diff --git a/gwpopulation/hyperpe.py b/gwpopulation/hyperpe.py
index 3cb54395..d2ce2c40 100644
--- a/gwpopulation/hyperpe.py
+++ b/gwpopulation/hyperpe.py
@@ -48,7 +48,7 @@ def __init__(self, posteriors, hyper_prior, sampling_prior=None,
         Parameters
         ----------
         posteriors: list
-            An list of pandas data frames of samples sets of samples.
+            A list of pandas data frames of samples sets of samples.
             Each set may have a different size.
             These can contain a `prior` column containing the original prior
             values.
@@ -111,7 +111,7 @@ def log_likelihood_ratio(self):
         self.parameters, added_keys = self.conversion_function(self.parameters)
         self.hyper_prior.parameters.update(self.parameters)
         ln_l = xp.sum(self._compute_per_event_ln_bayes_factors())
-        ln_l += self._get_selection_factor()
+        ln_l += self.n_posteriors * self._get_selection_factor()
         if added_keys is not None:
             for key in added_keys:
                 self.parameters.pop(key)
@@ -129,7 +129,7 @@ def _compute_per_event_ln_bayes_factors(self):
                    self.sampling_prior, axis=-1))
 
     def _get_selection_factor(self):
-        return - self.n_posteriors * xp.log(
+        return - xp.log(
             self.selection_function(self.parameters))
 
     def generate_extra_statistics(self, sample):
@@ -274,3 +274,66 @@ def _get_selection_factor(self):
 
     def generate_rate_posterior_sample(self):
         pass
+
+
+class PastroLikelihood(HyperparameterLikelihood):
+    """
+    A mixture model likelihood which utlises p_astro for the effective
+    noise likelihood.
+    This likelihood is marginalised over rate.
+
+    See Eq. (40) of https://arxiv.org/abs/1912.09708 for a definition.
+    """
+    def __init__(self, posteriors, hyper_prior, sampling_prior=None,
+                 ln_evidences=None, max_samples=1e100, pastro=None,
+                 selection_function=lambda args: 1,
+                 conversion_function=lambda args: (args, None),
+                 fiducial_selection=None, cupy=True):
+        """
+        Parameters
+        ----------
+        pastro: array
+            An array of pastro values corresponding to the event posteriors.
+        fiducial_selection: float
+            The visible spacetime volume described by the fiducial model
+            determined by the sampling prior distribution.        
+        """
+        if pastro is not None:
+            if fiducial_selection is not None:
+                logger.info('Fiducial VT set to {}'.format(fiducial_selection))
+                self.fiducial_selection = fiducial_selection
+            else:
+                logger.warning('No fiducial VT provided, defaulting to 1.0')
+                self.fiducial_selection = 1.0
+            if len(pastro) != len(posteriors):
+                raise ValueError('Number of pastro values provided are not '
+                                 'equal to the number of posteriors.')
+            self.pastro = pastro
+       
+        super().__init__(self)
+
+    def log_likelihood_ratio(self):
+        self.parameters, added_keys = self.conversion_function(self.parameters)
+        self.hyper_prior.parameters.update(self.parameters)
+        ln_l1 = self._compute_per_event_ln_bayes_factors()
+        ln_l1 += self._get_selection_factor()
+        ln_l1 += self._get_fiducial_selection_factor()
+
+        if added_keys is not None:
+            for key in added_keys:
+                self.parameters.pop(key)
+
+        ln_l2 = self._get_pastro_factor
+        ln_l2 = xp.nan_to_num(ln_l2)
+
+        ln_l = xp.sum(xp.logaddexp(ln_l1, ln_l2))
+        ln_l += 0.5 * self._get_selection_factor()
+
+        return float(xp.nan_to_num(ln_l))
+
+    def _get_pastro_factor(self):
+        pastro_factor = (1.0 - self.pastro)/self.pastro
+        return xp.log(pastro_factor)
+
+    def _get_fiducial_selection_factor(self):
+        return xp.log(self.fiducial_selection)