diff --git a/tests/v1/test_priors.py b/tests/v1/test_priors.py
index ea47e54f..37fd6590 100644
--- a/tests/v1/test_priors.py
+++ b/tests/v1/test_priors.py
@@ -8,7 +8,15 @@
 from scipy.stats import norm
 
 import petab.v1
-from petab.v1 import get_simulation_conditions
+from petab.v1 import (
+    ESTIMATE,
+    MEASUREMENT,
+    OBJECTIVE_PRIOR_TYPE,
+    OBSERVABLE_ID,
+    SIMULATION,
+    get_simulation_conditions,
+    get_simulation_df,
+)
 from petab.v1.priors import priors_to_measurements
 
 
@@ -17,20 +25,29 @@
 )
 def test_priors_to_measurements(problem_id):
     """Test the conversion of priors to measurements."""
+    # setup
     petab_problem_priors: petab.v1.Problem = (
         benchmark_models_petab.get_problem(problem_id)
     )
     petab_problem_priors.visualization_df = None
     assert petab.v1.lint_problem(petab_problem_priors) is False
-
     if problem_id == "Isensee_JCB2018":
         # required to match the stored simulation results below
         petab.v1.flatten_timepoint_specific_output_overrides(
             petab_problem_priors
         )
         assert petab.v1.lint_problem(petab_problem_priors) is False
+
     original_problem = deepcopy(petab_problem_priors)
+    x_scaled_dict = dict(
+        zip(
+            original_problem.x_free_ids,
+            original_problem.x_nominal_free_scaled,
+            strict=True,
+        )
+    )
 
+    # convert priors to measurements
     petab_problem_measurements = priors_to_measurements(petab_problem_priors)
 
     # check that the original problem is not modified
@@ -45,6 +62,7 @@ def test_priors_to_measurements(problem_id):
                 getattr(original_problem, attr)
             )
         ).empty, diff
+
     # check that measurements and observables were added
     assert petab.v1.lint_problem(petab_problem_measurements) is False
     assert (
@@ -59,6 +77,7 @@ def test_priors_to_measurements(problem_id):
         petab_problem_measurements.measurement_df.shape[0]
         > petab_problem_priors.measurement_df.shape[0]
     )
+
     # ensure we didn't introduce any new conditions
     assert len(
         get_simulation_conditions(petab_problem_measurements.measurement_df)
@@ -67,26 +86,40 @@ def test_priors_to_measurements(problem_id):
     # verify that the objective function value is the same
 
     # load/construct the simulation results
-    simulation_df_priors = petab.v1.get_simulation_df(
+    simulation_df_priors = get_simulation_df(
         Path(
             benchmark_models_petab.MODELS_DIR,
             problem_id,
             f"simulatedData_{problem_id}.tsv",
         )
     )
-    simulation_df_measurements = pd.concat(
-        [
-            petab_problem_measurements.measurement_df.rename(
-                columns={petab.v1.MEASUREMENT: petab.v1.SIMULATION}
-            )[
-                petab_problem_measurements.measurement_df[
-                    petab.v1.C.OBSERVABLE_ID
-                ].str.startswith("prior_")
-            ],
-            simulation_df_priors,
+    # for the prior observables, we need to "simulate" the model with the
+    #  nominal parameter values
+    simulated_prior_observables = (
+        petab_problem_measurements.measurement_df.rename(
+            columns={MEASUREMENT: SIMULATION}
+        )[
+            petab_problem_measurements.measurement_df[
+                OBSERVABLE_ID
+            ].str.startswith("prior_")
         ]
     )
 
+    def apply_parameter_values(row):
+        # apply the parameter values to the observable formula for the prior
+        if row[OBSERVABLE_ID].startswith("prior_"):
+            row[SIMULATION] = x_scaled_dict[
+                row[OBSERVABLE_ID].removeprefix("prior_")
+            ]
+        return row
+
+    simulated_prior_observables = simulated_prior_observables.apply(
+        apply_parameter_values, axis=1
+    )
+    simulation_df_measurements = pd.concat(
+        [simulation_df_priors, simulated_prior_observables]
+    )
+
     llh_priors = petab.v1.calculate_llh_for_table(
         petab_problem_priors.measurement_df,
         simulation_df_priors,
@@ -102,10 +135,8 @@ def test_priors_to_measurements(problem_id):
 
     # get prior objective function contribution
     parameter_ids = petab_problem_priors.parameter_df.index.values[
-        (petab_problem_priors.parameter_df[petab.v1.ESTIMATE] == 1)
-        & petab_problem_priors.parameter_df[
-            petab.v1.OBJECTIVE_PRIOR_TYPE
-        ].notna()
+        (petab_problem_priors.parameter_df[ESTIMATE] == 1)
+        & petab_problem_priors.parameter_df[OBJECTIVE_PRIOR_TYPE].notna()
     ]
     priors = petab.v1.get_priors_from_df(
         petab_problem_priors.parameter_df,
@@ -134,4 +165,4 @@ def test_priors_to_measurements(problem_id):
         llh_priors + prior_contrib, llh_measurements, rtol=1e-3, atol=1e-16
     ), (llh_priors + prior_contrib, llh_measurements)
     # check that the tolerance is not too high
-    assert np.abs(prior_contrib) > 1e-3 * np.abs(llh_priors)
+    assert np.abs(prior_contrib) > 1e-8 * np.abs(llh_priors)