diff --git a/AcquistionFunctions/PreferenceExpectedImprovement.py b/AcquistionFunctions/PreferenceExpectedImprovement.py
index b69595c..136fde8 100644
--- a/AcquistionFunctions/PreferenceExpectedImprovement.py
+++ b/AcquistionFunctions/PreferenceExpectedImprovement.py
@@ -12,9 +12,11 @@ class PreferenceExpectedImprovement:
         self.upper_bound = upper_bound
         self.lower_bound = lower_bound
 
+        self.initial_variance = 5.0
+
         self.user_model = None
         self.proposal_model_mean = np.array((nr_dims, 1))
-        self.proposal_model_covariance = np.diag(np.ones((nr_dims, )) * 5)
+        self.proposal_model_covariance = np.diag(np.ones((nr_dims, )) * self.initial_variance)
 
         self.rng = np.random.default_rng(seed=seed)
 
@@ -22,20 +24,37 @@ class PreferenceExpectedImprovement:
         pass
 
     def rejection_sampling(self):
-        samples = np.empty((self.nr_samples, self.nr_dims))
-        i = 0
-        while i < self.nr_samples:
-            pass
+        samples = np.empty((0, self.nr_dims))
+        while samples.shape[0] < self.nr_samples:
+            # sample from the multi variate gaussian distribution
+            sample = self.rng.multivariate_normal(
+                self.proposal_model_mean,
+                self.proposal_model_covariance
+            )
+
+            # check if the sample is within the bounds
+            if np.all(sample >= self.lower_bound) and np.all(sample <= self.upper_bound):
+                samples = np.append(samples, [sample], axis=0)
+
+        return samples
 
 
     def expected_improvement(self):
         pass
 
-    def update_user_preference_model(self):
-        pass
+    def update_user_preference_model(self, preferred_input, preference_array):
+        # Update mean to reflect preferred input
+        self.user_model_mean = preferred_input
 
-    def update_proposal_model(self):
-        pass
+        initial_variance = np.ones((self.nr_dims, )) * self.initial_variance
+        reduced_variance = initial_variance / 10.0
+        variances = np.where(preference_array, reduced_variance, initial_variance)
+        self.user_model_covariance = np.diag(variances)
+
+        def update_proposal_model(self, alpha=0.5):
+        # Update proposal model to be a weighted average of the current proposal model and the user model
+        self.proposal_model_mean = alpha * self.proposal_model_mean + (1 - alpha) * self.user_model_mean
+        self.proposal_model_covariance = alpha * self.proposal_model_covariance + (1 - alpha) * self.user_model_covariance
 
 
 if __name__ == '__main__':