Metropolis-Hastings algorithm

  • Thread starter Zaare
  • Start date
  • #1
54
0

Main Question or Discussion Point

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]?
 

Answers and Replies

  • #2
375
0
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.
 
  • #3
54
0
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.
 

Related Threads on Metropolis-Hastings algorithm

  • Last Post
Replies
1
Views
2K
Replies
0
Views
1K
  • Last Post
Replies
0
Views
2K
Replies
21
Views
5K
Replies
0
Views
3K
Replies
2
Views
2K
  • Last Post
Replies
1
Views
632
  • Last Post
Replies
1
Views
438
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
2
Views
868
Top