# Markov Chain Monte Carlo question

1. Jun 14, 2013

### 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

2. Jun 15, 2013

### 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?

3. Jun 15, 2013

### mjt042

Thanks and yes.

4. Jun 15, 2013

### 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.

5. Jun 16, 2013

### mjt042

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

6. Jun 16, 2013

### chiro

No the determinant for this is non-zero.

Consider the matrix

.4 .6
.4 .6

7. Jun 16, 2013

Thanks