Merge pull request #589 from SALib/fix-rsa-cvm-587

Switch to Cramer-von Mises test for RSA, remove normalization (fix #587)

README.rst

@@ -56,7 +56,7 @@ Included methods
 
 * PAWN (`Pianosi and Wagener 2018 <https://dx.doi.org/10.1016/j.envsoft.2018.07.019>`__, `Pianosi and Wagener 2015 <https://doi.org/10.1016/j.envsoft.2015.01.004>`__)
 
-* Regional Sensitivity Analysis (based on `Saltelli et al. 2008 <https://dx.doi.org/10.1002/9780470725184>`__, `Pianosi et al., 2016 <https://dx.doi.org/10.1016/j.envsoft.2016.02.008>`__)
+* Regional Sensitivity Analysis (based on `Hornberger and Spear, 1981 <https://www.osti.gov/biblio/6396608-approach-preliminary-analysis-environmental-systems>`__, `Saltelli et al. 2008 <https://dx.doi.org/10.1002/9780470725184>`__, `Pianosi et al., 2016 <https://dx.doi.org/10.1016/j.envsoft.2016.02.008>`__)
 
 
 **Contributing:** see `here <CONTRIBUTING.md>`__

docs/index.rst

@@ -37,7 +37,7 @@ Supported Methods
 * PAWN
   (`Pianosi and Wagener 2018 <https://dx.doi.org/10.1016/j.envsoft.2018.07.019>`__, `Pianosi and Wagener 2015 <https://doi.org/10.1016/j.envsoft.2015.01.004>`__)
 * Regional Sensitivity Analysis
-  (based on `Saltelli et al. 2008 <https://dx.doi.org/10.1002/9780470725184>`__, `Pianosi et al., 2016 <https://dx.doi.org/10.1016/j.envsoft.2016.02.008>`__)
+  (based on `Hornberger and Spear, 1981 <https://www.osti.gov/biblio/6396608-approach-preliminary-analysis-environmental-systems>`__, `Saltelli et al. 2008 <https://dx.doi.org/10.1002/9780470725184>`__, `Pianosi et al., 2016 <https://dx.doi.org/10.1016/j.envsoft.2016.02.008>`__)
 
 
 Getting Started

src/SALib/analyze/rsa.py

@@ -4,7 +4,7 @@
 
 import numpy as np
 import pandas as pd
-from scipy.stats import anderson_ksamp
+from scipy.stats import cramervonmises_2samp
 
 from . import common_args
 from ..util import read_param_file, ResultDict, extract_group_names, _check_groups
@@ -43,10 +43,11 @@ def analyze(
     (Y|b_{\\sim i})`. This aids in answering the question "where in factor space are
     outputs most sensitive to?"
 
-    The :math:`k`-sample Anderson-Darling test is used to compare distributions.
-    Results of the analysis are normalized so that values will be :math:`\\in [0, 1]`,
-    and indicate relative sensitivity across factor/output space. Larger values
-    indicate greater dissimilarity (thus, sensitivity).
+    The two-sample Cramér-von Mises (CvM) test is used to compare distributions.
+    Results of the analysis indicate sensitivity across factor/output space. As the
+    Cramér-von Mises criterion ranges from 0 to :math:`\\infty`, a value of zero will
+    indicates the two distributions being compared are identical, with larger values
+    indicating greater differences.
 
     Notes
     -----
@@ -86,20 +87,25 @@ def analyze(
 
     References
     ----------
-    1. Pianosi, F., K. Beven, J. Freer, J. W. Hall, J. Rougier, D. B. Stephenson, and
-    T. Wagener. 2016.
-    Sensitivity analysis of environmental models:
-    A systematic review with practical workflow.
-    Environmental Modelling & Software 79:214-232.
-    https://dx.doi.org/10.1016/j.envsoft.2016.02.008
-
-    2. Saltelli, A., M. Ratto, T. Andres, F. Campolongo, J. Cariboni, D. Gatelli,
-    M. Saisana, and S. Tarantola. 2008.
-    Global Sensitivity Analysis: The Primer.
-    Wiley, West Sussex, U.K.
-    https://dx.doi.org/10.1002/9780470725184
-    Accessible at:
-    http://www.andreasaltelli.eu/file/repository/Primer_Corrected_2022.pdf
+    1. Hornberger, G. M., and R. C. Spear. 1981.
+        Approach to the preliminary analysis of environmental systems.
+        Journal of Environmental Management 12:1.
+        https://www.osti.gov/biblio/6396608-approach-preliminary-analysis-environmental-systems
+
+    2. Pianosi, F., K. Beven, J. Freer, J. W. Hall, J. Rougier, D. B. Stephenson, and
+        T. Wagener. 2016.
+        Sensitivity analysis of environmental models:
+        A systematic review with practical workflow.
+        Environmental Modelling & Software 79:214-232.
+        https://dx.doi.org/10.1016/j.envsoft.2016.02.008
+
+    3. Saltelli, A., M. Ratto, T. Andres, F. Campolongo, J. Cariboni, D. Gatelli,
+        M. Saisana, and S. Tarantola. 2008.
+        Global Sensitivity Analysis: The Primer.
+        Wiley, West Sussex, U.K.
+        https://dx.doi.org/10.1002/9780470725184
+        Accessible at:
+        http://www.andreasaltelli.eu/file/repository/Primer_Corrected_2022.pdf
     """
     groups = _check_groups(problem)
     if not groups:
@@ -162,16 +168,16 @@ def rsa(X: np.ndarray, y: np.ndarray, bins: int = 10, target="X") -> np.ndarray:
             quants = np.quantile(t_arr, seq)
             b = (quants[0] <= t_arr) & (t_arr <= quants[1])
             if _has_samples(y, b):
-                r_s[0, d_i] = anderson_ksamp((m_arr[b], m_arr[~b])).statistic
+                r_s[0, d_i] = cramervonmises_2samp(m_arr[b], m_arr[~b]).statistic
 
             # Then assess the other bins
             for s in range(1, bins):
                 b = (quants[s] < t_arr) & (t_arr <= quants[s + 1])
 
                 if _has_samples(y, b):
-                    r_s[s, d_i] = anderson_ksamp((m_arr[b], m_arr[~b])).statistic
+                    r_s[s, d_i] = cramervonmises_2samp(m_arr[b], m_arr[~b]).statistic
 
-    return r_s / np.nanmax(r_s)
+    return r_s
 
 
 def _has_samples(y, sel):
@@ -216,7 +222,7 @@ def plot(self, factors=None):
     fig, ax = plt.subplots()
 
     xlabel = f"${self['target']}$ (Percentile)"
-    ylabel = "Relative $S_{i}$"
+    ylabel = "$CvM_{i}$"
 
     if factors is None:
         factors = slice(None)