Results 1 to 6 of 6

Math Help - Posterior distribution

  1. #1
    Member
    Joined
    Nov 2008
    From
    MD
    Posts
    165

    Posterior distribution

    Let theta denote the average number of defects per 100 feet of a certain type of magnetic tape. suppose that the value of the mean theta is unknown and the prior distribution of theta is a gamma distribution with parameters alpha=2 and beta=10. when a 1200 foot roll of this tape is inspected, exactly four defects are found. determine the posterior distribution of theta.

    i'm pretty sure the posterior is a gamma function i just need to figure out alpha and beta. do i multiply by 12...?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Oct 2009
    Posts
    340
    It seems to me that the distribution of the number of defects per 100 feet is missing. I'm guessing they want you to think of it as a Poisson process. If X is the number of defects in the 1200 foot thing, then we should have X|theta ~ Poisson(12theta). So, you want to get the distribution of theta|X, evaluated at X = 4. Use the fact that

    f_{\theta|X}(\theta|x) \propto f_{X|\theta}(x|\theta) f_\theta(\theta).

    You should get a gamma for the posterior I think.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2008
    From
    MD
    Posts
    165
    i got a gamma with alpha= 6 and beta= 22 for the posterior is this right??
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Oct 2009
    Posts
    340
    If you are using the rate parameterization of the gamma (which is NOT the one given here), then yes.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Nov 2008
    From
    MD
    Posts
    165
    what do you mean by the rate parameterization of the gama?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Senior Member
    Joined
    Oct 2009
    Posts
    340
    It is equivalent to using paramaterizing using lambda = 1 / beta in the paremeterization given on wikipedia.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: May 12th 2011, 03:43 PM
  2. Replies: 6
    Last Post: March 24th 2011, 05:57 PM
  3. normal distribution prior and posterior distribution proof
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: March 9th 2011, 06:12 PM
  4. Posterior distribution
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: February 24th 2010, 12:59 PM
  5. Posterior distribution
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: February 17th 2010, 04:10 AM

Search Tags


/mathhelpforum @mathhelpforum