If I understand correctly:
- statistics, narrowly construed, is all about using data to estimate probabilities.
- decision theory can then be applied to those probabilities in order to predict which decisions maximize expected utility.
I may be completely off the mark here, but I have a hunch that this is really the wrong way of going about it. Perhaps we should look for decision-theoretic methods that skip the estimation of probabilities altogether and make utility-maximizing decisions "straight from the data," so to speak. Imaginably, this could circumvent certain difficulties with the Bayesian paradigm, like finding an uninformative prior distribution.
Question. Have there been any attempts to unify statistics and decision theory into a single framework that refrains from estimating probabilities, and instead makes utility-maximizing decisions "straight from the data"?
If not, I would also be interested in answers of the form: "This probably wouldn't work because..."
Please keep it civilized, thanks.