Bayesian estimator

#1
Hello,
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:
W(m,s),
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))

or

2) evaluate the expectation of the model as a multivariate function of random variables
E(W(m,s))

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!
 

Dason

Ambassador to the humans
#2
Your question isn't clear to me. What are you trying to estimate? What is the question you're trying to answer?
 
#3
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?