But if you know the boxes were originally drawn from N(50,100) then the number on the box is no longer the correct Bayesian mean. All I’m arguing is that once you have your Bayesian expected value you don’t need to update it any further.
All I’m arguing is that once you have your Bayesian expected value you don’t need to update it any further.
That’s pretty uncontroversial, but in practice it means that you end up penalizing high-noise boxes with high values (and boosting high-noise boxes with low values), which I think is a nontrivial result.
But if you know the boxes were originally drawn from N(50,100) then the number on the box is no longer the correct Bayesian mean. All I’m arguing is that once you have your Bayesian expected value you don’t need to update it any further.
That’s pretty uncontroversial, but in practice it means that you end up penalizing high-noise boxes with high values (and boosting high-noise boxes with low values), which I think is a nontrivial result.