From c31919ba240647a7cb23d2c313f8091fbf9297ad Mon Sep 17 00:00:00 2001
From: Carlo Gottardo <carlo.gottardo91@gmail.com>
Date: Sun, 26 Apr 2020 14:24:03 +0200
Subject: [PATCH 01/24] fixed_vals add as argument to infer functions

---
 src/pyhf/infer/mle.py             | 17 +++++++++++++----
 src/pyhf/infer/test_statistics.py | 30 ++++++++++++++++++------------
 2 files changed, 31 insertions(+), 16 deletions(-)

diff --git a/src/pyhf/infer/mle.py b/src/pyhf/infer/mle.py
index 1391c67e02..82448d5958 100644
--- a/src/pyhf/infer/mle.py
+++ b/src/pyhf/infer/mle.py
@@ -47,7 +47,7 @@ def twice_nll(pars, data, pdf):
     return -2 * pdf.logpdf(pars, data)
 
 
-def fit(data, pdf, init_pars=None, par_bounds=None, **kwargs):
+def fit(data, pdf, init_pars=None, par_bounds=None, fixed_vals=None, **kwargs):
     r"""
     Run a unconstrained maximum likelihood fit.
     This is done by minimizing the objective function :func:`~pyhf.infer.mle.twice_nll`
@@ -96,10 +96,14 @@ def fit(data, pdf, init_pars=None, par_bounds=None, **kwargs):
     _, opt = get_backend()
     init_pars = init_pars or pdf.config.suggested_init()
     par_bounds = par_bounds or pdf.config.suggested_bounds()
-    return opt.minimize(twice_nll, data, pdf, init_pars, par_bounds, **kwargs)
+    return opt.minimize(
+        twice_nll, data, pdf, init_pars, par_bounds, fixed_vals, **kwargs
+    )
 
 
-def fixed_poi_fit(poi_val, data, pdf, init_pars=None, par_bounds=None, **kwargs):
+def fixed_poi_fit(
+    poi_val, data, pdf, init_pars=None, par_bounds=None, fixed_vals=None, **kwargs
+):
     r"""
     Run a maximum likelihood fit with the POI value fixed.
     This is done by minimizing the objective function of :func:`~pyhf.infer.mle.twice_nll`
@@ -152,6 +156,11 @@ def fixed_poi_fit(poi_val, data, pdf, init_pars=None, par_bounds=None, **kwargs)
         raise UnspecifiedPOI(
             'No POI is defined. A POI is required to fit with a fixed POI.'
         )
+
+    fixed_params = [(pdf.config.poi_index, poi_val)]
+    if fixed_vals:
+        fixed_params += fixed_vals
+
     _, opt = get_backend()
     init_pars = init_pars or pdf.config.suggested_init()
     par_bounds = par_bounds or pdf.config.suggested_bounds()
@@ -161,6 +170,6 @@ def fixed_poi_fit(poi_val, data, pdf, init_pars=None, par_bounds=None, **kwargs)
         pdf,
         init_pars,
         par_bounds,
-        [(pdf.config.poi_index, poi_val)],
+        fixed_params,
         **kwargs,
     )
diff --git a/src/pyhf/infer/test_statistics.py b/src/pyhf/infer/test_statistics.py
index c636d04ab6..d1cd663ecd 100644
--- a/src/pyhf/infer/test_statistics.py
+++ b/src/pyhf/infer/test_statistics.py
@@ -7,7 +7,7 @@
 log = logging.getLogger(__name__)
 
 
-def _qmu_like(mu, data, pdf, init_pars, par_bounds):
+def _qmu_like(mu, data, pdf, init_pars, par_bounds, fixed_vals):
     """
     Clipped version of _tmu_like where the returned test statistic
     is 0 if muhat > 0 else tmu_like_stat.
@@ -25,7 +25,9 @@ def _qmu_like(mu, data, pdf, init_pars, par_bounds):
     return qmu_like_stat
 
 
-def _tmu_like(mu, data, pdf, init_pars, par_bounds, return_fitted_pars=False):
+def _tmu_like(
+    mu, data, pdf, init_pars, par_bounds, fixed_vals, return_fitted_pars=False
+):
     """
     Basic Profile Likelihood test statistic.
 
@@ -34,10 +36,10 @@ def _tmu_like(mu, data, pdf, init_pars, par_bounds, return_fitted_pars=False):
     """
     tensorlib, optimizer = get_backend()
     mubhathat, fixed_poi_fit_lhood_val = fixed_poi_fit(
-        mu, data, pdf, init_pars, par_bounds, return_fitted_val=True
+        mu, data, pdf, init_pars, par_bounds, fixed_vals, return_fitted_val=True
     )
     muhatbhat, unconstrained_fit_lhood_val = fit(
-        data, pdf, init_pars, par_bounds, return_fitted_val=True
+        data, pdf, init_pars, par_bounds, fixed_vals, return_fitted_val=True
     )
     log_likelihood_ratio = fixed_poi_fit_lhood_val - unconstrained_fit_lhood_val
     tmu_like_stat = tensorlib.astensor(
@@ -48,7 +50,7 @@ def _tmu_like(mu, data, pdf, init_pars, par_bounds, return_fitted_pars=False):
     return tmu_like_stat
 
 
-def qmu(mu, data, pdf, init_pars, par_bounds):
+def qmu(mu, data, pdf, init_pars, par_bounds, fixed_vals):
     r"""
     The test statistic, :math:`q_{\mu}`, for establishing an upper
     limit on the strength parameter, :math:`\mu`, as defiend in
@@ -91,6 +93,7 @@ def qmu(mu, data, pdf, init_pars, par_bounds):
         pdf (~pyhf.pdf.Model): The HistFactory statistical model used in the likelihood ratio calculation
         init_pars (`list`): Values to initialize the model parameters at for the fit
         par_bounds (`list` of `list`\s or `tuple`\s): The extrema of values the model parameters are allowed to reach in the fit
+        fixed_vals(`list`): Parameters held constant in the fit
 
     Returns:
         Float: The calculated test statistic, :math:`q_{\mu}`
@@ -104,10 +107,10 @@ def qmu(mu, data, pdf, init_pars, par_bounds):
             'qmu test statistic used for fit configuration with POI bounded at zero.\n'
             + 'Use the qmu_tilde test statistic (pyhf.infer.test_statistics.qmu_tilde) instead.'
         )
-    return _qmu_like(mu, data, pdf, init_pars, par_bounds)
+    return _qmu_like(mu, data, pdf, init_pars, par_bounds, fixed_vals)
 
 
-def qmu_tilde(mu, data, pdf, init_pars, par_bounds):
+def qmu_tilde(mu, data, pdf, init_pars, par_bounds, fixed_vals):
     r"""
     The test statistic, :math:`\tilde{q}_{\mu}`, for establishing an upper
     limit on the strength parameter, :math:`\mu`, for models with
@@ -155,6 +158,7 @@ def qmu_tilde(mu, data, pdf, init_pars, par_bounds):
         pdf (~pyhf.pdf.Model): The statistical model adhering to the schema model.json
         init_pars (`list`): Values to initialize the model parameters at for the fit
         par_bounds (`list` of `list`\s or `tuple`\s): The extrema of values the model parameters are allowed to reach in the fit
+        fixed_vals(`list`): Parameters held constant in the fit
 
     Returns:
         Float: The calculated test statistic, :math:`\tilde{q}_{\mu}`
@@ -168,10 +172,10 @@ def qmu_tilde(mu, data, pdf, init_pars, par_bounds):
             'qmu_tilde test statistic used for fit configuration with POI not bounded at zero.\n'
             + 'Use the qmu test statistic (pyhf.infer.test_statistics.qmu) instead.'
         )
-    return _qmu_like(mu, data, pdf, init_pars, par_bounds)
+    return _qmu_like(mu, data, pdf, init_pars, par_bounds, fixed_vals)
 
 
-def tmu(mu, data, pdf, init_pars, par_bounds):
+def tmu(mu, data, pdf, init_pars, par_bounds, fixed_vals):
     r"""
     The test statistic, :math:`t_{\mu}`, for establishing a two-sided
     interval on the strength parameter, :math:`\mu`, as defiend in Equation (8)
@@ -208,6 +212,7 @@ def tmu(mu, data, pdf, init_pars, par_bounds):
         pdf (~pyhf.pdf.Model): The statistical model adhering to the schema model.json
         init_pars (`list`): Values to initialize the model parameters at for the fit
         par_bounds (`list` of `list`\s or `tuple`\s): The extrema of values the model parameters are allowed to reach in the fit
+        fixed_vals(`list`): Parameters held constant in the fit
 
     Returns:
         Float: The calculated test statistic, :math:`t_{\mu}`
@@ -221,10 +226,10 @@ def tmu(mu, data, pdf, init_pars, par_bounds):
             'tmu test statistic used for fit configuration with POI bounded at zero.\n'
             + 'Use the tmu_tilde test statistic (pyhf.infer.test_statistics.tmu_tilde) instead.'
         )
-    return _tmu_like(mu, data, pdf, init_pars, par_bounds)
+    return _tmu_like(mu, data, pdf, init_pars, par_bounds, fixed_vals)
 
 
-def tmu_tilde(mu, data, pdf, init_pars, par_bounds):
+def tmu_tilde(mu, data, pdf, init_pars, par_bounds, fixed_vals):
     r"""
     The test statistic, :math:`\tilde{t}_{\mu}`, for establishing a two-sided
     interval on the strength parameter, :math:`\mu`, for models with
@@ -266,6 +271,7 @@ def tmu_tilde(mu, data, pdf, init_pars, par_bounds):
         pdf (~pyhf.pdf.Model): The statistical model adhering to the schema model.json
         init_pars (`list`): Values to initialize the model parameters at for the fit
         par_bounds (`list` of `list`\s or `tuple`\s): The extrema of values the model parameters are allowed to reach in the fit
+        fixed_vals(`list`): Parameters held constant in the fit
 
     Returns:
         Float: The calculated test statistic, :math:`\tilde{t}_{\mu}`
@@ -279,4 +285,4 @@ def tmu_tilde(mu, data, pdf, init_pars, par_bounds):
             'tmu_tilde test statistic used for fit configuration with POI not bounded at zero.\n'
             + 'Use the tmu test statistic (pyhf.infer.test_statistics.tmu) instead.'
         )
-    return _tmu_like(mu, data, pdf, init_pars, par_bounds)
+    return _tmu_like(mu, data, pdf, init_pars, par_bounds, fixed_vals)

From 80dafdb320a6a0ed6a3a324fe253f1093b5d6d91 Mon Sep 17 00:00:00 2001
From: Carlo Gottardo <carlo.gottardo91@gmail.com>
Date: Sun, 26 Apr 2020 18:54:53 +0200
Subject: [PATCH 02/24] fixed_vals add as argument to infer functions

---
 src/pyhf/infer/calculators.py | 27 ++++++++++++++++++++++-----
 1 file changed, 22 insertions(+), 5 deletions(-)

diff --git a/src/pyhf/infer/calculators.py b/src/pyhf/infer/calculators.py
index 62f90329ab..528a3ba023 100644
--- a/src/pyhf/infer/calculators.py
+++ b/src/pyhf/infer/calculators.py
@@ -12,7 +12,7 @@
 from .test_statistics import qmu, qmu_tilde
 
 
-def generate_asimov_data(asimov_mu, data, pdf, init_pars, par_bounds):
+def generate_asimov_data(asimov_mu, data, pdf, init_pars, par_bounds, fixed_vals):
     """
     Compute Asimov Dataset (expected yields at best-fit values) for a given POI value.
 
@@ -22,12 +22,15 @@ def generate_asimov_data(asimov_mu, data, pdf, init_pars, par_bounds):
         pdf (~pyhf.pdf.Model): The statistical model adhering to the schema ``model.json``.
         init_pars (`tensor`): The initial parameter values to be used for fitting.
         par_bounds (`tensor`): The parameter value bounds to be used for fitting.
+        fixed_vals (`tensor`): Parameters to be held constant in the fit.
 
     Returns:
         Tensor: The Asimov dataset.
 
     """
-    bestfit_nuisance_asimov = fixed_poi_fit(asimov_mu, data, pdf, init_pars, par_bounds)
+    bestfit_nuisance_asimov = fixed_poi_fit(
+        asimov_mu, data, pdf, init_pars, par_bounds, fixed_vals
+    )
     return pdf.expected_data(bestfit_nuisance_asimov)
 
 
@@ -118,7 +121,9 @@ def expected_value(self, nsigma):
 class AsymptoticCalculator(object):
     """The Asymptotic Calculator."""
 
-    def __init__(self, data, pdf, init_pars=None, par_bounds=None, qtilde=False):
+    def __init__(
+        self, data, pdf, init_pars=None, par_bounds=None, fixed_vals=None, qtilde=False
+    ):
         """
         Asymptotic Calculator.
 
@@ -127,6 +132,7 @@ def __init__(self, data, pdf, init_pars=None, par_bounds=None, qtilde=False):
             pdf (~pyhf.pdf.Model): The statistical model adhering to the schema ``model.json``.
             init_pars (`tensor`): The initial parameter values to be used for fitting.
             par_bounds (`tensor`): The parameter value bounds to be used for fitting.
+            fixed_vals (`tensor`): Parameters to be held constant in the fit.
             qtilde (`bool`): Whether to use qtilde as the test statistic.
 
         Returns:
@@ -137,6 +143,7 @@ def __init__(self, data, pdf, init_pars=None, par_bounds=None, qtilde=False):
         self.pdf = pdf
         self.init_pars = init_pars or pdf.config.suggested_init()
         self.par_bounds = par_bounds or pdf.config.suggested_bounds()
+        self.fixed_vals = fixed_vals
         self.qtilde = qtilde
         self.sqrtqmuA_v = None
 
@@ -173,7 +180,12 @@ def teststatistic(self, poi_test):
         teststat_func = qmu_tilde if self.qtilde else qmu
 
         qmu_v = teststat_func(
-            poi_test, self.data, self.pdf, self.init_pars, self.par_bounds
+            poi_test,
+            self.data,
+            self.pdf,
+            self.init_pars,
+            self.par_bounds,
+            self.fixed_vals,
         )
         sqrtqmu_v = tensorlib.sqrt(qmu_v)
 
@@ -182,7 +194,12 @@ def teststatistic(self, poi_test):
             asimov_mu, self.data, self.pdf, self.init_pars, self.par_bounds
         )
         qmuA_v = teststat_func(
-            poi_test, asimov_data, self.pdf, self.init_pars, self.par_bounds
+            poi_test,
+            asimov_data,
+            self.pdf,
+            self.init_pars,
+            self.par_bounds,
+            self.fixed_vals,
         )
         self.sqrtqmuA_v = tensorlib.sqrt(qmuA_v)
 

From 32a7955f0abbe2717c10d8f1de01b00a45e10ab9 Mon Sep 17 00:00:00 2001
From: Carlo Gottardo <carlo.gottardo91@gmail.com>
Date: Sun, 26 Apr 2020 18:56:40 +0200
Subject: [PATCH 03/24] fixed_vals add as argument to infer functions

---
 src/pyhf/infer/__init__.py | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/src/pyhf/infer/__init__.py b/src/pyhf/infer/__init__.py
index 246d2df3b0..61700b9d84 100644
--- a/src/pyhf/infer/__init__.py
+++ b/src/pyhf/infer/__init__.py
@@ -6,7 +6,7 @@
 
 
 def hypotest(
-    poi_test, data, pdf, init_pars=None, par_bounds=None, qtilde=False, **kwargs
+    poi_test, data, pdf, init_pars=None, par_bounds=None, fixed_vals=None, qtilde=False, **kwargs
 ):
     r"""
     Compute :math:`p`-values and test statistics for a single value of the parameter of interest.
@@ -34,6 +34,7 @@ def hypotest(
         pdf (~pyhf.pdf.Model): The statistical model adhering to the schema ``model.json``
         init_pars (Array or Tensor): The initial parameter values to be used for minimization
         par_bounds (Array or Tensor): The parameter value bounds to be used for minimization
+        fixed_vals (list of tuples): Parameters to be held constant and their value
         qtilde (Bool): When ``True`` perform the calculation using the alternative
          test statistic, :math:`\tilde{q}_{\mu}`, as defined under the Wald
          approximation in Equation (62) of :xref:`arXiv:1007.1727`.
@@ -120,7 +121,7 @@ def hypotest(
     par_bounds = par_bounds or pdf.config.suggested_bounds()
     tensorlib, _ = get_backend()
 
-    calc = AsymptoticCalculator(data, pdf, init_pars, par_bounds, qtilde=qtilde)
+    calc = AsymptoticCalculator(data, pdf, init_pars, par_bounds, fixed_vals, qtilde=qtilde)
     teststat = calc.teststatistic(poi_test)
     sig_plus_bkg_distribution, b_only_distribution = calc.distributions(poi_test)
 

From eb90ed5885f9afc395ef607f4ebcfdbc9ff77c9d Mon Sep 17 00:00:00 2001
From: Carlo Gottardo <carlo.gottardo91@gmail.com>
Date: Sun, 26 Apr 2020 22:24:24 +0200
Subject: [PATCH 04/24] tested

---
 src/pyhf/infer/calculators.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/pyhf/infer/calculators.py b/src/pyhf/infer/calculators.py
index 528a3ba023..b6e1c1404b 100644
--- a/src/pyhf/infer/calculators.py
+++ b/src/pyhf/infer/calculators.py
@@ -191,7 +191,7 @@ def teststatistic(self, poi_test):
 
         asimov_mu = 0.0
         asimov_data = generate_asimov_data(
-            asimov_mu, self.data, self.pdf, self.init_pars, self.par_bounds
+            asimov_mu, self.data, self.pdf, self.init_pars, self.par_bounds, self.fixed_vals
         )
         qmuA_v = teststat_func(
             poi_test,

From bf72f330b01afa97893a95ff99c306e8f0b4e919 Mon Sep 17 00:00:00 2001
From: Carlo Gottardo <carlo.gottardo91@gmail.com>
Date: Sun, 26 Apr 2020 23:28:31 +0200
Subject: [PATCH 05/24] black formatting

---
 src/pyhf/infer/__init__.py    | 13 +++++++++++--
 src/pyhf/infer/calculators.py |  7 ++++++-
 2 files changed, 17 insertions(+), 3 deletions(-)

diff --git a/src/pyhf/infer/__init__.py b/src/pyhf/infer/__init__.py
index 61700b9d84..89c2d24773 100644
--- a/src/pyhf/infer/__init__.py
+++ b/src/pyhf/infer/__init__.py
@@ -6,7 +6,14 @@
 
 
 def hypotest(
-    poi_test, data, pdf, init_pars=None, par_bounds=None, fixed_vals=None, qtilde=False, **kwargs
+    poi_test,
+    data,
+    pdf,
+    init_pars=None,
+    par_bounds=None,
+    fixed_vals=None,
+    qtilde=False,
+    **kwargs,
 ):
     r"""
     Compute :math:`p`-values and test statistics for a single value of the parameter of interest.
@@ -121,7 +128,9 @@ def hypotest(
     par_bounds = par_bounds or pdf.config.suggested_bounds()
     tensorlib, _ = get_backend()
 
-    calc = AsymptoticCalculator(data, pdf, init_pars, par_bounds, fixed_vals, qtilde=qtilde)
+    calc = AsymptoticCalculator(
+        data, pdf, init_pars, par_bounds, fixed_vals, qtilde=qtilde
+    )
     teststat = calc.teststatistic(poi_test)
     sig_plus_bkg_distribution, b_only_distribution = calc.distributions(poi_test)
 
diff --git a/src/pyhf/infer/calculators.py b/src/pyhf/infer/calculators.py
index b6e1c1404b..fb07d089e6 100644
--- a/src/pyhf/infer/calculators.py
+++ b/src/pyhf/infer/calculators.py
@@ -191,7 +191,12 @@ def teststatistic(self, poi_test):
 
         asimov_mu = 0.0
         asimov_data = generate_asimov_data(
-            asimov_mu, self.data, self.pdf, self.init_pars, self.par_bounds, self.fixed_vals
+            asimov_mu,
+            self.data,
+            self.pdf,
+            self.init_pars,
+            self.par_bounds,
+            self.fixed_vals,
         )
         qmuA_v = teststat_func(
             poi_test,

From 5f8e16ff1b3173e2be606dae7adf4b5a2571f830 Mon Sep 17 00:00:00 2001
From: Carlo Gottardo <carlo.gottardo91@gmail.com>
Date: Sun, 26 Apr 2020 23:56:49 +0200
Subject: [PATCH 06/24] added fixed_vals positional argument to test backends

---
 tests/test_backend_consistency.py | 7 ++++++-
 1 file changed, 6 insertions(+), 1 deletion(-)

diff --git a/tests/test_backend_consistency.py b/tests/test_backend_consistency.py
index 61f9b8579c..86fd3578fe 100644
--- a/tests/test_backend_consistency.py
+++ b/tests/test_backend_consistency.py
@@ -115,7 +115,12 @@ def test_hypotest_qmu_tilde(
         pyhf.set_backend(backend)
 
         qmu_tilde = pyhf.infer.test_statistics.qmu_tilde(
-            1.0, data, pdf, pdf.config.suggested_init(), pdf.config.suggested_bounds()
+            1.0,
+            data,
+            pdf,
+            pdf.config.suggested_init(),
+            pdf.config.suggested_bounds(),
+            None,
         )
         test_statistic.append(qmu_tilde)
 

From 9437118b76125a905f695808f83b5c1abc64efb0 Mon Sep 17 00:00:00 2001
From: Carlo Gottardo <carlo.gottardo91@gmail.com>
Date: Mon, 27 Apr 2020 11:45:20 +0200
Subject: [PATCH 07/24] Adding NP fix and shift in test_backend_consistency

---
 tests/test_backend_consistency.py | 104 ++++++++++++++++++------------
 1 file changed, 64 insertions(+), 40 deletions(-)

diff --git a/tests/test_backend_consistency.py b/tests/test_backend_consistency.py
index 86fd3578fe..5c46f5ab24 100644
--- a/tests/test_backend_consistency.py
+++ b/tests/test_backend_consistency.py
@@ -75,6 +75,8 @@ def test_hypotest_qmu_tilde(
     """
 
     source = generate_source_static(n_bins)
+    bkg_unc_10pc_up = [x + 0.10 * x for x in source['bindata']['bkg']]
+    bkg_unc_10pc_dn = [x - 0.10 * x for x in source['bindata']['bkg']]
 
     signal_sample = {
         'name': 'signal',
@@ -90,7 +92,13 @@ def test_hypotest_qmu_tilde(
                 'name': 'uncorr_bkguncrt',
                 'type': 'shapesys',
                 'data': source['bindata']['bkgerr'],
-            }
+            },
+            {
+                'name': 'norm_bkgunc',
+                'type': 'histosys',
+                'hi_data': bkg_unc_10pc_up,
+                'lo_data': bkg_unc_10pc_dn,
+            },
         ],
     }
     samples = (
@@ -101,6 +109,19 @@ def test_hypotest_qmu_tilde(
     spec = {'channels': [{'name': 'singlechannel', 'samples': samples}]}
     pdf = pyhf.Model(spec)
 
+    #   get norm_bkgunc index to set it constatnt
+    norm_bkgunc_idx = -1
+    for idx, par in enumerate(pdf.config.par_map):
+        if par == "norm_bkgunc":
+            norm_bkgunc_idx = idx
+    #   Floating norm_bkgunc, fixed at nominal, plus/minus 1 sigma
+    param_tests = [
+        None,
+        (norm_bkgunc_idx, 0.0),
+        (norm_bkgunc_idx, -1.0),
+        (norm_bkgunc_idx, 1.0),
+    ]
+
     data = source['bindata']['data'] + pdf.config.auxdata
 
     backends = [
@@ -110,44 +131,47 @@ def test_hypotest_qmu_tilde(
         pyhf.tensor.jax_backend(precision='64b'),
     ]
 
-    test_statistic = []
-    for backend in backends:
-        pyhf.set_backend(backend)
-
-        qmu_tilde = pyhf.infer.test_statistics.qmu_tilde(
-            1.0,
-            data,
-            pdf,
-            pdf.config.suggested_init(),
-            pdf.config.suggested_bounds(),
-            None,
-        )
-        test_statistic.append(qmu_tilde)
-
-    # compare to NumPy/SciPy
-    test_statistic = np.array(test_statistic)
-    numpy_ratio = np.divide(test_statistic, test_statistic[0])
-    numpy_ratio_delta_unity = np.absolute(np.subtract(numpy_ratio, 1))
-
-    # compare tensor libraries to each other
-    tensors_ratio = np.divide(test_statistic[1], test_statistic[2])
-    tensors_ratio_delta_unity = np.absolute(np.subtract(tensors_ratio, 1))
-
-    try:
-        assert (numpy_ratio_delta_unity < tolerance['numpy']).all()
-    except AssertionError:
-        print(
-            'Ratio to NumPy+SciPy exceeded tolerance of {}: {}'.format(
-                tolerance['numpy'], numpy_ratio_delta_unity.tolist()
+    for p in param_tests:
+        fixed_vals = [p]
+
+        test_statistic = []
+        for backend in backends:
+            pyhf.set_backend(backend)
+
+            qmu_tilde = pyhf.infer.test_statistics.qmu_tilde(
+                1.0,
+                data,
+                pdf,
+                pdf.config.suggested_init(),
+                pdf.config.suggested_bounds(),
+                fixed_vals,
+            )
+            test_statistic.append(qmu_tilde)
+
+        # compare to NumPy/SciPy
+        test_statistic = np.array(test_statistic)
+        numpy_ratio = np.divide(test_statistic, test_statistic[0])
+        numpy_ratio_delta_unity = np.absolute(np.subtract(numpy_ratio, 1))
+
+        # compare tensor libraries to each other
+        tensors_ratio = np.divide(test_statistic[1], test_statistic[2])
+        tensors_ratio_delta_unity = np.absolute(np.subtract(tensors_ratio, 1))
+
+        try:
+            assert (numpy_ratio_delta_unity < tolerance['numpy']).all()
+        except AssertionError:
+            print(
+                'Ratio to NumPy+SciPy exceeded tolerance of {}: {}'.format(
+                    tolerance['numpy'], numpy_ratio_delta_unity.tolist()
+                )
             )
-        )
-        assert False
-    try:
-        assert (tensors_ratio_delta_unity < tolerance['tensors']).all()
-    except AssertionError:
-        print(
-            'Ratio between tensor backends exceeded tolerance of {}: {}'.format(
-                tolerance['tensors'], tensors_ratio_delta_unity.tolist()
+            assert False
+        try:
+            assert (tensors_ratio_delta_unity < tolerance['tensors']).all()
+        except AssertionError:
+            print(
+                'Ratio between tensor backends exceeded tolerance of {}: {}'.format(
+                    tolerance['tensors'], tensors_ratio_delta_unity.tolist()
+                )
             )
-        )
-        assert False
+            assert False

From 40b781b4f0f5c830848c253e15927c811301fca4 Mon Sep 17 00:00:00 2001
From: Carlo Gottardo <carlo.gottardo91@gmail.com>
Date: Mon, 27 Apr 2020 12:41:11 +0200
Subject: [PATCH 08/24] correct histosys data structure in
 test_backend_consistency

---
 tests/test_backend_consistency.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/tests/test_backend_consistency.py b/tests/test_backend_consistency.py
index 5c46f5ab24..bf4edecc85 100644
--- a/tests/test_backend_consistency.py
+++ b/tests/test_backend_consistency.py
@@ -96,11 +96,11 @@ def test_hypotest_qmu_tilde(
             {
                 'name': 'norm_bkgunc',
                 'type': 'histosys',
-                'hi_data': bkg_unc_10pc_up,
-                'lo_data': bkg_unc_10pc_dn,
+                'data': {'hi_data': bkg_unc_10pc_up, 'lo_data': bkg_unc_10pc_dn,},
             },
         ],
     }
+    print(background_sample)
     samples = (
         [background_sample, signal_sample]
         if invert_order

From bcd477d7e3f16554766502db1f362feea208c3e8 Mon Sep 17 00:00:00 2001
From: Carlo Gottardo <carlo.gottardo91@gmail.com>
Date: Mon, 27 Apr 2020 13:08:44 +0200
Subject: [PATCH 09/24] fix test_backend_consistency

---
 tests/test_backend_consistency.py | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/tests/test_backend_consistency.py b/tests/test_backend_consistency.py
index bf4edecc85..32d8faae93 100644
--- a/tests/test_backend_consistency.py
+++ b/tests/test_backend_consistency.py
@@ -116,10 +116,10 @@ def test_hypotest_qmu_tilde(
             norm_bkgunc_idx = idx
     #   Floating norm_bkgunc, fixed at nominal, plus/minus 1 sigma
     param_tests = [
-        None,
-        (norm_bkgunc_idx, 0.0),
-        (norm_bkgunc_idx, -1.0),
-        (norm_bkgunc_idx, 1.0),
+        [],
+        [(norm_bkgunc_idx, 0.0)],
+        [(norm_bkgunc_idx, 1.0)],
+        [(norm_bkgunc_idx, -1.0)],
     ]
 
     data = source['bindata']['data'] + pdf.config.auxdata
@@ -132,7 +132,7 @@ def test_hypotest_qmu_tilde(
     ]
 
     for p in param_tests:
-        fixed_vals = [p]
+        fixed_vals = p
 
         test_statistic = []
         for backend in backends:

From cc774e7ca1744c04fe510ef4995941bdb725ed9c Mon Sep 17 00:00:00 2001
From: Carlo Gottardo <carlo.gottardo91@gmail.com>
Date: Tue, 5 May 2020 15:26:25 +0200
Subject: [PATCH 10/24] NP index fix in test_backend_consistency.py

---
 tests/test_backend_consistency.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/tests/test_backend_consistency.py b/tests/test_backend_consistency.py
index 32d8faae93..736ac5ca00 100644
--- a/tests/test_backend_consistency.py
+++ b/tests/test_backend_consistency.py
@@ -96,7 +96,7 @@ def test_hypotest_qmu_tilde(
             {
                 'name': 'norm_bkgunc',
                 'type': 'histosys',
-                'data': {'hi_data': bkg_unc_10pc_up, 'lo_data': bkg_unc_10pc_dn,},
+                'data': {'hi_data': bkg_unc_10pc_up, 'lo_data': bkg_unc_10pc_dn},
             },
         ],
     }
@@ -114,6 +114,7 @@ def test_hypotest_qmu_tilde(
     for idx, par in enumerate(pdf.config.par_map):
         if par == "norm_bkgunc":
             norm_bkgunc_idx = idx
+
     #   Floating norm_bkgunc, fixed at nominal, plus/minus 1 sigma
     param_tests = [
         [],

From d9e197208037da567207ab3f1a44da82d4134ade Mon Sep 17 00:00:00 2001
From: Carlo Gottardo <carlo.gottardo91@gmail.com>
Date: Tue, 5 May 2020 15:42:05 +0200
Subject: [PATCH 11/24] Need 5 percent tolerane for 500 bin fit with TF

---
 tests/test_backend_consistency.py | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/tests/test_backend_consistency.py b/tests/test_backend_consistency.py
index 736ac5ca00..7824bacf38 100644
--- a/tests/test_backend_consistency.py
+++ b/tests/test_backend_consistency.py
@@ -58,8 +58,11 @@ def generate_source_poisson(n_bins):
 
 @pytest.mark.parametrize('n_bins', bins, ids=bin_ids)
 @pytest.mark.parametrize('invert_order', [False, True], ids=['normal', 'inverted'])
+@pytest.mark.parametrize(
+    'fix_param', [None, 0.0, 1.0, -1.0], ids=['none', 'central', 'up', 'down']
+)
 def test_hypotest_qmu_tilde(
-    n_bins, invert_order, tolerance={'numpy': 1e-02, 'tensors': 5e-03}
+    n_bins, invert_order, fix_param, tolerance={'numpy': 1e-02, 'tensors': 5e-03}
 ):
     """
     Check that the different backends all compute a test statistic

From 9d45958650615785e326e072e530d37c5d3b6b2c Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Thu, 3 Sep 2020 18:54:07 -0400
Subject: [PATCH 12/24] pass in fixed_vals by converting to fixed_params

---
 src/pyhf/infer/mle.py | 38 +++++++++++++++++++++++++++++++++-----
 1 file changed, 33 insertions(+), 5 deletions(-)

diff --git a/src/pyhf/infer/mle.py b/src/pyhf/infer/mle.py
index 82448d5958..f30dbe1e9b 100644
--- a/src/pyhf/infer/mle.py
+++ b/src/pyhf/infer/mle.py
@@ -96,8 +96,23 @@ def fit(data, pdf, init_pars=None, par_bounds=None, fixed_vals=None, **kwargs):
     _, opt = get_backend()
     init_pars = init_pars or pdf.config.suggested_init()
     par_bounds = par_bounds or pdf.config.suggested_bounds()
+
+    # get fixed params from the model
+    model_fixed_params = [
+        (index, init)
+        for index, (init, is_fixed) in enumerate(
+            zip(init_pars, pdf.config.suggested_fixed())
+        )
+        if is_fixed
+    ]
+    # add user-defined ones at the end
+    fixed_params = model_fixed_params + (fixed_vals or [])
+
+    # de-dupe and use last-appended result for each index
+    fixed_params = list(dict(fixed_params))
+
     return opt.minimize(
-        twice_nll, data, pdf, init_pars, par_bounds, fixed_vals, **kwargs
+        twice_nll, data, pdf, init_pars, par_bounds, fixed_params, **kwargs
     )
 
 
@@ -157,13 +172,26 @@ def fixed_poi_fit(
             'No POI is defined. A POI is required to fit with a fixed POI.'
         )
 
-    fixed_params = [(pdf.config.poi_index, poi_val)]
-    if fixed_vals:
-        fixed_params += fixed_vals
-
     _, opt = get_backend()
     init_pars = init_pars or pdf.config.suggested_init()
     par_bounds = par_bounds or pdf.config.suggested_bounds()
+
+    # get fixed params from the model
+    model_fixed_params = [
+        (index, init)
+        for index, (init, is_fixed) in enumerate(
+            zip(init_pars, pdf.config.suggested_fixed())
+        )
+        if is_fixed
+    ]
+    # add user-defined ones at the end
+    fixed_params = model_fixed_params + (fixed_vals or [])
+    # add the fixed POI
+    fixed_params += [(pdf.config.poi_index, poi_val)]
+
+    # de-dupe and use last-appended result for each index
+    fixed_params = list(dict(fixed_params))
+
     return opt.minimize(
         twice_nll,
         data,

From d3c3b47e046c354702e70e8a05b4d733fd9eb497 Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Thu, 3 Sep 2020 19:45:55 -0400
Subject: [PATCH 13/24] make sure we propagate fixed_vals correctly everywhere

---
 src/pyhf/infer/__init__.py        | 16 +++++++++++++++-
 src/pyhf/infer/calculators.py     | 15 +++++++++++++++
 src/pyhf/infer/mle.py             | 10 +++++-----
 src/pyhf/infer/test_statistics.py | 19 +++++++++++--------
 4 files changed, 46 insertions(+), 14 deletions(-)

diff --git a/src/pyhf/infer/__init__.py b/src/pyhf/infer/__init__.py
index 89c2d24773..3b5c739eeb 100644
--- a/src/pyhf/infer/__init__.py
+++ b/src/pyhf/infer/__init__.py
@@ -126,7 +126,19 @@ def hypotest(
     """
     init_pars = init_pars or pdf.config.suggested_init()
     par_bounds = par_bounds or pdf.config.suggested_bounds()
-    tensorlib, _ = get_backend()
+    # get fixed vals from the model
+    model_fixed_vals = [
+        (index, init)
+        for index, (init, is_fixed) in enumerate(
+            zip(init_pars, pdf.config.suggested_fixed())
+        )
+        if is_fixed
+    ]
+    # add user-defined ones at the end
+    fixed_vals = model_fixed_vals + (fixed_vals or [])
+
+    # de-dupe and use last-appended result for each index
+    fixed_vals = list(dict(fixed_vals))
 
     calc = AsymptoticCalculator(
         data, pdf, init_pars, par_bounds, fixed_vals, qtilde=qtilde
@@ -137,6 +149,8 @@ def hypotest(
     CLsb = sig_plus_bkg_distribution.pvalue(teststat)
     CLb = b_only_distribution.pvalue(teststat)
     CLs = CLsb / CLb
+
+    tensorlib, _ = get_backend()
     # Ensure that all CL values are 0-d tensors
     CLsb, CLb, CLs = (
         tensorlib.astensor(CLsb),
diff --git a/src/pyhf/infer/calculators.py b/src/pyhf/infer/calculators.py
index fb07d089e6..aafd33c3f9 100644
--- a/src/pyhf/infer/calculators.py
+++ b/src/pyhf/infer/calculators.py
@@ -143,6 +143,21 @@ def __init__(
         self.pdf = pdf
         self.init_pars = init_pars or pdf.config.suggested_init()
         self.par_bounds = par_bounds or pdf.config.suggested_bounds()
+
+        # get fixed vals from the model
+        model_fixed_vals = [
+            (index, init)
+            for index, (init, is_fixed) in enumerate(
+                zip(init_pars, pdf.config.suggested_fixed())
+            )
+            if is_fixed
+        ]
+        # add user-defined ones at the end
+        fixed_vals = model_fixed_vals + (fixed_vals or [])
+
+        # de-dupe and use last-appended result for each index
+        fixed_vals = list(dict(fixed_vals))
+
         self.fixed_vals = fixed_vals
         self.qtilde = qtilde
         self.sqrtqmuA_v = None
diff --git a/src/pyhf/infer/mle.py b/src/pyhf/infer/mle.py
index f30dbe1e9b..a6166398ce 100644
--- a/src/pyhf/infer/mle.py
+++ b/src/pyhf/infer/mle.py
@@ -97,8 +97,8 @@ def fit(data, pdf, init_pars=None, par_bounds=None, fixed_vals=None, **kwargs):
     init_pars = init_pars or pdf.config.suggested_init()
     par_bounds = par_bounds or pdf.config.suggested_bounds()
 
-    # get fixed params from the model
-    model_fixed_params = [
+    # get fixed vals from the model
+    model_fixed_vals = [
         (index, init)
         for index, (init, is_fixed) in enumerate(
             zip(init_pars, pdf.config.suggested_fixed())
@@ -106,13 +106,13 @@ def fit(data, pdf, init_pars=None, par_bounds=None, fixed_vals=None, **kwargs):
         if is_fixed
     ]
     # add user-defined ones at the end
-    fixed_params = model_fixed_params + (fixed_vals or [])
+    fixed_vals = model_fixed_vals + (fixed_vals or [])
 
     # de-dupe and use last-appended result for each index
-    fixed_params = list(dict(fixed_params))
+    fixed_vals = list(dict(fixed_vals))
 
     return opt.minimize(
-        twice_nll, data, pdf, init_pars, par_bounds, fixed_params, **kwargs
+        twice_nll, data, pdf, init_pars, par_bounds, fixed_vals, **kwargs
     )
 
 
diff --git a/src/pyhf/infer/test_statistics.py b/src/pyhf/infer/test_statistics.py
index d1cd663ecd..7bd4c4fdb3 100644
--- a/src/pyhf/infer/test_statistics.py
+++ b/src/pyhf/infer/test_statistics.py
@@ -17,7 +17,7 @@ def _qmu_like(mu, data, pdf, init_pars, par_bounds, fixed_vals):
     """
     tensorlib, optimizer = get_backend()
     tmu_like_stat, (_, muhatbhat) = _tmu_like(
-        mu, data, pdf, init_pars, par_bounds, return_fitted_pars=True
+        mu, data, pdf, init_pars, par_bounds, fixed_vals, return_fitted_pars=True
     )
     qmu_like_stat = tensorlib.where(
         muhatbhat[pdf.config.poi_index] > mu, tensorlib.astensor(0.0), tmu_like_stat
@@ -84,7 +84,8 @@ def qmu(mu, data, pdf, init_pars, par_bounds, fixed_vals):
         >>> init_pars = model.config.suggested_init()
         >>> par_bounds = model.config.suggested_bounds()
         >>> par_bounds[model.config.poi_index] = [-10.0, 10.0]
-        >>> pyhf.infer.test_statistics.qmu(test_mu, data, model, init_pars, par_bounds)
+        >>> fixed_vals = []
+        >>> pyhf.infer.test_statistics.qmu(test_mu, data, model, init_pars, par_bounds, [])
         array(3.9549891)
 
     Args:
@@ -93,7 +94,7 @@ def qmu(mu, data, pdf, init_pars, par_bounds, fixed_vals):
         pdf (~pyhf.pdf.Model): The HistFactory statistical model used in the likelihood ratio calculation
         init_pars (`list`): Values to initialize the model parameters at for the fit
         par_bounds (`list` of `list`\s or `tuple`\s): The extrema of values the model parameters are allowed to reach in the fit
-        fixed_vals(`list`): Parameters held constant in the fit
+        fixed_vals (`list`): Parameters held constant in the fit
 
     Returns:
         Float: The calculated test statistic, :math:`q_{\mu}`
@@ -158,7 +159,7 @@ def qmu_tilde(mu, data, pdf, init_pars, par_bounds, fixed_vals):
         pdf (~pyhf.pdf.Model): The statistical model adhering to the schema model.json
         init_pars (`list`): Values to initialize the model parameters at for the fit
         par_bounds (`list` of `list`\s or `tuple`\s): The extrema of values the model parameters are allowed to reach in the fit
-        fixed_vals(`list`): Parameters held constant in the fit
+        fixed_vals (`list`): Parameters held constant in the fit
 
     Returns:
         Float: The calculated test statistic, :math:`\tilde{q}_{\mu}`
@@ -203,7 +204,8 @@ def tmu(mu, data, pdf, init_pars, par_bounds, fixed_vals):
         >>> init_pars = model.config.suggested_init()
         >>> par_bounds = model.config.suggested_bounds()
         >>> par_bounds[model.config.poi_index] = [-10.0, 10.0]
-        >>> pyhf.infer.test_statistics.tmu(test_mu, data, model, init_pars, par_bounds)
+        >>> fixed_vals = []
+        >>> pyhf.infer.test_statistics.tmu(test_mu, data, model, init_pars, par_bounds, [])
         array(3.9549891)
 
     Args:
@@ -212,7 +214,7 @@ def tmu(mu, data, pdf, init_pars, par_bounds, fixed_vals):
         pdf (~pyhf.pdf.Model): The statistical model adhering to the schema model.json
         init_pars (`list`): Values to initialize the model parameters at for the fit
         par_bounds (`list` of `list`\s or `tuple`\s): The extrema of values the model parameters are allowed to reach in the fit
-        fixed_vals(`list`): Parameters held constant in the fit
+        fixed_vals (`list`): Parameters held constant in the fit
 
     Returns:
         Float: The calculated test statistic, :math:`t_{\mu}`
@@ -262,7 +264,8 @@ def tmu_tilde(mu, data, pdf, init_pars, par_bounds, fixed_vals):
         >>> test_mu = 1.0
         >>> init_pars = model.config.suggested_init()
         >>> par_bounds = model.config.suggested_bounds()
-        >>> pyhf.infer.test_statistics.tmu_tilde(test_mu, data, model, init_pars, par_bounds)
+        >>> fixed_vals = []
+        >>> pyhf.infer.test_statistics.tmu_tilde(test_mu, data, model, init_pars, par_bounds, [])
         array(3.93824492)
 
     Args:
@@ -271,7 +274,7 @@ def tmu_tilde(mu, data, pdf, init_pars, par_bounds, fixed_vals):
         pdf (~pyhf.pdf.Model): The statistical model adhering to the schema model.json
         init_pars (`list`): Values to initialize the model parameters at for the fit
         par_bounds (`list` of `list`\s or `tuple`\s): The extrema of values the model parameters are allowed to reach in the fit
-        fixed_vals(`list`): Parameters held constant in the fit
+        fixed_vals (`list`): Parameters held constant in the fit
 
     Returns:
         Float: The calculated test statistic, :math:`\tilde{t}_{\mu}`

From e0c82d1e5f6433abdf9e80ef7e13d9296be78482 Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Thu, 3 Sep 2020 19:48:10 -0400
Subject: [PATCH 14/24] fix up doc a bit

---
 src/pyhf/infer/test_statistics.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/pyhf/infer/test_statistics.py b/src/pyhf/infer/test_statistics.py
index 7bd4c4fdb3..b4d03182a2 100644
--- a/src/pyhf/infer/test_statistics.py
+++ b/src/pyhf/infer/test_statistics.py
@@ -150,7 +150,7 @@ def qmu_tilde(mu, data, pdf, init_pars, par_bounds, fixed_vals):
         >>> test_mu = 1.0
         >>> init_pars = model.config.suggested_init()
         >>> par_bounds = model.config.suggested_bounds()
-        >>> pyhf.infer.test_statistics.qmu_tilde(test_mu, data, model, init_pars, par_bounds)
+        >>> pyhf.infer.test_statistics.qmu_tilde(test_mu, data, model, init_pars, par_bounds, [])
         array(3.93824492)
 
     Args:

From 0c232a6ba51d4d854188c9779669dfe6c262f44c Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Thu, 3 Sep 2020 19:54:25 -0400
Subject: [PATCH 15/24] fix up notational difference

---
 src/pyhf/infer/mle.py | 13 +++++++------
 1 file changed, 7 insertions(+), 6 deletions(-)

diff --git a/src/pyhf/infer/mle.py b/src/pyhf/infer/mle.py
index a6166398ce..bf581eeb51 100644
--- a/src/pyhf/infer/mle.py
+++ b/src/pyhf/infer/mle.py
@@ -176,8 +176,8 @@ def fixed_poi_fit(
     init_pars = init_pars or pdf.config.suggested_init()
     par_bounds = par_bounds or pdf.config.suggested_bounds()
 
-    # get fixed params from the model
-    model_fixed_params = [
+    # get fixed vals from the model
+    model_fixed_vals = [
         (index, init)
         for index, (init, is_fixed) in enumerate(
             zip(init_pars, pdf.config.suggested_fixed())
@@ -185,12 +185,13 @@ def fixed_poi_fit(
         if is_fixed
     ]
     # add user-defined ones at the end
-    fixed_params = model_fixed_params + (fixed_vals or [])
+    fixed_vals = model_fixed_vals + (fixed_vals or [])
+
     # add the fixed POI
-    fixed_params += [(pdf.config.poi_index, poi_val)]
+    fixed_vals = fixed_vals + [(pdf.config.poi_index, poi_val)]
 
     # de-dupe and use last-appended result for each index
-    fixed_params = list(dict(fixed_params))
+    fixed_vals = list(dict(fixed_vals))
 
     return opt.minimize(
         twice_nll,
@@ -198,6 +199,6 @@ def fixed_poi_fit(
         pdf,
         init_pars,
         par_bounds,
-        fixed_params,
+        fixed_vals,
         **kwargs,
     )

From aada2e97fabbdb1128f6f30e5182532f3bc9f879 Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Thu, 3 Sep 2020 20:00:25 -0400
Subject: [PATCH 16/24] undo changes to tests for now

---
 tests/test_backend_consistency.py | 105 ++++++++++--------------------
 1 file changed, 36 insertions(+), 69 deletions(-)

diff --git a/tests/test_backend_consistency.py b/tests/test_backend_consistency.py
index 7824bacf38..61f9b8579c 100644
--- a/tests/test_backend_consistency.py
+++ b/tests/test_backend_consistency.py
@@ -58,11 +58,8 @@ def generate_source_poisson(n_bins):
 
 @pytest.mark.parametrize('n_bins', bins, ids=bin_ids)
 @pytest.mark.parametrize('invert_order', [False, True], ids=['normal', 'inverted'])
-@pytest.mark.parametrize(
-    'fix_param', [None, 0.0, 1.0, -1.0], ids=['none', 'central', 'up', 'down']
-)
 def test_hypotest_qmu_tilde(
-    n_bins, invert_order, fix_param, tolerance={'numpy': 1e-02, 'tensors': 5e-03}
+    n_bins, invert_order, tolerance={'numpy': 1e-02, 'tensors': 5e-03}
 ):
     """
     Check that the different backends all compute a test statistic
@@ -78,8 +75,6 @@ def test_hypotest_qmu_tilde(
     """
 
     source = generate_source_static(n_bins)
-    bkg_unc_10pc_up = [x + 0.10 * x for x in source['bindata']['bkg']]
-    bkg_unc_10pc_dn = [x - 0.10 * x for x in source['bindata']['bkg']]
 
     signal_sample = {
         'name': 'signal',
@@ -95,15 +90,9 @@ def test_hypotest_qmu_tilde(
                 'name': 'uncorr_bkguncrt',
                 'type': 'shapesys',
                 'data': source['bindata']['bkgerr'],
-            },
-            {
-                'name': 'norm_bkgunc',
-                'type': 'histosys',
-                'data': {'hi_data': bkg_unc_10pc_up, 'lo_data': bkg_unc_10pc_dn},
-            },
+            }
         ],
     }
-    print(background_sample)
     samples = (
         [background_sample, signal_sample]
         if invert_order
@@ -112,20 +101,6 @@ def test_hypotest_qmu_tilde(
     spec = {'channels': [{'name': 'singlechannel', 'samples': samples}]}
     pdf = pyhf.Model(spec)
 
-    #   get norm_bkgunc index to set it constatnt
-    norm_bkgunc_idx = -1
-    for idx, par in enumerate(pdf.config.par_map):
-        if par == "norm_bkgunc":
-            norm_bkgunc_idx = idx
-
-    #   Floating norm_bkgunc, fixed at nominal, plus/minus 1 sigma
-    param_tests = [
-        [],
-        [(norm_bkgunc_idx, 0.0)],
-        [(norm_bkgunc_idx, 1.0)],
-        [(norm_bkgunc_idx, -1.0)],
-    ]
-
     data = source['bindata']['data'] + pdf.config.auxdata
 
     backends = [
@@ -135,47 +110,39 @@ def test_hypotest_qmu_tilde(
         pyhf.tensor.jax_backend(precision='64b'),
     ]
 
-    for p in param_tests:
-        fixed_vals = p
-
-        test_statistic = []
-        for backend in backends:
-            pyhf.set_backend(backend)
-
-            qmu_tilde = pyhf.infer.test_statistics.qmu_tilde(
-                1.0,
-                data,
-                pdf,
-                pdf.config.suggested_init(),
-                pdf.config.suggested_bounds(),
-                fixed_vals,
-            )
-            test_statistic.append(qmu_tilde)
-
-        # compare to NumPy/SciPy
-        test_statistic = np.array(test_statistic)
-        numpy_ratio = np.divide(test_statistic, test_statistic[0])
-        numpy_ratio_delta_unity = np.absolute(np.subtract(numpy_ratio, 1))
-
-        # compare tensor libraries to each other
-        tensors_ratio = np.divide(test_statistic[1], test_statistic[2])
-        tensors_ratio_delta_unity = np.absolute(np.subtract(tensors_ratio, 1))
-
-        try:
-            assert (numpy_ratio_delta_unity < tolerance['numpy']).all()
-        except AssertionError:
-            print(
-                'Ratio to NumPy+SciPy exceeded tolerance of {}: {}'.format(
-                    tolerance['numpy'], numpy_ratio_delta_unity.tolist()
-                )
+    test_statistic = []
+    for backend in backends:
+        pyhf.set_backend(backend)
+
+        qmu_tilde = pyhf.infer.test_statistics.qmu_tilde(
+            1.0, data, pdf, pdf.config.suggested_init(), pdf.config.suggested_bounds()
+        )
+        test_statistic.append(qmu_tilde)
+
+    # compare to NumPy/SciPy
+    test_statistic = np.array(test_statistic)
+    numpy_ratio = np.divide(test_statistic, test_statistic[0])
+    numpy_ratio_delta_unity = np.absolute(np.subtract(numpy_ratio, 1))
+
+    # compare tensor libraries to each other
+    tensors_ratio = np.divide(test_statistic[1], test_statistic[2])
+    tensors_ratio_delta_unity = np.absolute(np.subtract(tensors_ratio, 1))
+
+    try:
+        assert (numpy_ratio_delta_unity < tolerance['numpy']).all()
+    except AssertionError:
+        print(
+            'Ratio to NumPy+SciPy exceeded tolerance of {}: {}'.format(
+                tolerance['numpy'], numpy_ratio_delta_unity.tolist()
             )
-            assert False
-        try:
-            assert (tensors_ratio_delta_unity < tolerance['tensors']).all()
-        except AssertionError:
-            print(
-                'Ratio between tensor backends exceeded tolerance of {}: {}'.format(
-                    tolerance['tensors'], tensors_ratio_delta_unity.tolist()
-                )
+        )
+        assert False
+    try:
+        assert (tensors_ratio_delta_unity < tolerance['tensors']).all()
+    except AssertionError:
+        print(
+            'Ratio between tensor backends exceeded tolerance of {}: {}'.format(
+                tolerance['tensors'], tensors_ratio_delta_unity.tolist()
             )
-            assert False
+        )
+        assert False

From 61b97ec0741a0e0c534c15bca57ec7b574fea1d0 Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Thu, 3 Sep 2020 20:16:09 -0400
Subject: [PATCH 17/24] fixed it up

---
 src/pyhf/infer/__init__.py    | 2 +-
 src/pyhf/infer/calculators.py | 2 +-
 src/pyhf/infer/mle.py         | 4 ++--
 3 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/src/pyhf/infer/__init__.py b/src/pyhf/infer/__init__.py
index 3b5c739eeb..f9f6e2570a 100644
--- a/src/pyhf/infer/__init__.py
+++ b/src/pyhf/infer/__init__.py
@@ -138,7 +138,7 @@ def hypotest(
     fixed_vals = model_fixed_vals + (fixed_vals or [])
 
     # de-dupe and use last-appended result for each index
-    fixed_vals = list(dict(fixed_vals))
+    fixed_vals = list(dict(fixed_vals).items())
 
     calc = AsymptoticCalculator(
         data, pdf, init_pars, par_bounds, fixed_vals, qtilde=qtilde
diff --git a/src/pyhf/infer/calculators.py b/src/pyhf/infer/calculators.py
index aafd33c3f9..5f7e53be58 100644
--- a/src/pyhf/infer/calculators.py
+++ b/src/pyhf/infer/calculators.py
@@ -156,7 +156,7 @@ def __init__(
         fixed_vals = model_fixed_vals + (fixed_vals or [])
 
         # de-dupe and use last-appended result for each index
-        fixed_vals = list(dict(fixed_vals))
+        fixed_vals = list(dict(fixed_vals).items())
 
         self.fixed_vals = fixed_vals
         self.qtilde = qtilde
diff --git a/src/pyhf/infer/mle.py b/src/pyhf/infer/mle.py
index bf581eeb51..b5cdb8a803 100644
--- a/src/pyhf/infer/mle.py
+++ b/src/pyhf/infer/mle.py
@@ -109,7 +109,7 @@ def fit(data, pdf, init_pars=None, par_bounds=None, fixed_vals=None, **kwargs):
     fixed_vals = model_fixed_vals + (fixed_vals or [])
 
     # de-dupe and use last-appended result for each index
-    fixed_vals = list(dict(fixed_vals))
+    fixed_vals = list(dict(fixed_vals).items())
 
     return opt.minimize(
         twice_nll, data, pdf, init_pars, par_bounds, fixed_vals, **kwargs
@@ -191,7 +191,7 @@ def fixed_poi_fit(
     fixed_vals = fixed_vals + [(pdf.config.poi_index, poi_val)]
 
     # de-dupe and use last-appended result for each index
-    fixed_vals = list(dict(fixed_vals))
+    fixed_vals = list(dict(fixed_vals).items())
 
     return opt.minimize(
         twice_nll,

From 702b2171b73f04bb743c2a1e4a50a265cc6edf9d Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Thu, 3 Sep 2020 20:28:22 -0400
Subject: [PATCH 18/24] get tests passing

---
 tests/test_backend_consistency.py |  7 ++++++-
 tests/test_infer.py               |  3 +++
 tests/test_teststats.py           | 16 ++++++++--------
 3 files changed, 17 insertions(+), 9 deletions(-)

diff --git a/tests/test_backend_consistency.py b/tests/test_backend_consistency.py
index 61f9b8579c..b42f7afaed 100644
--- a/tests/test_backend_consistency.py
+++ b/tests/test_backend_consistency.py
@@ -115,7 +115,12 @@ def test_hypotest_qmu_tilde(
         pyhf.set_backend(backend)
 
         qmu_tilde = pyhf.infer.test_statistics.qmu_tilde(
-            1.0, data, pdf, pdf.config.suggested_init(), pdf.config.suggested_bounds()
+            1.0,
+            data,
+            pdf,
+            pdf.config.suggested_init(),
+            pdf.config.suggested_bounds(),
+            [],
         )
         test_statistic.append(qmu_tilde)
 
diff --git a/tests/test_infer.py b/tests/test_infer.py
index 527ec60f1c..2a2b4c9a2b 100644
--- a/tests/test_infer.py
+++ b/tests/test_infer.py
@@ -138,6 +138,9 @@ def suggested_init(self):
         def suggested_bounds(self):
             return [[0.0, 10.0], [0.0, 10.0]]
 
+        def suggested_fixed(self):
+            return [False, False]
+
     class NonPyhfModel(object):
         def __init__(self, spec):
             self.sig, self.nominal, self.uncert = spec
diff --git a/tests/test_teststats.py b/tests/test_teststats.py
index bd942152e4..aca8f9f361 100644
--- a/tests/test_teststats.py
+++ b/tests/test_teststats.py
@@ -12,7 +12,7 @@ def test_qmu(caplog):
     par_bounds = model.config.suggested_bounds()
 
     with caplog.at_level(logging.WARNING, "pyhf.infer.test_statistics"):
-        pyhf.infer.test_statistics.qmu(mu, data, model, init_pars, par_bounds)
+        pyhf.infer.test_statistics.qmu(mu, data, model, init_pars, par_bounds, [])
         assert "WARNING  qmu test statistic used for fit" in caplog.text
         caplog.clear()
 
@@ -26,7 +26,7 @@ def test_qmu_tilde(caplog):
 
     par_bounds[model.config.poi_index] = [-10, 10]
     with caplog.at_level(logging.WARNING, "pyhf.infer.test_statistics"):
-        pyhf.infer.test_statistics.qmu_tilde(mu, data, model, init_pars, par_bounds)
+        pyhf.infer.test_statistics.qmu_tilde(mu, data, model, init_pars, par_bounds, [])
         assert "WARNING  qmu_tilde test statistic used for fit" in caplog.text
         caplog.clear()
 
@@ -38,7 +38,7 @@ def test_tmu(caplog):
     init_pars = model.config.suggested_init()
     par_bounds = model.config.suggested_bounds()
     with caplog.at_level(logging.WARNING, "pyhf.infer.test_statistics"):
-        pyhf.infer.test_statistics.tmu(mu, data, model, init_pars, par_bounds)
+        pyhf.infer.test_statistics.tmu(mu, data, model, init_pars, par_bounds, [])
         assert "WARNING  tmu test statistic used for fit" in caplog.text
         caplog.clear()
 
@@ -52,7 +52,7 @@ def test_tmu_tilde(caplog):
 
     par_bounds[model.config.poi_index] = [-10, 10]
     with caplog.at_level(logging.WARNING, "pyhf.infer.test_statistics"):
-        pyhf.infer.test_statistics.tmu_tilde(mu, data, model, init_pars, par_bounds)
+        pyhf.infer.test_statistics.tmu_tilde(mu, data, model, init_pars, par_bounds, [])
         assert "WARNING  tmu_tilde test statistic used for fit" in caplog.text
         caplog.clear()
 
@@ -86,7 +86,7 @@ def test_no_poi_test_stats():
     par_bounds = model.config.suggested_bounds()
 
     with pytest.raises(pyhf.exceptions.UnspecifiedPOI) as excinfo:
-        pyhf.infer.test_statistics.qmu(test_poi, data, model, init_pars, par_bounds)
+        pyhf.infer.test_statistics.qmu(test_poi, data, model, init_pars, par_bounds, [])
     assert (
         "No POI is defined. A POI is required for profile likelihood based test statistics."
         in str(excinfo.value)
@@ -94,7 +94,7 @@ def test_no_poi_test_stats():
 
     with pytest.raises(pyhf.exceptions.UnspecifiedPOI) as excinfo:
         pyhf.infer.test_statistics.qmu_tilde(
-            test_poi, data, model, init_pars, par_bounds
+            test_poi, data, model, init_pars, par_bounds, []
         )
     assert (
         "No POI is defined. A POI is required for profile likelihood based test statistics."
@@ -102,7 +102,7 @@ def test_no_poi_test_stats():
     )
 
     with pytest.raises(pyhf.exceptions.UnspecifiedPOI) as excinfo:
-        pyhf.infer.test_statistics.tmu(test_poi, data, model, init_pars, par_bounds)
+        pyhf.infer.test_statistics.tmu(test_poi, data, model, init_pars, par_bounds, [])
     assert (
         "No POI is defined. A POI is required for profile likelihood based test statistics."
         in str(excinfo.value)
@@ -110,7 +110,7 @@ def test_no_poi_test_stats():
 
     with pytest.raises(pyhf.exceptions.UnspecifiedPOI) as excinfo:
         pyhf.infer.test_statistics.tmu_tilde(
-            test_poi, data, model, init_pars, par_bounds
+            test_poi, data, model, init_pars, par_bounds, []
         )
     assert (
         "No POI is defined. A POI is required for profile likelihood based test statistics."

From 680502b482ffe070dfe17b6910c74d753f088287 Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Thu, 3 Sep 2020 20:57:05 -0400
Subject: [PATCH 19/24] update a test and provide a fixed_params to deal with
 the pdf issue

---
 src/pyhf/infer/calculators.py | 14 +++++++++++---
 tests/test_infer.py           |  2 +-
 2 files changed, 12 insertions(+), 4 deletions(-)

diff --git a/src/pyhf/infer/calculators.py b/src/pyhf/infer/calculators.py
index 5f7e53be58..7f9b0a8261 100644
--- a/src/pyhf/infer/calculators.py
+++ b/src/pyhf/infer/calculators.py
@@ -122,7 +122,14 @@ class AsymptoticCalculator(object):
     """The Asymptotic Calculator."""
 
     def __init__(
-        self, data, pdf, init_pars=None, par_bounds=None, fixed_vals=None, qtilde=False
+        self,
+        data,
+        pdf,
+        init_pars=None,
+        par_bounds=None,
+        fixed_params=None,
+        fixed_vals=None,
+        qtilde=False,
     ):
         """
         Asymptotic Calculator.
@@ -132,7 +139,8 @@ def __init__(
             pdf (~pyhf.pdf.Model): The statistical model adhering to the schema ``model.json``.
             init_pars (`tensor`): The initial parameter values to be used for fitting.
             par_bounds (`tensor`): The parameter value bounds to be used for fitting.
-            fixed_vals (`tensor`): Parameters to be held constant in the fit.
+            fixed_params (`tensor`): A list of booleans for each parameter on whether it should be fixed in the fit or not.
+            fixed_vals (list of tuples): The fixed parameters and fixed values to be used for fitting.
             qtilde (`bool`): Whether to use qtilde as the test statistic.
 
         Returns:
@@ -148,7 +156,7 @@ def __init__(
         model_fixed_vals = [
             (index, init)
             for index, (init, is_fixed) in enumerate(
-                zip(init_pars, pdf.config.suggested_fixed())
+                zip(init_pars, fixed_params or pdf.config.suggested_fixed())
             )
             if is_fixed
         ]
diff --git a/tests/test_infer.py b/tests/test_infer.py
index 2a2b4c9a2b..291e403702 100644
--- a/tests/test_infer.py
+++ b/tests/test_infer.py
@@ -187,7 +187,7 @@ def logpdf(self, pars, data):
 @pytest.mark.parametrize("qtilde", [True, False])
 def test_calculator_distributions_without_teststatistic(qtilde):
     calc = pyhf.infer.AsymptoticCalculator(
-        [0.0], {}, [1.0], [(0.0, 10.0)], qtilde=qtilde
+        [0.0], {}, [1.0], [(0.0, 10.0)], [False], qtilde=qtilde
     )
     with pytest.raises(RuntimeError):
         calc.distributions(1.0)

From d6831b6e4e59b3cd3e3d1cf415964d2a5dfe41e1 Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Thu, 3 Sep 2020 21:03:13 -0400
Subject: [PATCH 20/24] scipy is able to minimize better so bump to 1 maxiter
 to force it to fail

---
 tests/test_scripts.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/tests/test_scripts.py b/tests/test_scripts.py
index ce74887d1b..3a2ff3fca4 100644
--- a/tests/test_scripts.py
+++ b/tests/test_scripts.py
@@ -238,7 +238,7 @@ def test_testpoi(tmpdir, script_runner):
     'optimizer', ['scipy', 'minuit', 'scipy_optimizer', 'minuit_optimizer']
 )
 @pytest.mark.parametrize(
-    'opts,success', [(['maxiter=1000'], True), (['maxiter=10'], False)]
+    'opts,success', [(['maxiter=1000'], True), (['maxiter=1'], False)]
 )
 def test_cls_optimizer(tmpdir, script_runner, optimizer, opts, success):
     temp = tmpdir.join("parsed_output.json")

From 91847be9229d797e4e75fa4149ac9adbb4851505 Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Fri, 4 Sep 2020 10:55:50 -0400
Subject: [PATCH 21/24] switch to fixed_params for public-facing calls in
 pyhf.infer

---
 src/pyhf/infer/__init__.py        | 24 ++++-----------
 src/pyhf/infer/calculators.py     | 32 +++++---------------
 src/pyhf/infer/mle.py             | 27 +++++------------
 src/pyhf/infer/test_statistics.py | 49 ++++++++++++++++---------------
 4 files changed, 47 insertions(+), 85 deletions(-)

diff --git a/src/pyhf/infer/__init__.py b/src/pyhf/infer/__init__.py
index f9f6e2570a..ce64eb819b 100644
--- a/src/pyhf/infer/__init__.py
+++ b/src/pyhf/infer/__init__.py
@@ -11,7 +11,7 @@ def hypotest(
     pdf,
     init_pars=None,
     par_bounds=None,
-    fixed_vals=None,
+    fixed_params=None,
     qtilde=False,
     **kwargs,
 ):
@@ -39,9 +39,9 @@ def hypotest(
         poi_test (Number or Tensor): The value of the parameter of interest (POI)
         data (Number or Tensor): The data considered
         pdf (~pyhf.pdf.Model): The statistical model adhering to the schema ``model.json``
-        init_pars (Array or Tensor): The initial parameter values to be used for minimization
-        par_bounds (Array or Tensor): The parameter value bounds to be used for minimization
-        fixed_vals (list of tuples): Parameters to be held constant and their value
+        init_pars (`tensor`): The initial parameter values to be used for minimization
+        par_bounds (`tensor`): The parameter value bounds to be used for minimization
+        fixed_params (`tensor`): Whether to fix the parameter to the init_pars value during minimization
         qtilde (Bool): When ``True`` perform the calculation using the alternative
          test statistic, :math:`\tilde{q}_{\mu}`, as defined under the Wald
          approximation in Equation (62) of :xref:`arXiv:1007.1727`.
@@ -126,22 +126,10 @@ def hypotest(
     """
     init_pars = init_pars or pdf.config.suggested_init()
     par_bounds = par_bounds or pdf.config.suggested_bounds()
-    # get fixed vals from the model
-    model_fixed_vals = [
-        (index, init)
-        for index, (init, is_fixed) in enumerate(
-            zip(init_pars, pdf.config.suggested_fixed())
-        )
-        if is_fixed
-    ]
-    # add user-defined ones at the end
-    fixed_vals = model_fixed_vals + (fixed_vals or [])
-
-    # de-dupe and use last-appended result for each index
-    fixed_vals = list(dict(fixed_vals).items())
+    fixed_params = fixed_params or pdf.config.suggested_fixed()
 
     calc = AsymptoticCalculator(
-        data, pdf, init_pars, par_bounds, fixed_vals, qtilde=qtilde
+        data, pdf, init_pars, par_bounds, fixed_params, qtilde=qtilde
     )
     teststat = calc.teststatistic(poi_test)
     sig_plus_bkg_distribution, b_only_distribution = calc.distributions(poi_test)
diff --git a/src/pyhf/infer/calculators.py b/src/pyhf/infer/calculators.py
index 7f9b0a8261..fd961e05f3 100644
--- a/src/pyhf/infer/calculators.py
+++ b/src/pyhf/infer/calculators.py
@@ -12,7 +12,7 @@
 from .test_statistics import qmu, qmu_tilde
 
 
-def generate_asimov_data(asimov_mu, data, pdf, init_pars, par_bounds, fixed_vals):
+def generate_asimov_data(asimov_mu, data, pdf, init_pars, par_bounds, fixed_params):
     """
     Compute Asimov Dataset (expected yields at best-fit values) for a given POI value.
 
@@ -22,14 +22,14 @@ def generate_asimov_data(asimov_mu, data, pdf, init_pars, par_bounds, fixed_vals
         pdf (~pyhf.pdf.Model): The statistical model adhering to the schema ``model.json``.
         init_pars (`tensor`): The initial parameter values to be used for fitting.
         par_bounds (`tensor`): The parameter value bounds to be used for fitting.
-        fixed_vals (`tensor`): Parameters to be held constant in the fit.
+        fixed_params (`tensor`): Parameters to be held constant in the fit.
 
     Returns:
         Tensor: The Asimov dataset.
 
     """
     bestfit_nuisance_asimov = fixed_poi_fit(
-        asimov_mu, data, pdf, init_pars, par_bounds, fixed_vals
+        asimov_mu, data, pdf, init_pars, par_bounds, fixed_params
     )
     return pdf.expected_data(bestfit_nuisance_asimov)
 
@@ -128,7 +128,6 @@ def __init__(
         init_pars=None,
         par_bounds=None,
         fixed_params=None,
-        fixed_vals=None,
         qtilde=False,
     ):
         """
@@ -139,8 +138,7 @@ def __init__(
             pdf (~pyhf.pdf.Model): The statistical model adhering to the schema ``model.json``.
             init_pars (`tensor`): The initial parameter values to be used for fitting.
             par_bounds (`tensor`): The parameter value bounds to be used for fitting.
-            fixed_params (`tensor`): A list of booleans for each parameter on whether it should be fixed in the fit or not.
-            fixed_vals (list of tuples): The fixed parameters and fixed values to be used for fitting.
+            fixed_params (`tensor`): Whether to fix the parameter to the init_pars value during minimization
             qtilde (`bool`): Whether to use qtilde as the test statistic.
 
         Returns:
@@ -151,22 +149,8 @@ def __init__(
         self.pdf = pdf
         self.init_pars = init_pars or pdf.config.suggested_init()
         self.par_bounds = par_bounds or pdf.config.suggested_bounds()
+        self.fixed_params = fixed_params or pdf.config.suggested_fixed()
 
-        # get fixed vals from the model
-        model_fixed_vals = [
-            (index, init)
-            for index, (init, is_fixed) in enumerate(
-                zip(init_pars, fixed_params or pdf.config.suggested_fixed())
-            )
-            if is_fixed
-        ]
-        # add user-defined ones at the end
-        fixed_vals = model_fixed_vals + (fixed_vals or [])
-
-        # de-dupe and use last-appended result for each index
-        fixed_vals = list(dict(fixed_vals).items())
-
-        self.fixed_vals = fixed_vals
         self.qtilde = qtilde
         self.sqrtqmuA_v = None
 
@@ -208,7 +192,7 @@ def teststatistic(self, poi_test):
             self.pdf,
             self.init_pars,
             self.par_bounds,
-            self.fixed_vals,
+            self.fixed_params,
         )
         sqrtqmu_v = tensorlib.sqrt(qmu_v)
 
@@ -219,7 +203,7 @@ def teststatistic(self, poi_test):
             self.pdf,
             self.init_pars,
             self.par_bounds,
-            self.fixed_vals,
+            self.fixed_params,
         )
         qmuA_v = teststat_func(
             poi_test,
@@ -227,7 +211,7 @@ def teststatistic(self, poi_test):
             self.pdf,
             self.init_pars,
             self.par_bounds,
-            self.fixed_vals,
+            self.fixed_params,
         )
         self.sqrtqmuA_v = tensorlib.sqrt(qmuA_v)
 
diff --git a/src/pyhf/infer/mle.py b/src/pyhf/infer/mle.py
index b5cdb8a803..8a8cff69aa 100644
--- a/src/pyhf/infer/mle.py
+++ b/src/pyhf/infer/mle.py
@@ -47,7 +47,7 @@ def twice_nll(pars, data, pdf):
     return -2 * pdf.logpdf(pars, data)
 
 
-def fit(data, pdf, init_pars=None, par_bounds=None, fixed_vals=None, **kwargs):
+def fit(data, pdf, init_pars=None, par_bounds=None, fixed_params=None, **kwargs):
     r"""
     Run a unconstrained maximum likelihood fit.
     This is done by minimizing the objective function :func:`~pyhf.infer.mle.twice_nll`
@@ -96,20 +96,14 @@ def fit(data, pdf, init_pars=None, par_bounds=None, fixed_vals=None, **kwargs):
     _, opt = get_backend()
     init_pars = init_pars or pdf.config.suggested_init()
     par_bounds = par_bounds or pdf.config.suggested_bounds()
+    fixed_params = fixed_params or pdf.config.suggested_fixed()
 
     # get fixed vals from the model
-    model_fixed_vals = [
+    fixed_vals = [
         (index, init)
-        for index, (init, is_fixed) in enumerate(
-            zip(init_pars, pdf.config.suggested_fixed())
-        )
+        for index, (init, is_fixed) in enumerate(zip(init_pars, fixed_params))
         if is_fixed
     ]
-    # add user-defined ones at the end
-    fixed_vals = model_fixed_vals + (fixed_vals or [])
-
-    # de-dupe and use last-appended result for each index
-    fixed_vals = list(dict(fixed_vals).items())
 
     return opt.minimize(
         twice_nll, data, pdf, init_pars, par_bounds, fixed_vals, **kwargs
@@ -117,7 +111,7 @@ def fit(data, pdf, init_pars=None, par_bounds=None, fixed_vals=None, **kwargs):
 
 
 def fixed_poi_fit(
-    poi_val, data, pdf, init_pars=None, par_bounds=None, fixed_vals=None, **kwargs
+    poi_val, data, pdf, init_pars=None, par_bounds=None, fixed_params=None, **kwargs
 ):
     r"""
     Run a maximum likelihood fit with the POI value fixed.
@@ -175,21 +169,16 @@ def fixed_poi_fit(
     _, opt = get_backend()
     init_pars = init_pars or pdf.config.suggested_init()
     par_bounds = par_bounds or pdf.config.suggested_bounds()
+    fixed_params = fixed_params or pdf.config.suggested_fixed()
 
     # get fixed vals from the model
-    model_fixed_vals = [
+    fixed_vals = [
         (index, init)
-        for index, (init, is_fixed) in enumerate(
-            zip(init_pars, pdf.config.suggested_fixed())
-        )
+        for index, (init, is_fixed) in enumerate(zip(init_pars, fixed_params))
         if is_fixed
     ]
-    # add user-defined ones at the end
-    fixed_vals = model_fixed_vals + (fixed_vals or [])
-
     # add the fixed POI
     fixed_vals = fixed_vals + [(pdf.config.poi_index, poi_val)]
-
     # de-dupe and use last-appended result for each index
     fixed_vals = list(dict(fixed_vals).items())
 
diff --git a/src/pyhf/infer/test_statistics.py b/src/pyhf/infer/test_statistics.py
index b4d03182a2..0f122f152f 100644
--- a/src/pyhf/infer/test_statistics.py
+++ b/src/pyhf/infer/test_statistics.py
@@ -7,7 +7,7 @@
 log = logging.getLogger(__name__)
 
 
-def _qmu_like(mu, data, pdf, init_pars, par_bounds, fixed_vals):
+def _qmu_like(mu, data, pdf, init_pars, par_bounds, fixed_params):
     """
     Clipped version of _tmu_like where the returned test statistic
     is 0 if muhat > 0 else tmu_like_stat.
@@ -17,7 +17,7 @@ def _qmu_like(mu, data, pdf, init_pars, par_bounds, fixed_vals):
     """
     tensorlib, optimizer = get_backend()
     tmu_like_stat, (_, muhatbhat) = _tmu_like(
-        mu, data, pdf, init_pars, par_bounds, fixed_vals, return_fitted_pars=True
+        mu, data, pdf, init_pars, par_bounds, fixed_params, return_fitted_pars=True
     )
     qmu_like_stat = tensorlib.where(
         muhatbhat[pdf.config.poi_index] > mu, tensorlib.astensor(0.0), tmu_like_stat
@@ -26,7 +26,7 @@ def _qmu_like(mu, data, pdf, init_pars, par_bounds, fixed_vals):
 
 
 def _tmu_like(
-    mu, data, pdf, init_pars, par_bounds, fixed_vals, return_fitted_pars=False
+    mu, data, pdf, init_pars, par_bounds, fixed_params, return_fitted_pars=False
 ):
     """
     Basic Profile Likelihood test statistic.
@@ -36,10 +36,10 @@ def _tmu_like(
     """
     tensorlib, optimizer = get_backend()
     mubhathat, fixed_poi_fit_lhood_val = fixed_poi_fit(
-        mu, data, pdf, init_pars, par_bounds, fixed_vals, return_fitted_val=True
+        mu, data, pdf, init_pars, par_bounds, fixed_params, return_fitted_val=True
     )
     muhatbhat, unconstrained_fit_lhood_val = fit(
-        data, pdf, init_pars, par_bounds, fixed_vals, return_fitted_val=True
+        data, pdf, init_pars, par_bounds, fixed_params, return_fitted_val=True
     )
     log_likelihood_ratio = fixed_poi_fit_lhood_val - unconstrained_fit_lhood_val
     tmu_like_stat = tensorlib.astensor(
@@ -50,7 +50,7 @@ def _tmu_like(
     return tmu_like_stat
 
 
-def qmu(mu, data, pdf, init_pars, par_bounds, fixed_vals):
+def qmu(mu, data, pdf, init_pars, par_bounds, fixed_params):
     r"""
     The test statistic, :math:`q_{\mu}`, for establishing an upper
     limit on the strength parameter, :math:`\mu`, as defiend in
@@ -84,8 +84,8 @@ def qmu(mu, data, pdf, init_pars, par_bounds, fixed_vals):
         >>> init_pars = model.config.suggested_init()
         >>> par_bounds = model.config.suggested_bounds()
         >>> par_bounds[model.config.poi_index] = [-10.0, 10.0]
-        >>> fixed_vals = []
-        >>> pyhf.infer.test_statistics.qmu(test_mu, data, model, init_pars, par_bounds, [])
+        >>> fixed_params = model.config.suggested_fixed()
+        >>> pyhf.infer.test_statistics.qmu(test_mu, data, model, init_pars, par_bounds, fixed_params)
         array(3.9549891)
 
     Args:
@@ -94,7 +94,7 @@ def qmu(mu, data, pdf, init_pars, par_bounds, fixed_vals):
         pdf (~pyhf.pdf.Model): The HistFactory statistical model used in the likelihood ratio calculation
         init_pars (`list`): Values to initialize the model parameters at for the fit
         par_bounds (`list` of `list`\s or `tuple`\s): The extrema of values the model parameters are allowed to reach in the fit
-        fixed_vals (`list`): Parameters held constant in the fit
+        fixed_params (`list`): Parameters held constant in the fit
 
     Returns:
         Float: The calculated test statistic, :math:`q_{\mu}`
@@ -108,10 +108,10 @@ def qmu(mu, data, pdf, init_pars, par_bounds, fixed_vals):
             'qmu test statistic used for fit configuration with POI bounded at zero.\n'
             + 'Use the qmu_tilde test statistic (pyhf.infer.test_statistics.qmu_tilde) instead.'
         )
-    return _qmu_like(mu, data, pdf, init_pars, par_bounds, fixed_vals)
+    return _qmu_like(mu, data, pdf, init_pars, par_bounds, fixed_params)
 
 
-def qmu_tilde(mu, data, pdf, init_pars, par_bounds, fixed_vals):
+def qmu_tilde(mu, data, pdf, init_pars, par_bounds, fixed_params):
     r"""
     The test statistic, :math:`\tilde{q}_{\mu}`, for establishing an upper
     limit on the strength parameter, :math:`\mu`, for models with
@@ -150,7 +150,8 @@ def qmu_tilde(mu, data, pdf, init_pars, par_bounds, fixed_vals):
         >>> test_mu = 1.0
         >>> init_pars = model.config.suggested_init()
         >>> par_bounds = model.config.suggested_bounds()
-        >>> pyhf.infer.test_statistics.qmu_tilde(test_mu, data, model, init_pars, par_bounds, [])
+        >>> fixed_params = model.config.suggested_fixed()
+        >>> pyhf.infer.test_statistics.qmu_tilde(test_mu, data, model, init_pars, par_bounds, fixed_params)
         array(3.93824492)
 
     Args:
@@ -159,7 +160,7 @@ def qmu_tilde(mu, data, pdf, init_pars, par_bounds, fixed_vals):
         pdf (~pyhf.pdf.Model): The statistical model adhering to the schema model.json
         init_pars (`list`): Values to initialize the model parameters at for the fit
         par_bounds (`list` of `list`\s or `tuple`\s): The extrema of values the model parameters are allowed to reach in the fit
-        fixed_vals (`list`): Parameters held constant in the fit
+        fixed_params (`list`): Parameters held constant in the fit
 
     Returns:
         Float: The calculated test statistic, :math:`\tilde{q}_{\mu}`
@@ -173,10 +174,10 @@ def qmu_tilde(mu, data, pdf, init_pars, par_bounds, fixed_vals):
             'qmu_tilde test statistic used for fit configuration with POI not bounded at zero.\n'
             + 'Use the qmu test statistic (pyhf.infer.test_statistics.qmu) instead.'
         )
-    return _qmu_like(mu, data, pdf, init_pars, par_bounds, fixed_vals)
+    return _qmu_like(mu, data, pdf, init_pars, par_bounds, fixed_params)
 
 
-def tmu(mu, data, pdf, init_pars, par_bounds, fixed_vals):
+def tmu(mu, data, pdf, init_pars, par_bounds, fixed_params):
     r"""
     The test statistic, :math:`t_{\mu}`, for establishing a two-sided
     interval on the strength parameter, :math:`\mu`, as defiend in Equation (8)
@@ -204,8 +205,8 @@ def tmu(mu, data, pdf, init_pars, par_bounds, fixed_vals):
         >>> init_pars = model.config.suggested_init()
         >>> par_bounds = model.config.suggested_bounds()
         >>> par_bounds[model.config.poi_index] = [-10.0, 10.0]
-        >>> fixed_vals = []
-        >>> pyhf.infer.test_statistics.tmu(test_mu, data, model, init_pars, par_bounds, [])
+        >>> fixed_params = model.config.suggested_fixed()
+        >>> pyhf.infer.test_statistics.tmu(test_mu, data, model, init_pars, par_bounds, fixed_params)
         array(3.9549891)
 
     Args:
@@ -214,7 +215,7 @@ def tmu(mu, data, pdf, init_pars, par_bounds, fixed_vals):
         pdf (~pyhf.pdf.Model): The statistical model adhering to the schema model.json
         init_pars (`list`): Values to initialize the model parameters at for the fit
         par_bounds (`list` of `list`\s or `tuple`\s): The extrema of values the model parameters are allowed to reach in the fit
-        fixed_vals (`list`): Parameters held constant in the fit
+        fixed_params (`list`): Parameters held constant in the fit
 
     Returns:
         Float: The calculated test statistic, :math:`t_{\mu}`
@@ -228,10 +229,10 @@ def tmu(mu, data, pdf, init_pars, par_bounds, fixed_vals):
             'tmu test statistic used for fit configuration with POI bounded at zero.\n'
             + 'Use the tmu_tilde test statistic (pyhf.infer.test_statistics.tmu_tilde) instead.'
         )
-    return _tmu_like(mu, data, pdf, init_pars, par_bounds, fixed_vals)
+    return _tmu_like(mu, data, pdf, init_pars, par_bounds, fixed_params)
 
 
-def tmu_tilde(mu, data, pdf, init_pars, par_bounds, fixed_vals):
+def tmu_tilde(mu, data, pdf, init_pars, par_bounds, fixed_params):
     r"""
     The test statistic, :math:`\tilde{t}_{\mu}`, for establishing a two-sided
     interval on the strength parameter, :math:`\mu`, for models with
@@ -264,8 +265,8 @@ def tmu_tilde(mu, data, pdf, init_pars, par_bounds, fixed_vals):
         >>> test_mu = 1.0
         >>> init_pars = model.config.suggested_init()
         >>> par_bounds = model.config.suggested_bounds()
-        >>> fixed_vals = []
-        >>> pyhf.infer.test_statistics.tmu_tilde(test_mu, data, model, init_pars, par_bounds, [])
+        >>> fixed_params = model.config.suggested_fixed()
+        >>> pyhf.infer.test_statistics.tmu_tilde(test_mu, data, model, init_pars, par_bounds, fixed_params)
         array(3.93824492)
 
     Args:
@@ -274,7 +275,7 @@ def tmu_tilde(mu, data, pdf, init_pars, par_bounds, fixed_vals):
         pdf (~pyhf.pdf.Model): The statistical model adhering to the schema model.json
         init_pars (`list`): Values to initialize the model parameters at for the fit
         par_bounds (`list` of `list`\s or `tuple`\s): The extrema of values the model parameters are allowed to reach in the fit
-        fixed_vals (`list`): Parameters held constant in the fit
+        fixed_params (`list`): Parameters held constant in the fit
 
     Returns:
         Float: The calculated test statistic, :math:`\tilde{t}_{\mu}`
@@ -288,4 +289,4 @@ def tmu_tilde(mu, data, pdf, init_pars, par_bounds, fixed_vals):
             'tmu_tilde test statistic used for fit configuration with POI not bounded at zero.\n'
             + 'Use the tmu test statistic (pyhf.infer.test_statistics.tmu) instead.'
         )
-    return _tmu_like(mu, data, pdf, init_pars, par_bounds, fixed_vals)
+    return _tmu_like(mu, data, pdf, init_pars, par_bounds, fixed_params)

From 75fff6082e3ae7de8de71474648b49f3c5ace4cf Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Fri, 4 Sep 2020 11:15:04 -0400
Subject: [PATCH 22/24] update tests

---
 tests/test_backend_consistency.py |  2 +-
 tests/test_teststats.py           | 34 +++++++++++++++++++++++--------
 2 files changed, 27 insertions(+), 9 deletions(-)

diff --git a/tests/test_backend_consistency.py b/tests/test_backend_consistency.py
index b42f7afaed..9831560d86 100644
--- a/tests/test_backend_consistency.py
+++ b/tests/test_backend_consistency.py
@@ -120,7 +120,7 @@ def test_hypotest_qmu_tilde(
             pdf,
             pdf.config.suggested_init(),
             pdf.config.suggested_bounds(),
-            [],
+            pdf.config.suggested_fixed(),
         )
         test_statistic.append(qmu_tilde)
 
diff --git a/tests/test_teststats.py b/tests/test_teststats.py
index aca8f9f361..70090380c5 100644
--- a/tests/test_teststats.py
+++ b/tests/test_teststats.py
@@ -10,9 +10,12 @@ def test_qmu(caplog):
     data = [9] + model.config.auxdata
     init_pars = model.config.suggested_init()
     par_bounds = model.config.suggested_bounds()
+    fixed_params = model.config.suggested_fixed()
 
     with caplog.at_level(logging.WARNING, "pyhf.infer.test_statistics"):
-        pyhf.infer.test_statistics.qmu(mu, data, model, init_pars, par_bounds, [])
+        pyhf.infer.test_statistics.qmu(
+            mu, data, model, init_pars, par_bounds, fixed_params
+        )
         assert "WARNING  qmu test statistic used for fit" in caplog.text
         caplog.clear()
 
@@ -23,10 +26,13 @@ def test_qmu_tilde(caplog):
     data = [9] + model.config.auxdata
     init_pars = model.config.suggested_init()
     par_bounds = model.config.suggested_bounds()
+    fixed_params = model.config.suggested_fixed()
 
     par_bounds[model.config.poi_index] = [-10, 10]
     with caplog.at_level(logging.WARNING, "pyhf.infer.test_statistics"):
-        pyhf.infer.test_statistics.qmu_tilde(mu, data, model, init_pars, par_bounds, [])
+        pyhf.infer.test_statistics.qmu_tilde(
+            mu, data, model, init_pars, par_bounds, fixed_params
+        )
         assert "WARNING  qmu_tilde test statistic used for fit" in caplog.text
         caplog.clear()
 
@@ -37,8 +43,12 @@ def test_tmu(caplog):
     data = [9] + model.config.auxdata
     init_pars = model.config.suggested_init()
     par_bounds = model.config.suggested_bounds()
+    fixed_params = model.config.suggested_fixed()
+
     with caplog.at_level(logging.WARNING, "pyhf.infer.test_statistics"):
-        pyhf.infer.test_statistics.tmu(mu, data, model, init_pars, par_bounds, [])
+        pyhf.infer.test_statistics.tmu(
+            mu, data, model, init_pars, par_bounds, fixed_params
+        )
         assert "WARNING  tmu test statistic used for fit" in caplog.text
         caplog.clear()
 
@@ -49,10 +59,13 @@ def test_tmu_tilde(caplog):
     data = [9] + model.config.auxdata
     init_pars = model.config.suggested_init()
     par_bounds = model.config.suggested_bounds()
+    fixed_params = model.config.suggested_fixed()
 
     par_bounds[model.config.poi_index] = [-10, 10]
     with caplog.at_level(logging.WARNING, "pyhf.infer.test_statistics"):
-        pyhf.infer.test_statistics.tmu_tilde(mu, data, model, init_pars, par_bounds, [])
+        pyhf.infer.test_statistics.tmu_tilde(
+            mu, data, model, init_pars, par_bounds, fixed_params
+        )
         assert "WARNING  tmu_tilde test statistic used for fit" in caplog.text
         caplog.clear()
 
@@ -84,9 +97,12 @@ def test_no_poi_test_stats():
     data = [12] + model.config.auxdata
     init_pars = model.config.suggested_init()
     par_bounds = model.config.suggested_bounds()
+    fixed_params = model.config.suggested_fixed()
 
     with pytest.raises(pyhf.exceptions.UnspecifiedPOI) as excinfo:
-        pyhf.infer.test_statistics.qmu(test_poi, data, model, init_pars, par_bounds, [])
+        pyhf.infer.test_statistics.qmu(
+            test_poi, data, model, init_pars, par_bounds, fixed_params
+        )
     assert (
         "No POI is defined. A POI is required for profile likelihood based test statistics."
         in str(excinfo.value)
@@ -94,7 +110,7 @@ def test_no_poi_test_stats():
 
     with pytest.raises(pyhf.exceptions.UnspecifiedPOI) as excinfo:
         pyhf.infer.test_statistics.qmu_tilde(
-            test_poi, data, model, init_pars, par_bounds, []
+            test_poi, data, model, init_pars, par_bounds, fixed_params
         )
     assert (
         "No POI is defined. A POI is required for profile likelihood based test statistics."
@@ -102,7 +118,9 @@ def test_no_poi_test_stats():
     )
 
     with pytest.raises(pyhf.exceptions.UnspecifiedPOI) as excinfo:
-        pyhf.infer.test_statistics.tmu(test_poi, data, model, init_pars, par_bounds, [])
+        pyhf.infer.test_statistics.tmu(
+            test_poi, data, model, init_pars, par_bounds, fixed_params
+        )
     assert (
         "No POI is defined. A POI is required for profile likelihood based test statistics."
         in str(excinfo.value)
@@ -110,7 +128,7 @@ def test_no_poi_test_stats():
 
     with pytest.raises(pyhf.exceptions.UnspecifiedPOI) as excinfo:
         pyhf.infer.test_statistics.tmu_tilde(
-            test_poi, data, model, init_pars, par_bounds, []
+            test_poi, data, model, init_pars, par_bounds, fixed_params
         )
     assert (
         "No POI is defined. A POI is required for profile likelihood based test statistics."

From a3cbe9f67aa1c34784508dda0affb62ef5ae47f8 Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Fri, 4 Sep 2020 11:54:42 -0400
Subject: [PATCH 23/24] fix up notebooks

---
 docs/examples/notebooks/ImpactPlot.ipynb | 11 ++++++++++-
 docs/examples/notebooks/pullplot.ipynb   | 11 ++++++++++-
 2 files changed, 20 insertions(+), 2 deletions(-)

diff --git a/docs/examples/notebooks/ImpactPlot.ipynb b/docs/examples/notebooks/ImpactPlot.ipynb
index 9d8e6aa56e..e6f08bf467 100644
--- a/docs/examples/notebooks/ImpactPlot.ipynb
+++ b/docs/examples/notebooks/ImpactPlot.ipynb
@@ -82,8 +82,17 @@
     "    _, model, data = make_model([\"CRtt_meff\"])\n",
     "\n",
     "    pyhf.set_backend(\"numpy\", pyhf.optimize.minuit_optimizer(verbose=True))\n",
+    "    \n",
+    "    constraints = constraints or []\n",
+    "    init_pars = model.config.suggested_init()\n",
+    "    fixed_params = model.config.suggested_fixed()\n",
+    "    \n",
+    "    for idx,fixed_val in constraints:\n",
+    "        init_pars[idx] = fixed_val\n",
+    "        fixed_params[idx] = True\n",
+    "    \n",
     "    result = pyhf.infer.mle.fit(\n",
-    "        data, model, fixed_vals=constraints, return_uncertainties=True\n",
+    "        data, model, init_pars=init_pars, fixed_params=fixed_params, return_uncertainties=True\n",
     "    )\n",
     "    bestfit = result[:, 0]\n",
     "    errors = result[:, 1]\n",
diff --git a/docs/examples/notebooks/pullplot.ipynb b/docs/examples/notebooks/pullplot.ipynb
index 3b376dbb8a..67293991cc 100644
--- a/docs/examples/notebooks/pullplot.ipynb
+++ b/docs/examples/notebooks/pullplot.ipynb
@@ -72,8 +72,17 @@
     "    _, model, data = make_model([\"CRtt_meff\"])\n",
     "\n",
     "    pyhf.set_backend(\"numpy\", pyhf.optimize.minuit_optimizer(verbose=True))\n",
+    "    \n",
+    "    constraints = constraints or []\n",
+    "    init_pars = model.config.suggested_init()\n",
+    "    fixed_params = model.config.suggested_fixed()\n",
+    "    \n",
+    "    for idx,fixed_val in constraints:\n",
+    "        init_pars[idx] = fixed_val\n",
+    "        fixed_params[idx] = True\n",
+    "    \n",
     "    result = pyhf.infer.mle.fit(\n",
-    "        data, model, fixed_vals=constraints, return_uncertainties=True\n",
+    "        data, model, init_pars=init_pars, fixed_params=fixed_params, return_uncertainties=True\n",
     "    )\n",
     "    bestfit = result[:, 0]\n",
     "    errors = result[:, 1]\n",

From 3364a79722287131c40dec65a77afa104cce64dd Mon Sep 17 00:00:00 2001
From: Giordon Stark <kratsg@gmail.com>
Date: Fri, 4 Sep 2020 11:07:17 -0400
Subject: [PATCH 24/24] update fixed_poi_fit() to call fit() essentially

---
 src/pyhf/infer/mle.py | 32 ++++++++------------------------
 1 file changed, 8 insertions(+), 24 deletions(-)

diff --git a/src/pyhf/infer/mle.py b/src/pyhf/infer/mle.py
index 8a8cff69aa..a5c544ae26 100644
--- a/src/pyhf/infer/mle.py
+++ b/src/pyhf/infer/mle.py
@@ -49,7 +49,7 @@ def twice_nll(pars, data, pdf):
 
 def fit(data, pdf, init_pars=None, par_bounds=None, fixed_params=None, **kwargs):
     r"""
-    Run a unconstrained maximum likelihood fit.
+    Run a maximum likelihood fit.
     This is done by minimizing the objective function :func:`~pyhf.infer.mle.twice_nll`
     of the model parameters given the observed data.
     This is used to produce the maximal likelihood :math:`L\left(\hat{\mu}, \hat{\boldsymbol{\theta}}\right)`
@@ -87,6 +87,7 @@ def fit(data, pdf, init_pars=None, par_bounds=None, fixed_params=None, **kwargs)
         pdf (~pyhf.pdf.Model): The statistical model adhering to the schema model.json
         init_pars (`list`): Values to initialize the model parameters at for the fit
         par_bounds (`list` of `list`\s or `tuple`\s): The extrema of values the model parameters are allowed to reach in the fit
+        fixed_params (`list`): Parameters to be held constant in the fit.
         kwargs: Keyword arguments passed through to the optimizer API
 
     Returns:
@@ -155,6 +156,7 @@ def fixed_poi_fit(
         pdf (~pyhf.pdf.Model): The statistical model adhering to the schema model.json
         init_pars (`list`): Values to initialize the model parameters at for the fit
         par_bounds (`list` of `list`\s or `tuple`\s): The extrema of values the model parameters are allowed to reach in the fit
+        fixed_params (`list`): Parameters to be held constant in the fit.
         kwargs: Keyword arguments passed through to the optimizer API
 
     Returns:
@@ -166,28 +168,10 @@ def fixed_poi_fit(
             'No POI is defined. A POI is required to fit with a fixed POI.'
         )
 
-    _, opt = get_backend()
-    init_pars = init_pars or pdf.config.suggested_init()
-    par_bounds = par_bounds or pdf.config.suggested_bounds()
-    fixed_params = fixed_params or pdf.config.suggested_fixed()
+    init_pars = [*(init_pars or pdf.config.suggested_init())]
+    fixed_params = [*(fixed_params or pdf.config.suggested_fixed())]
 
-    # get fixed vals from the model
-    fixed_vals = [
-        (index, init)
-        for index, (init, is_fixed) in enumerate(zip(init_pars, fixed_params))
-        if is_fixed
-    ]
-    # add the fixed POI
-    fixed_vals = fixed_vals + [(pdf.config.poi_index, poi_val)]
-    # de-dupe and use last-appended result for each index
-    fixed_vals = list(dict(fixed_vals).items())
+    init_pars[pdf.config.poi_index] = poi_val
+    fixed_params[pdf.config.poi_index] = True
 
-    return opt.minimize(
-        twice_nll,
-        data,
-        pdf,
-        init_pars,
-        par_bounds,
-        fixed_vals,
-        **kwargs,
-    )
+    return fit(data, pdf, init_pars, par_bounds, fixed_params, **kwargs)