Estimating Expected Profits

The added benefit of Gibbs Sampling are given here. Now, what's interesting from the Gibbs standpoint is, that I can come out and extend traditional taking posterior means of my model and then pointing that into the profit function. What I can do, is I can now go back and come out with what's the true posterior profit function. So I can take each of these Gibbs xxx, and I can run it through this non-linear equation, even though its a pretty simple non-linear equation, it's still non-linear. And I can come out with what is going to be the posterior profit function. Which again, you know, what I'd stress is that it makes it very nice, because its a nice systematic framework all the way from tweaking the data and modeling it and coming out with the shrinkage estimates and now I can go back and think about what going to be the effect on the profit posterior. Now, Blattberg and George did a paper where they are thinking about the same type of problem, there they suggest with coming out with more efficient estimates based on using the loss-function, using the profit function as your loss function and then coming out with more efficient estimates from that. What I'm thinking here, is you know, I'm not thinking about just an estimate. I just want to know what is the total distribution. So, from the distribution I want to go back and infer something about pricing.

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