Log CDF methods for several distributions

pymc3/distributions/continuous.py

@@ -152,6 +152,18 @@ def logp(self, value):
         return bound(-tt.log(upper - lower),
                      value >= lower, value <= upper)
 
+    def logcdf(self, value):
+        return tt.switch(
+            tt.or_(tt.lt(value, self.lower), tt.gt(value, self.upper)),
+            -np.inf,
+            tt.switch(
+                tt.eq(value, self.upper),
+                0,
+                tt.log((value - self.lower)) -
+                tt.log((self.upper - self.lower))
+            )
+        )
+
 
 class Flat(Continuous):
     """
@@ -240,10 +252,10 @@ def logcdf(self, value):
         return tt.switch(
             tt.lt(z, -1.0),
             tt.log(tt.erfcx(-z / tt.sqrt(2.)) / 2.) -
-            tt.sqr(tt.abs_(z)) / 2,
+            tt.sqr(z) / 2,
             tt.log1p(-tt.erfc(z / tt.sqrt(2.)) / 2.)
         )
-        
+
 
 class HalfNormal(PositiveContinuous):
     R"""
@@ -295,6 +307,15 @@ def logp(self, value):
                      value >= 0,
                      tau > 0, sd > 0)
 
+    def logcdf(self, value):
+        sd = self.sd
+        z = zvalue(value, mu=0, sd=sd)
+        return tt.switch(
+            tt.lt(z, -1.0),
+            tt.log(tt.erfcx(-z / tt.sqrt(2.))) - tt.sqr(z),
+            tt.log1p(-tt.erfc(z / tt.sqrt(2.)))
+        )
+
 
 class Wald(PositiveContinuous):
     R"""
@@ -591,6 +612,20 @@ def logp(self, value):
 
         return -tt.log(2 * b) - abs(value - mu) / b
 
+    def logcdf(self, value):
+        a = self.mu
+        b = self.b
+        y = (value - a) / b
+        return tt.switch(
+            tt.le(value, a),
+            tt.log(0.5) + y,
+            tt.switch(
+                tt.gt(y, 1),
+                tt.log1p(-0.5 * tt.exp(-y)),
+                tt.log(1 - 0.5 * tt.exp(-y))
+            )
+        )
+
 
 class Lognormal(PositiveContinuous):
     R"""
@@ -655,6 +690,22 @@ def logp(self, value):
                      - tt.log(value),
                      tau > 0)
 
+    def logcdf(self, value):
+        mu = self.mu
+        sd = self.sd
+        z = zvalue(tt.log(value), mu=mu, sd=sd)
+
+        return tt.switch(
+            tt.le(value, 0),
+            -np.inf,
+            tt.switch(
+                tt.lt(z, -1.0),
+                tt.log(tt.erfcx(-z / tt.sqrt(2.)) / 2.) -
+                tt.sqr(z) / 2,
+                tt.log1p(-tt.erfc(z / tt.sqrt(2.)) / 2.)
+            )
+        )
+
 
 class StudentT(Continuous):
     R"""
@@ -833,6 +884,9 @@ def logp(self, value):
                      - tt.log1p(((value - alpha) / beta)**2),
                      beta > 0)
 
+    def logcdf (self, value):
+          return tt.log(0.5 + tt.arctan ((value - self.alpha) / self.beta) / np.pi)
+
 
 class HalfCauchy(PositiveContinuous):
     R"""
@@ -1360,3 +1414,21 @@ def logp(self, value):
                          tt.switch(tt.eq(value, c), tt.log(2 / (upper - lower)),
                          tt.switch(alltrue_elemwise([c < value, value <= upper]),
                          tt.log(2 * (upper - value) / ((upper - lower) * (upper - c))),np.inf)))
+
+    def logcdf(self, value):
+        l = self.lower
+        u = self.upper
+        c = self.c
+        return tt.switch(
+            tt.le(value, l),
+            -np.inf,
+            tt.switch(
+                tt.le(value, c),
+                tt.log(((value - l) ** 2) / ((u - l) * (c - l))),
+                tt.switch(
+                    tt.lt(value, u),
+                    tt.log1p(-((u - value) ** 2) / ((u - l) * (u - c))),
+                    0
+                )
+            )
+        )

pymc3/tests/test_distributions.py

@@ -366,11 +366,15 @@ def test_uniform(self):
         self.pymc3_matches_scipy(
             Uniform, Runif, {'lower': -Rplusunif, 'upper': Rplusunif},
             lambda value, lower, upper: sp.uniform.logpdf(value, lower, upper - lower))
+        self.check_logcdf(Uniform, Runif, {'lower': -Rplusunif, 'upper': Rplusunif},
+                          lambda value, lower, upper: sp.uniform.logcdf(value, lower, upper - lower))
 
     def test_triangular(self):
         self.pymc3_matches_scipy(
             Triangular, Runif, {'lower': -Rplusunif, 'c': Runif, 'upper': Rplusunif},
             lambda value, c, lower, upper: sp.triang.logpdf(value, c-lower, lower, upper-lower))
+        self.check_logcdf(Triangular, Runif, {'lower': -Rplusunif, 'c': Runif, 'upper': Rplusunif},
+                          lambda value, c, lower, upper: sp.triang.logcdf(value, c-lower, lower, upper-lower))
 
     def test_bound_normal(self):
         PositiveNormal = Bound(Normal, lower=0.)
@@ -390,12 +394,14 @@ def test_flat(self):
     def test_normal(self):
         self.pymc3_matches_scipy(Normal, R, {'mu': R, 'sd': Rplus},
                                  lambda value, mu, sd: sp.norm.logpdf(value, mu, sd))
-        self.check_logcdf(Normal, R, {'mu': R, 'sd': Rplus}, 
+        self.check_logcdf(Normal, R, {'mu': R, 'sd': Rplus},
                                 lambda value, mu, sd: sp.norm.logcdf(value, mu, sd))
 
     def test_half_normal(self):
         self.pymc3_matches_scipy(HalfNormal, Rplus, {'sd': Rplus},
                                  lambda value, sd: sp.halfnorm.logpdf(value, scale=sd))
+        self.check_logcdf(HalfNormal, Rplus, {'sd': Rplus},
+                          lambda value, sd: sp.halfnorm.logcdf(value, scale=sd))
 
     def test_chi_squared(self):
         self.pymc3_matches_scipy(ChiSquared, Rplus, {'nu': Rplusdunif},
@@ -452,11 +458,15 @@ def test_fun(value, mu, alpha):
     def test_laplace(self):
         self.pymc3_matches_scipy(Laplace, R, {'mu': R, 'b': Rplus},
                                  lambda value, mu, b: sp.laplace.logpdf(value, mu, b))
+        self.check_logcdf(Laplace, R, {'mu': R, 'b': Rplus},
+                          lambda value, mu, b: sp.laplace.logcdf(value, mu, b))
 
     def test_lognormal(self):
         self.pymc3_matches_scipy(
             Lognormal, Rplus, {'mu': R, 'tau': Rplusbig},
             lambda value, mu, tau: sp.lognorm.logpdf(value, tau**-.5, 0, np.exp(mu)))
+        self.check_logcdf(Lognormal, Rplus, {'mu': R, 'tau': Rplusbig},
+                          lambda value, mu, tau: sp.lognorm.logcdf(value, tau**-.5, 0, np.exp(mu)))
 
     def test_t(self):
         self.pymc3_matches_scipy(StudentT, R, {'nu': Rplus, 'mu': R, 'lam': Rplus},
@@ -465,6 +475,8 @@ def test_t(self):
     def test_cauchy(self):
         self.pymc3_matches_scipy(Cauchy, R, {'alpha': R, 'beta': Rplusbig},
                                  lambda value, alpha, beta: sp.cauchy.logpdf(value, alpha, beta))
+        self.check_logcdf(Cauchy, R, {'alpha': R, 'beta': Rplusbig},
+                          lambda value, alpha, beta: sp.cauchy.logcdf(value, alpha, beta))
 
     def test_half_cauchy(self):
         self.pymc3_matches_scipy(HalfCauchy, Rplus, {'beta': Rplusbig},