bayesian credibility estimate

Discussion in 'CS1' started by Alfie, Apr 18, 2023.

  1. Alfie

    Alfie Keen member

    hi, i think i have found a gap in my knowledge. i have three questions on this topic can you please help?

    1) i thought that we always did Z*mle+(1-Z)*prior mean
    but now im thinking maybe prior mean isnt right - is it whatever bayesian type we are splitting ie if splitting under all or nothing would it be Z*mle+(1-Z)*prior estimate under all or nothing
    2)do we assume the mle is x/n unless we are told to find the mle in a previous part. i have never found a question where the mle is not x/n without a earlier part making us find it?
    3) i have found that we do not do the product part of the likelihood here sum as sumx and power n. is it true we do not treat the likelihood as n likelihoods but just as singular for these quetsions?

    thank you
     
    Last edited: Apr 18, 2023
  2. Andrea Goude

    Andrea Goude ActEd Tutor Staff Member

    1) credibility formula=Z*xbar+(1-Z)*mu, under Bayesian credibility, under quadratic loss = Z*mle+(1-Z)*prior mean, I have not seen others, it does say simple cases in the syllabus objective
    2) you would have to work out the MLE, generally it is sumx/n, but you would need to work it out unless it is given
    3) it would really depend on the particular question
     
    Alfie likes this.
  3. Alfie

    Alfie Keen member

    thank you so much!
     

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