Ch 14 Question 6

Discussion in 'CS1' started by Molly, Feb 24, 2023.

  1. Molly

    Molly Ton up Member

    Hi all,

    Just wondering, why do we chose to find what C is in this question? Normally we would just use the format of f_post to find a matching distribution in the tables, why cant we do this here too? Is it because f_post is piecewise defined? and if so, do we always find C when f_post is defined this way?

    and why can we then just drop the piecewise format later in the quetsion and just have f_post(\theta)=e^-(\theta-x)?

    Thanks
     
    Last edited: Feb 24, 2023
    Molly, Feb 24, 2023
    #1
  2. Andrea Goude

    Andrea Goude ActEd Tutor Staff Member

    Hi Molly

    As you say we would normally spot the distribution but here this does not match one in the Tables so we need to find C.

    The pdf of the posterior will always sum to 1 over the support of the distribution so we can use this to find the constant.

    It is in the posterior distribution f_post = e^x*e^-theta = e^-(theta-x).

    Thanks
    Andrea
     
    Andrea Goude, Feb 27, 2023
    #2
    Molly likes this.
  3. Molly

    Molly Ton up Member

    Hi Andrea,

    Thank you for this, so general rule of thumb if it doesnt match a distribution i must find C - thats great thanks!

    Just a follow up question, is the reason it doesnt match those on the tables because it is piecewise defined?

    Thanks
     
    Molly, Mar 2, 2023
    #3

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