CT6 September 2006 question 5 (i) "all or nothing loss"

Discussion in 'CT6' started by sir_highbury, Nov 12, 2017.

  1. sir_highbury

    sir_highbury Member

    why f(g/x) is maximised at the mode of the posterior distribution?
     
  2. John Lee

    John Lee ActEd Tutor Staff Member

    because the mode is the maximum value of the PDF by definition.
     
  3. sir_highbury

    sir_highbury Member

    Hi John,
    thanks for your reply. sorry my question was not complete.
    Looking at the loss function:
    1. quadratic loss -> mean
    2. absolute error loss -> median
    3. all or nothing loss -> mode
    I do not get these 3 relations.
    Thanks again, SH
     
  4. John Lee

    John Lee ActEd Tutor Staff Member

    Apologies for the delay. I have been unwell.

    Essentially what we are doing is finding the result that minimises the expected loss.

    So we are doing:

    \(min \int (loss function) * (posterior PDF)\)
     

Share This Page