Hi all,

Please, I have a question about decision analysis.

Following the Decision Analysis section from Stan Users Guide, suppose I have:

where the expectation is taken with respect to the posterior distribution of outcomes x conditional on decisions d, p(x\vert d).

If the decisions are continuous (eg, how much money to invest), I wonder if it is possible to derive a posterior distribution for the maximizer d^*. For instance, for each posterior draw s, I compute {d^*}^{(s)} = \textrm{arg max}_d \ \big[U(x) \mid d \big]^{(s)} (ie., the â€śoptimal decision for each posterior drawâ€ť).

My underlying motivation is to run decision analysis for different settings/datasets, which seem to yield slightly different optimal decisions. So I wanted to have an idea of how much uncertainty there is around those â€śoptimizersâ€ť.

Does this make any sense?

Thank you!