Additional-Review-(marginalization-over-joint-population+EoS-uncertainty).md

@@ -41,13 +41,13 @@ w_i = \frac{\sum_p p(\theta_i|\Lambda_p)}{p(\theta_i|\mathrm{default\ PE})}
 This implies that the total sum would be
 
 ```math
-S_\mathrm{old} = \sum_i w_i \Theta_i = \sum_i \left(\frac{\sum_p p(\theta_i)|\Lambda_p)}{p(\theta_i|\mathrm{default\ PE})}\right) \Theta_i = \sum_p \sum_i \frac{p(\theta_i|\Lambda_p)}{p(\theta_i|\mathrm{default\ PE})} \Theta_i
+S_\mathrm{old} = \sum_i w_i \Theta_i = \sum_i \left(\frac{\sum_p p(\theta_i|\Lambda_p)}{p(\theta_i|\mathrm{default\ PE})}\right) \Theta_i = \sum_p \sum_i \frac{p(\theta_i|\Lambda_p)}{p(\theta_i|\mathrm{default\ PE})} \Theta_i
 ```
 
 It is straightforward to show that
 
 ```math
-\sum_i \frac{p(\theta_i|\Lambda)}{p(\theta_i|\mathrm{default\ PE})} \Theta_i \approx \int d\theta p(\theta|\mathrm{data},\Lambda) \Theta(\theta) \frac{p(\mathrm{data}|\Lambda)}{p(\mathrm{data}|\mathrm{default\ PE})}
+\sum_i \frac{p(\theta_i|\Lambda)}{p(\theta_i|\mathrm{default\ PE})} \Theta_i \approx \left(\frac{p(\mathrm{data}|\Lambda)}{p(\mathrm{data}|\mathrm{default\ PE})}\right) \int d\theta p(\theta|\mathrm{data},\Lambda) \Theta(\theta)
 ```
 
 which implies the total sum would approximate