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Metropolis-Hastings algorithm

  1. Mar 18, 2012 #1
    I digged out this old tread, but it is closed. I'll repost, but with my question.
    https://www.physicsforums.com/showthread.php?t=74004&highlight=metropolis

    [itex]\pi(x)[/itex]

    and
    [itex]\pi(y)[/itex]

    and
    [itex]q(y,x)[/itex] is the jump distribution

    in the relation:
    [itex]\alpha(x,y)= \min \left( 1,\frac{\pi (y)q(y,x)}{\pi (x)q(x,y)} \right)[/itex]

    Say, my jump distribution(aka transition prob) is normal(0,1). How do you write out [itex]q(y,x)[/itex]? Is it [itex]\frac{1}{\sqrt{2\pi }\sigma }{{e}^{\frac{{{(x-0)}^{2}}}{2{{\sigma }^{2}}}}}[/itex]?

    But this doesn't make sense, because it doesn't involve y, since [itex]q(y,x)[/itex] means given y, the transition probability of getting x. We are suppose to relate y to x in the equation.
     
    Last edited: Mar 18, 2012
  2. jcsd
  3. Mar 19, 2012 #2
    Variables x, y, z, in algebra, are place holders.

    q(y,x)=normal(0,1) means y=0 x=1

    Algebra is a incomplete story of placeholders. Be careful where you can plugin the values.
     
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