Redefined I = D_A + D_B - D_AB, and logS = logR - I, such that I is t…

…he previous log I, the logarithm is incorporated in I. Updated all relevant lines in anesthetic/tension.py and tests/test_tension.py.

anesthetic/tension.py

@@ -17,7 +17,7 @@ def stats(A, B, AB, nsamples=None, beta=None):  # noqa: D301
     - ``I``: information ratio
 
       .. math::
-        I = exp(D_{KL}^{A} + D_{KL}^{B} - D_{KL}^{AB})
+        I = D_{KL}^{A} + D_{KL}^{B} - D_{KL}^{AB}
 
     - ``logS``: suspiciousness
 
@@ -90,7 +90,7 @@ def stats(A, B, AB, nsamples=None, beta=None):  # noqa: D301
     samples['logR'] = statsAB['logZ'] - statsA['logZ'] - statsB['logZ']
     samples.set_label('logR', r'$\ln\mathcal{R}$')
 
-    samples['I'] = np.exp(statsA['D_KL'] + statsB['D_KL'] - statsAB['D_KL'])
+    samples['I'] = statsA['D_KL'] + statsB['D_KL'] - statsAB['D_KL']
     samples.set_label('I', r'$\mathcal{I}$')
 
     samples['logS'] = statsAB['logL_P'] - statsA['logL_P'] - statsB['logL_P']

tests/test_tension.py

@@ -46,10 +46,10 @@ def test_tension_stats_compatible_gaussian():
     logS_exact = d / 2 - dmu_cov_dmu_AB / 2
     assert s.logS.mean() == approx(logS_exact, abs=3*s.logS.std())
 
-    I_exact = np.exp(logV - d / 2 - slogdet(2*np.pi*(covA+covB))[1] / 2)
+    I_exact = logV - d / 2 - slogdet(2*np.pi*(covA+covB))[1] / 2
     assert s.I.mean() == approx(I_exact, abs=3*s.I.std())
 
-    assert s.logS.mean() == approx(s.logR.mean() - np.log(s.I).mean(),
+    assert s.logS.mean() == approx(s.logR.mean() - s.I.mean(),
                                    abs=3*s.logS.std())
 
     assert s.get_labels().tolist() == ([r'$\ln\mathcal{R}$',
@@ -106,10 +106,10 @@ def test_tension_stats_incompatible_gaussian():
     logS_exact = d / 2 - dmu_cov_dmu_AB / 2
     assert s.logS.mean() == approx(logS_exact, abs=3*s.logS.std())
 
-    I_exact = np.exp(logV - d / 2 - slogdet(2*np.pi*(covA+covB))[1] / 2)
+    I_exact = logV - d / 2 - slogdet(2*np.pi*(covA+covB))[1] / 2
     assert s.I.mean() == approx(I_exact, abs=3*s.I.std())
 
-    assert s.logS.mean() == approx(s.logR.mean() - np.log(s.I).mean(),
+    assert s.logS.mean() == approx(s.logR.mean() - s.I.mean(),
                                    abs=3*s.logS.std())
 
     assert s.get_labels().tolist() == ([r'$\ln\mathcal{R}$',