diff --git a/src/pyhf/constraints.py b/src/pyhf/constraints.py
index 30ef835e79..73b45b05c5 100644
--- a/src/pyhf/constraints.py
+++ b/src/pyhf/constraints.py
@@ -45,7 +45,7 @@ def __init__(self, pdfconfig, batch_size=None):
             if not parset.pdf_type == 'normal':
                 continue
 
-            normal_constraint_data.append(thisauxdata)
+            normal_constraint_data.append(default_backend.astensor(thisauxdata))
 
             # many constraints are defined on a unit gaussian
             # but we reserved the possibility that a paramset
@@ -53,9 +53,11 @@ def __init__(self, pdfconfig, batch_size=None):
             # by the paramset associated to staterror modifiers.
             # Such parsets define a 'sigmas' attribute
             try:
-                normal_constraint_sigmas.append(parset.sigmas)
+                normal_constraint_sigmas.append(default_backend.astensor(parset.sigmas))
             except AttributeError:
-                normal_constraint_sigmas.append([1.0] * len(thisauxdata))
+                normal_constraint_sigmas.append(
+                    default_backend.astensor([1.0] * len(thisauxdata))
+                )
 
         self._normal_data = None
         self._sigmas = None
diff --git a/src/pyhf/modifiers/histosys.py b/src/pyhf/modifiers/histosys.py
index d23e6c1ff3..31c059c68d 100644
--- a/src/pyhf/modifiers/histosys.py
+++ b/src/pyhf/modifiers/histosys.py
@@ -31,11 +31,17 @@ def __init__(self, config):
         self.required_parsets = {}
 
     def collect(self, thismod, nom):
+        default_backend = pyhf.default_backend
         lo_data = thismod['data']['lo_data'] if thismod else nom
         hi_data = thismod['data']['hi_data'] if thismod else nom
         maskval = bool(thismod)
         mask = [maskval] * len(nom)
-        return {'lo_data': lo_data, 'hi_data': hi_data, 'mask': mask, 'nom_data': nom}
+        return {
+            'lo_data': default_backend.astensor(lo_data),
+            'hi_data': default_backend.astensor(hi_data),
+            'mask': default_backend.astensor(mask, dtype='bool'),
+            'nom_data': default_backend.astensor(nom),
+        }
 
     def append(self, key, channel, sample, thismod, defined_samp):
         self.builder_data.setdefault(key, {}).setdefault(sample, {}).setdefault(
diff --git a/src/pyhf/modifiers/shapefactor.py b/src/pyhf/modifiers/shapefactor.py
index 6c65c2e8c9..b0a0abb003 100644
--- a/src/pyhf/modifiers/shapefactor.py
+++ b/src/pyhf/modifiers/shapefactor.py
@@ -142,9 +142,17 @@ def __init__(self, modifiers, pdfconfig, builder_data, batch_size=None):
             for m in keys
         ]
 
-        global_concatenated_bin_indices = [
-            [[j for c in pdfconfig.channels for j in range(pdfconfig.channel_nbins[c])]]
-        ]
+        global_concatenated_bin_indices = default_backend.astensor(
+            [
+                [
+                    [
+                        j
+                        for c in pdfconfig.channels
+                        for j in range(pdfconfig.channel_nbins[c])
+                    ]
+                ]
+            ]
+        )
 
         self._access_field = default_backend.tile(
             global_concatenated_bin_indices,
diff --git a/src/pyhf/modifiers/shapesys.py b/src/pyhf/modifiers/shapesys.py
index 5b5466857f..078db7253b 100644
--- a/src/pyhf/modifiers/shapesys.py
+++ b/src/pyhf/modifiers/shapesys.py
@@ -117,9 +117,17 @@ def __init__(self, modifiers, pdfconfig, builder_data, batch_size=None):
                 for m in keys
             ]
         )
-        global_concatenated_bin_indices = [
-            [[j for c in pdfconfig.channels for j in range(pdfconfig.channel_nbins[c])]]
-        ]
+        global_concatenated_bin_indices = default_backend.astensor(
+            [
+                [
+                    [
+                        j
+                        for c in pdfconfig.channels
+                        for j in range(pdfconfig.channel_nbins[c])
+                    ]
+                ]
+            ]
+        )
 
         self._access_field = default_backend.tile(
             global_concatenated_bin_indices,
diff --git a/src/pyhf/modifiers/staterror.py b/src/pyhf/modifiers/staterror.py
index e028b8f5db..377610010b 100644
--- a/src/pyhf/modifiers/staterror.py
+++ b/src/pyhf/modifiers/staterror.py
@@ -144,9 +144,17 @@ def __init__(self, modifiers, pdfconfig, builder_data, batch_size=None):
                 for m in keys
             ]
         )
-        global_concatenated_bin_indices = [
-            [[j for c in pdfconfig.channels for j in range(pdfconfig.channel_nbins[c])]]
-        ]
+        global_concatenated_bin_indices = default_backend.astensor(
+            [
+                [
+                    [
+                        j
+                        for c in pdfconfig.channels
+                        for j in range(pdfconfig.channel_nbins[c])
+                    ]
+                ]
+            ]
+        )
 
         self._access_field = default_backend.tile(
             global_concatenated_bin_indices,