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The added benefit of Gibbs Sampling are given here. What's interesting from the Gibbs standpoint is that I can extend traditional taking posterior means of my model and then pointing that into the profit function. I can now go back and come out with the true posterior profit function. So I can take each of these Gibbs Sample, 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. Again 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 to coming out with the shrinkage estimates, and now I can think about what the effect is going to be on the profit posterior. Now, Blattberg and George did a paper where they are thinking about the same type of problem. There they suggest 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. Here, though, I'm not thinking about just an estimate. I just want to know what is the total distribution. From the distribution I want to infer something about pricing.
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