# Is it rational to select a parameter posterior value because it maximizes utility, even if probability is low?

I did Bayesian parameter estimation and I have now an estimate of the posterior distribution for my model parameters (say I have 2000 samples). Now I would like to make the optimal decision under my utility function.

Question: should I calculate the utility on each of my 2000 samples and choose the optimal one, without regard to the relative probabilities of each? Or equivalently, is it rational to select a value for a parameter based on the fact it maximizes utility, even if this parameter value has a low posterior probability ?

• The Bayesian decision theory consists in finding the decision minimizing the posterior expected utility. Not the utility on every value of the parameter $\theta$. I suggest you read Berger (1985) or Bernardo and Smith (1993). – Xi'an May 22 at 17:01