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Metropolis-Hastings algorithm

  1. May 2, 2005 #1
    I'm having trouble understanding how to find an expression for [tex]\pi(x)[/tex] and [tex]\pi(y)[/tex] in the relation:
    [tex]
    \alpha \left( {x,y} \right) = \min \left( {1,\frac{{\pi \left( y \right)q\left( {y,x} \right)}}{{\pi \left( x \right)q\left( {x,y} \right)}}} \right)
    [/tex]
    For example, If I want to simulate Normal Distribution (Expectation value m and standard deviation s), how can I find expressions for [tex]\pi(x)[/tex] and [tex]\pi(y)[/tex]? Or are they equal: [tex]\pi(x)=\pi(y)[/tex]?
     
  2. jcsd
  3. May 2, 2005 #2
    I've never used this algorithm, but the values of x and y are calculated/generated according to the algorithm and are different. One of the values, depending on how you are defining x and y, should come from the proposal distribution.

    And pi(x) = the normal distribution probability of x, for your particular example.
     
  4. May 3, 2005 #3
    I see. I was hopeing I could find a "short cut" which would simplify the expression for pi(x), but I suppose I can't.
    Thanks for the help.
     
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