Fix prior changing

Some of the priors we previously weren't able to change the limits after creating them. This MR makes that possible for all priors with finite domains and adds a test of it.

It required some rewriting of a few priors.

I did branch this form a different unmerged branch, but I think I removed everything new.

bilby/core/prior.py

@@ -799,7 +799,8 @@ class Cosine(Prior):
         This maps to the inverse CDF. This has been analytically solved for this case.
         """
         Prior.test_valid_for_rescaling(val)
-        return np.arcsin(-1 + val * 2)
+        norm = 1 / (np.sin(self.maximum) - np.sin(self.minimum))
+        return np.arcsin(val / norm + np.sin(self.minimum))
 
     def prob(self, val):
         """Return the prior probability of val. Defined over [-pi/2, pi/2].
@@ -844,7 +845,8 @@ class Sine(Prior):
         This maps to the inverse CDF. This has been analytically solved for this case.
         """
         Prior.test_valid_for_rescaling(val)
-        return np.arccos(1 - val * 2)
+        norm = 1 / (np.cos(self.minimum) - np.cos(self.maximum))
+        return np.arccos(np.cos(self.minimum) - val / norm)
 
     def prob(self, val):
         """Return the prior probability of val. Defined over [0, pi].
@@ -1279,16 +1281,16 @@ class Beta(Prior):
             See superclass
 
         """
-        Prior.__init__(self, minimum=minimum, maximum=maximum, name=name,
-                       latex_label=latex_label, unit=unit)
-
         if alpha <= 0. or beta <= 0.:
             raise ValueError("alpha and beta must both be positive values")
 
-        self.alpha = alpha
-        self.beta = beta
-        self._loc = minimum
-        self._scale = maximum - minimum
+        self._alpha = alpha
+        self._beta = beta
+        self._minimum = minimum
+        self._maximum = maximum
+        Prior.__init__(self, minimum=minimum, maximum=maximum, name=name,
+                       latex_label=latex_label, unit=unit)
+        self._set_dist()
 
     def rescale(self, val):
         """
@@ -1299,8 +1301,7 @@ class Beta(Prior):
         Prior.test_valid_for_rescaling(val)
 
         # use scipy distribution percentage point function (ppf)
-        return scipy.stats.beta.ppf(
-            val, self.alpha, self.beta, loc=self._loc, scale=self._scale)
+        return self._dist.ppf(val)
 
     def prob(self, val):
         """Return the prior probability of val.
@@ -1314,8 +1315,7 @@ class Beta(Prior):
         float: Prior probability of val
         """
 
-        spdf = scipy.stats.beta.pdf(
-            val, self.alpha, self.beta, loc=self._loc, scale=self._scale)
+        spdf = self._dist.pdf(val)
         if np.all(np.isfinite(spdf)):
             return spdf
 
@@ -1328,8 +1328,7 @@ class Beta(Prior):
             return 0.
 
     def ln_prob(self, val):
-        spdf = scipy.stats.beta.logpdf(
-            val, self.alpha, self.beta, loc=self._loc, scale=self._scale)
+        spdf = self._dist.logpdf(val)
         if np.all(np.isfinite(spdf)):
             return spdf
 
@@ -1340,6 +1339,48 @@ class Beta(Prior):
         else:
             return -np.inf
 
+    def _set_dist(self):
+        """Try/except to stop it falling over at instantiation"""
+        self._dist = scipy.stats.beta(
+            a=self.alpha, b=self.beta, loc=self.minimum,
+            scale=(self.maximum - self.minimum))
+
+    @property
+    def maximum(self):
+        return self._maximum
+
+    @maximum.setter
+    def maximum(self, maximum):
+        self._maximum = maximum
+        self._set_dist()
+
+    @property
+    def minimum(self):
+        return self._minimum
+
+    @minimum.setter
+    def minimum(self, minimum):
+        self._minimum = minimum
+        self._set_dist()
+
+    @property
+    def alpha(self):
+        return self._alpha
+
+    @alpha.setter
+    def alpha(self, alpha):
+        self._alpha = alpha
+        self._set_dist()
+
+    @property
+    def beta(self):
+        return self._beta
+
+    @beta.setter
+    def beta(self, beta):
+        self._beta = beta
+        self._set_dist()
+
 
 class Logistic(Prior):
     def __init__(self, mu, scale, name=None, latex_label=None, unit=None):
@@ -1605,7 +1646,7 @@ class Interped(Prior):
         Prior.__init__(self, name=name, latex_label=latex_label, unit=unit,
                        minimum=np.nanmax(np.array((min(xx), minimum))),
                        maximum=np.nanmin(np.array((max(xx), maximum))))
-        self.__update_instance()
+        self._update_instance()
 
     def __eq__(self, other):
         if self.__class__ != other.__class__:
@@ -1656,7 +1697,7 @@ class Interped(Prior):
     def minimum(self, minimum):
         self._minimum = minimum
         if '_maximum' in self.__dict__ and self._maximum < np.inf:
-            self.__update_instance()
+            self._update_instance()
 
     @property
     def maximum(self):
@@ -1675,14 +1716,14 @@ class Interped(Prior):
     def maximum(self, maximum):
         self._maximum = maximum
         if '_minimum' in self.__dict__ and self._minimum < np.inf:
-            self.__update_instance()
+            self._update_instance()
 
-    def __update_instance(self):
+    def _update_instance(self):
         self.xx = np.linspace(self.minimum, self.maximum, len(self.xx))
         self.yy = self.__all_interpolated(self.xx)
-        self.__initialize_attributes()
+        self._initialize_attributes()
 
-    def __initialize_attributes(self):
+    def _initialize_attributes(self):
         if np.trapz(self.yy, self.xx) != 1:
             logger.debug('Supplied PDF for {} is not normalised, normalising.'.format(self.name))
         self.yy /= np.trapz(self.yy, self.xx)