Markov Chain Monte Carlo question

[mjt042]

I was wondering if anyone could help me with this problem dealing with Markov Chain Monte Carlo
-Find a regular transition matrix that is not time reversible, i.e., doesn't satisfy the
balance equations?
My understanding from Markov Chain Monte Carlo is that for the transition matrix to be regular the matrix has to have all positives entries and each row will add up to one. I was thinking the trick to this problem for it not satisfy the balance equation would be to take the transpose of the transition matrix. I was hoping someone could give me a hint if I am on the right track of thinking and where to go from there.

Thanks

 

[chiro]

Hey mjt042 and welcome to the forums.

When you mean time reversible do you mean going from transition matrix at state n+1 back to n?

 

[mjt042]

Thanks and yes.

 

[chiro]

Consider a matrix with linearly dependent rows (i.e. a determinant of zero) that still satisfy the probability conditions.

In this situation things are not time reversible since you can not solve for the inverse.

 

[mjt042]

.4 .6
.6 .4 so the matrix to the left would work?

 

[chiro]

No the determinant for this is non-zero.

Consider the matrix

.4 .6
.4 .6

 

[mjt042]

Thanks