feat(backport): Improve warnings for qmu and qmu_tilde for the set POI bounds (#2426)

* Backport PR #2390
* Add Lorenz Gaertner to contributors list.

Co-authored-by: Lorenz Gaertner <[email protected]>

Author: matthewfeickert

docs/contributors.rst

@@ -33,3 +33,4 @@ Contributors include:
 - Beojan Stanislaus
 - Daniel Werner
 - Jonas Rembser
+- Lorenz Gaertner

src/pyhf/infer/test_statistics.py

@@ -134,7 +134,8 @@ def qmu(mu, data, pdf, init_pars, par_bounds, fixed_params, return_fitted_pars=F
     if par_bounds[pdf.config.poi_index][0] == 0:
         log.warning(
             '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.'
+            + 'Use the qmu_tilde test statistic (pyhf.infer.test_statistics.qmu_tilde) instead.\n'
+            + 'If you called this from pyhf.infer.mle or pyhf.infer.hypotest, set test_stat="qtilde".'
         )
     return _qmu_like(
         mu,
@@ -229,7 +230,8 @@ def qmu_tilde(
     if par_bounds[pdf.config.poi_index][0] != 0:
         log.warning(
             '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.'
+            + 'Use the qmu test statistic (pyhf.infer.test_statistics.qmu) instead.\n'
+            + 'If you called this from pyhf.infer.mle or pyhf.infer.hypotest, set test_stat="q".'
         )
     return _qmu_like(
         mu,