How do I derive the posterior density of a Weibull Distribution?© BrainMass Inc. brainmass.com October 1, 2020, 4:38 pm ad1c9bdddf
The question is very general. Therefore, I've got to start from Bayesian estimation and an example follows. Please refer to the attachment.
Now let's focus on the problem of estimation of a 1 dimensional parameter. Mean Squared Error corresponds to using
The risk function of a procedure (estimator) is
Now consider using a prior with density . The Bayes risk of is
How should we choose to minimize ? The solution lies in recognizing that is really a joint density
For this joint density the conditional density of X given is just the model . From now on I write the model as to emphasize this fact. We can now compute a ...
The solution answers the question(s) below. Posterior density of Weibull distribution