Bayesian estimator

can anyone please help with Bayesian estimatiors?
If my model is a function of unknown parameters I am drawing inference about, say Weibull distribution with scale s and shape m:
what is the proper Bayesian estimator for that model?

I see two options:

1) evaluate the model for point estimates (e.g. a posterior mean) of s,m
W(E(m), E(s))


2) evaluate the expectation of the model as a multivariate function of random variables

The second option seems correct from a math point of view but has some practical disadvantages. The properties of the original model are lost, i.e. the result is not a Weibull distribution anymore.

Any help or hint to literature are very appreciated!


Ambassador to the humans
Your question isn't clear to me. What are you trying to estimate? What is the question you're trying to answer?
Given the model (Weibull distribution) and some data (from experiments), I am trying to infer on the model parameters. In the Bayesian inference, the parameters are treated as random variables. The question: Do I take point estimates of the parameters and apply them in the model or do I evaluate the an estimator of the model? I.e. do I treat the model as a function of random variables?