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Bayesian probability: The lighthouse problem

  1. Jan 16, 2009 #1
    1. The problem statement, all variables and given/known data
    Hi all.

    Please take a look at this problem: http://web.gps.caltech.edu/classes/ge193/practicals/practical3/Lighthouse.pdf

    I am stuck at question 2 and 3. For question 1 I get the following:

    [tex]
    d_k = \beta \tan(\theta_k)+\alpha.
    [/tex]

    For question 2 and 3, I know I have to use Bayes' sentence for probability density functions (PDF's), so for question 2 I get:

    [tex]
    p(\theta_k\,\, |\,\, \alpha, \beta) = \frac{p(\alpha,\beta\,\,|\,\,\theta_k)\pi^{-1}}{C},
    [/tex]

    where C is some constant that normalizes the PDF and I have assumed that the prior probability on [itex]\theta_k[/itex] is [itex]\pi^{-1}[/itex] (I was told to do this).

    Could you guys tell me, what the next step is?

    Thanks in advance.

    Best regards,
    Niles.
     
  2. jcsd
  3. Jan 16, 2009 #2

    Avodyne

    User Avatar
    Science Advisor

    You're not supposed to use Bayes' theorem for #2. The answer to #2 is given by the statement that the pulses are emitted at "random azimuths". This presumably means that [itex]\theta_k[/itex] is uniformly distributed between 0 and [itex]2\pi[/itex].
     
  4. Jan 17, 2009 #3
    Thanks! I'll keep working on it from here.
     
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