is it likelihood, log likelihood, -log likelihood, -2 log likelihood?
It is the latter, but that is not clear.

Applies to 

https://scikit-hep.org/pyhf/_generated/pyhf.infer.mle.fixed_poi_fit.html
or
https://scikit-hep.org/pyhf/_generated/pyhf.infer.mle.fit.html

## Is your feature request related to a problem? Please describe.

I wasn't sure, so I had to try a few things to figure it out.

### Describe the solution you'd like

Add a note to the documentation for the convention.

### Describe alternatives you've considered

banging my head against the wall.

# Relevant Issues and Pull Requests



--- END ISSUE ---

Below are some code segments, each from a relevant file. One or more of these files may contain bugs.
--- BEGIN FILES ---
Path: `src/pyhf/infer/mle.py`
Content:
```
1 """Module for Maximum Likelihood Estimation."""
2 from .. import get_backend
3 from ..exceptions import UnspecifiedPOI
4 
5 
6 def twice_nll(pars, data, pdf):
7     """
8     Twice the negative Log-Likelihood.
9 
10     Args:
11         data (`tensor`): The data
12         pdf (~pyhf.pdf.Model): The statistical model adhering to the schema model.json
13 
14     Returns:
15         Twice the negative log likelihood.
16 
17     """
18     return -2 * pdf.logpdf(pars, data)
19 
20 
21 def fit(data, pdf, init_pars=None, par_bounds=None, **kwargs):
22     """
23     Run a unconstrained maximum likelihood fit.
24 
25     Example:
26         >>> import pyhf
27         >>> pyhf.set_backend("numpy")
28         >>> model = pyhf.simplemodels.hepdata_like(
29         ...     signal_data=[12.0, 11.0], bkg_data=[50.0, 52.0], bkg_uncerts=[3.0, 7.0]
30         ... )
31         >>> observations = [51, 48]
32         >>> data = pyhf.tensorlib.astensor(observations + model.config.auxdata)
33         >>> pyhf.infer.mle.fit(data, model, return_fitted_val=True)
34         (array([0.        , 1.0030512 , 0.96266961]), array([24.98393521]))
35 
36     Args:
37         data (`tensor`): The data
38         pdf (~pyhf.pdf.Model): The statistical model adhering to the schema model.json
39         init_pars (`list`): Values to initialize the model parameters at for the fit
40         par_bounds (`list` of `list`\s or `tuple`\s): The extrema of values the model parameters are allowed to reach in the fit
41         kwargs: Keyword arguments passed through to the optimizer API
42 
43     Returns:
44         See optimizer API
45 
46     """
47     _, opt = get_backend()
48     init_pars = init_pars or pdf.config.suggested_init()
49     par_bounds = par_bounds or pdf.config.suggested_bounds()
50     return opt.minimize(twice_nll, data, pdf, init_pars, par_bounds, **kwargs)
51 
52 
53 def fixed_poi_fit(poi_val, data, pdf, init_pars=None, par_bounds=None, **kwargs):
54     """
55     Run a maximum likelihood fit with the POI value fixed.
56 
57     Example:
58         >>> import pyhf
59         >>> pyhf.set_backend("numpy")
60         >>> model = pyhf.simplemodels.hepdata_like(
61         ...     signal_data=[12.0, 11.0], bkg_data=[50.0, 52.0], bkg_uncerts=[3.0, 7.0]
62         ... )
63         >>> observations = [51, 48]
64         >>> data = pyhf.tensorlib.astensor(observations + model.config.auxdata)
65         >>> test_poi = 1.0
66         >>> pyhf.infer.mle.fixed_poi_fit(test_poi, data, model, return_fitted_val=True)
67         (array([1.        , 0.97224597, 0.87553894]), array([28.92218013]))
68 
69     Args:
70         data: The data
71         pdf (~pyhf.pdf.Model): The statistical model adhering to the schema model.json
72         init_pars (`list`): Values to initialize the model parameters at for the fit
73         par_bounds (`list` of `list`\s or `tuple`\s): The extrema of values the model parameters are allowed to reach in the fit
74         kwargs: Keyword arguments passed through to the optimizer API
75 
76     Returns:
77         See optimizer API
78 
79     """
80     if pdf.config.poi_index is None:
81         raise UnspecifiedPOI(
82             'No POI is defined. A POI is required to fit with a fixed POI.'
83         )
84     _, opt = get_backend()
85     init_pars = init_pars or pdf.config.suggested_init()
86     par_bounds = par_bounds or pdf.config.suggested_bounds()
87     return opt.minimize(
88         twice_nll,
89         data,
90         pdf,
91         init_pars,
92         par_bounds,
93         [(pdf.config.poi_index, poi_val)],
94         **kwargs,
95     )
96
```
--- END FILES ---

Please first localize the bug based on the issue statement, and then generate a patch according to the `git diff` format fenced by three backticks.

Here is an example:

```diff
diff --git a/examples/server_async.py b/examples/server_async.py
--- a/examples/server_async.py
+++ b/examples/server_async.py
@@ -313,4 +313,4 @@
 
 
 if __name__ == "__main__":
-    asyncio.run(run_async_server("."), debug=True)
+    asyncio.run(run_async_server(), debug=True)
diff --git a/examples/server_sync.py b/examples/server_sync.py
--- a/examples/server_sync.py
+++ b/examples/server_sync.py
@@ -313,5 +313,5 @@
 
 
 if __name__ == "__main__":
-    server = run_sync_server(".")
+    server = run_sync_server()
     server.shutdown()

```

diff --git a/src/pyhf/infer/mle.py b/src/pyhf/infer/mle.py
--- a/src/pyhf/infer/mle.py
+++ b/src/pyhf/infer/mle.py
@@ -22,6 +22,10 @@
     """
     Run a unconstrained maximum likelihood fit.
 
+    .. note::
+
+        :func:`twice_nll` is the objective function.
+
     Example:
         >>> import pyhf
         >>> pyhf.set_backend("numpy")
@@ -54,6 +58,10 @@
     """
     Run a maximum likelihood fit with the POI value fixed.
 
+    .. note::
+
+        :func:`twice_nll` is the objective function.
+
     Example:
         >>> import pyhf
         >>> pyhf.set_backend("numpy")

{"golden_diff": "diff --git a/src/pyhf/infer/mle.py b/src/pyhf/infer/mle.py\n--- a/src/pyhf/infer/mle.py\n+++ b/src/pyhf/infer/mle.py\n@@ -22,6 +22,10 @@\n     \"\"\"\n     Run a unconstrained maximum likelihood fit.\n \n+    .. note::\n+\n+        :func:`twice_nll` is the objective function.\n+\n     Example:\n         >>> import pyhf\n         >>> pyhf.set_backend(\"numpy\")\n@@ -54,6 +58,10 @@\n     \"\"\"\n     Run a maximum likelihood fit with the POI value fixed.\n \n+    .. note::\n+\n+        :func:`twice_nll` is the objective function.\n+\n     Example:\n         >>> import pyhf\n         >>> pyhf.set_backend(\"numpy\")\n", "issue": "Documentation: meaning of value for return_fitted_val=True\n# Description\r\n\r\nIn this code snippet from the documentation \r\n\r\n```python\r\n>>> pyhf.infer.mle.fixed_poi_fit(test_poi, data, model, return_fitted_val=True)\r\n(array([1.        , 0.97224597, 0.87553894]), array([28.92218013]))\r\n```\r\n\r\nit isn't clear what the meaning of `array([28.92218013])` is. Is it likelihood, log likelihood, -log likelihood, -2 log likelihood?\r\nIt is the latter, but that is not clear.\r\n\r\nApplies to \r\n\r\nhttps://scikit-hep.org/pyhf/_generated/pyhf.infer.mle.fixed_poi_fit.html\r\nor\r\nhttps://scikit-hep.org/pyhf/_generated/pyhf.infer.mle.fit.html\r\n\r\n## Is your feature request related to a problem? Please describe.\r\n\r\nI wasn't sure, so I had to try a few things to figure it out.\r\n\r\n### Describe the solution you'd like\r\n\r\nAdd a note to the documentation for the convention.\r\n\r\n### Describe alternatives you've considered\r\n\r\nbanging my head against the wall.\r\n\r\n# Relevant Issues and Pull Requests\r\n\r\n\n", "before_files": [{"content": "\"\"\"Module for Maximum Likelihood Estimation.\"\"\"\nfrom .. import get_backend\nfrom ..exceptions import UnspecifiedPOI\n\n\ndef twice_nll(pars, data, pdf):\n    \"\"\"\n    Twice the negative Log-Likelihood.\n\n    Args:\n        data (`tensor`): The data\n        pdf (~pyhf.pdf.Model): The statistical model adhering to the schema model.json\n\n    Returns:\n        Twice the negative log likelihood.\n\n    \"\"\"\n    return -2 * pdf.logpdf(pars, data)\n\n\ndef fit(data, pdf, init_pars=None, par_bounds=None, **kwargs):\n    \"\"\"\n    Run a unconstrained maximum likelihood fit.\n\n    Example:\n        >>> import pyhf\n        >>> pyhf.set_backend(\"numpy\")\n        >>> model = pyhf.simplemodels.hepdata_like(\n        ...     signal_data=[12.0, 11.0], bkg_data=[50.0, 52.0], bkg_uncerts=[3.0, 7.0]\n        ... )\n        >>> observations = [51, 48]\n        >>> data = pyhf.tensorlib.astensor(observations + model.config.auxdata)\n        >>> pyhf.infer.mle.fit(data, model, return_fitted_val=True)\n        (array([0.        , 1.0030512 , 0.96266961]), array([24.98393521]))\n\n    Args:\n        data (`tensor`): The data\n        pdf (~pyhf.pdf.Model): The statistical model adhering to the schema model.json\n        init_pars (`list`): Values to initialize the model parameters at for the fit\n        par_bounds (`list` of `list`\\s or `tuple`\\s): The extrema of values the model parameters are allowed to reach in the fit\n        kwargs: Keyword arguments passed through to the optimizer API\n\n    Returns:\n        See optimizer API\n\n    \"\"\"\n    _, opt = get_backend()\n    init_pars = init_pars or pdf.config.suggested_init()\n    par_bounds = par_bounds or pdf.config.suggested_bounds()\n    return opt.minimize(twice_nll, data, pdf, init_pars, par_bounds, **kwargs)\n\n\ndef fixed_poi_fit(poi_val, data, pdf, init_pars=None, par_bounds=None, **kwargs):\n    \"\"\"\n    Run a maximum likelihood fit with the POI value fixed.\n\n    Example:\n        >>> import pyhf\n        >>> pyhf.set_backend(\"numpy\")\n        >>> model = pyhf.simplemodels.hepdata_like(\n        ...     signal_data=[12.0, 11.0], bkg_data=[50.0, 52.0], bkg_uncerts=[3.0, 7.0]\n        ... )\n        >>> observations = [51, 48]\n        >>> data = pyhf.tensorlib.astensor(observations + model.config.auxdata)\n        >>> test_poi = 1.0\n        >>> pyhf.infer.mle.fixed_poi_fit(test_poi, data, model, return_fitted_val=True)\n        (array([1.        , 0.97224597, 0.87553894]), array([28.92218013]))\n\n    Args:\n        data: The data\n        pdf (~pyhf.pdf.Model): The statistical model adhering to the schema model.json\n        init_pars (`list`): Values to initialize the model parameters at for the fit\n        par_bounds (`list` of `list`\\s or `tuple`\\s): The extrema of values the model parameters are allowed to reach in the fit\n        kwargs: Keyword arguments passed through to the optimizer API\n\n    Returns:\n        See optimizer API\n\n    \"\"\"\n    if pdf.config.poi_index is None:\n        raise UnspecifiedPOI(\n            'No POI is defined. A POI is required to fit with a fixed POI.'\n        )\n    _, opt = get_backend()\n    init_pars = init_pars or pdf.config.suggested_init()\n    par_bounds = par_bounds or pdf.config.suggested_bounds()\n    return opt.minimize(\n        twice_nll,\n        data,\n        pdf,\n        init_pars,\n        par_bounds,\n        [(pdf.config.poi_index, poi_val)],\n        **kwargs,\n    )\n", "path": "src/pyhf/infer/mle.py"}], "after_files": [{"content": "\"\"\"Module for Maximum Likelihood Estimation.\"\"\"\nfrom .. import get_backend\nfrom ..exceptions import UnspecifiedPOI\n\n\ndef twice_nll(pars, data, pdf):\n    \"\"\"\n    Twice the negative Log-Likelihood.\n\n    Args:\n        data (`tensor`): The data\n        pdf (~pyhf.pdf.Model): The statistical model adhering to the schema model.json\n\n    Returns:\n        Twice the negative log likelihood.\n\n    \"\"\"\n    return -2 * pdf.logpdf(pars, data)\n\n\ndef fit(data, pdf, init_pars=None, par_bounds=None, **kwargs):\n    \"\"\"\n    Run a unconstrained maximum likelihood fit.\n\n    .. note::\n\n        :func:`twice_nll` is the objective function.\n\n    Example:\n        >>> import pyhf\n        >>> pyhf.set_backend(\"numpy\")\n        >>> model = pyhf.simplemodels.hepdata_like(\n        ...     signal_data=[12.0, 11.0], bkg_data=[50.0, 52.0], bkg_uncerts=[3.0, 7.0]\n        ... )\n        >>> observations = [51, 48]\n        >>> data = pyhf.tensorlib.astensor(observations + model.config.auxdata)\n        >>> pyhf.infer.mle.fit(data, model, return_fitted_val=True)\n        (array([0.        , 1.0030512 , 0.96266961]), array([24.98393521]))\n\n    Args:\n        data (`tensor`): The data\n        pdf (~pyhf.pdf.Model): The statistical model adhering to the schema model.json\n        init_pars (`list`): Values to initialize the model parameters at for the fit\n        par_bounds (`list` of `list`\\s or `tuple`\\s): The extrema of values the model parameters are allowed to reach in the fit\n        kwargs: Keyword arguments passed through to the optimizer API\n\n    Returns:\n        See optimizer API\n\n    \"\"\"\n    _, opt = get_backend()\n    init_pars = init_pars or pdf.config.suggested_init()\n    par_bounds = par_bounds or pdf.config.suggested_bounds()\n    return opt.minimize(twice_nll, data, pdf, init_pars, par_bounds, **kwargs)\n\n\ndef fixed_poi_fit(poi_val, data, pdf, init_pars=None, par_bounds=None, **kwargs):\n    \"\"\"\n    Run a maximum likelihood fit with the POI value fixed.\n\n    .. note::\n\n        :func:`twice_nll` is the objective function.\n\n    Example:\n        >>> import pyhf\n        >>> pyhf.set_backend(\"numpy\")\n        >>> model = pyhf.simplemodels.hepdata_like(\n        ...     signal_data=[12.0, 11.0], bkg_data=[50.0, 52.0], bkg_uncerts=[3.0, 7.0]\n        ... )\n        >>> observations = [51, 48]\n        >>> data = pyhf.tensorlib.astensor(observations + model.config.auxdata)\n        >>> test_poi = 1.0\n        >>> pyhf.infer.mle.fixed_poi_fit(test_poi, data, model, return_fitted_val=True)\n        (array([1.        , 0.97224597, 0.87553894]), array([28.92218013]))\n\n    Args:\n        data: The data\n        pdf (~pyhf.pdf.Model): The statistical model adhering to the schema model.json\n        init_pars (`list`): Values to initialize the model parameters at for the fit\n        par_bounds (`list` of `list`\\s or `tuple`\\s): The extrema of values the model parameters are allowed to reach in the fit\n        kwargs: Keyword arguments passed through to the optimizer API\n\n    Returns:\n        See optimizer API\n\n    \"\"\"\n    if pdf.config.poi_index is None:\n        raise UnspecifiedPOI(\n            'No POI is defined. A POI is required to fit with a fixed POI.'\n        )\n    _, opt = get_backend()\n    init_pars = init_pars or pdf.config.suggested_init()\n    par_bounds = par_bounds or pdf.config.suggested_bounds()\n    return opt.minimize(\n        twice_nll,\n        data,\n        pdf,\n        init_pars,\n        par_bounds,\n        [(pdf.config.poi_index, poi_val)],\n        **kwargs,\n    )\n", "path": "src/pyhf/infer/mle.py"}]}