Let say that you created 2 marketing campaigns. You sent 200 impressions on these campaigns as follow:
Campaign A : Got 100 impressions and 2 successes with a value of 1.5$ per success
Campaign B : Got 100 impressions and 1 success with a value of 2$ per success
Using the Jeffrey prior 0.5,0.5 how do you calculate $\mathbb{P}(A > B)$ or $\mathbb{P}(A < B)$?
Here is a online calculator : https://win-vector.shinyapps.io/CampaignPlanner/ > Choose task "Evaluate Campaign". For the given problem the result is $\mathbb{P}(A > B)$ = 0.6144371 = 61%
How to get this number?