Simulate
-
N = 100,000 people
-
Real world is one draw of gammas from the prior distribution for each person
-
How much we should update our guess of that person's treatment effects towards the overall ATE depends on what happens in a bunch of simulated worlds
-
So now we make 1000 more columns, each of which are a simulated world, where we redraw gamma from the prior distribution for every individual
-
In each simulated world, for each individual, we can compute beta_i -- their treatment effect -- and beta_ATE, the average treatment effect
-
How much we update in the real-world depends on how beta_i and beta_ATE correlate across the 1000 simulations for each individual
6206972597