[R] visualizing transition probability matrices

[Thomas W Blackwell]

On Mon, 6 Oct 2003, Tamas Papp wrote:

> I have a couple of (~200) 3x3 transition probability matrices (ie each
> defines a Markov chain). They are all estimated from the same
> underlying process, so it ie meaningful to take their elemetwise mean
> and standard deviation. [1]
>
> First question: supposing that they are given in a list l, how do I
> get their elementwise mean and standard deviation? Fortunately, the
> mean of trans. prob. matrices also remains a transition probability
> matrix. I'm not sure if taking the standard deviation is meaningful,
> though. Any suggestions?
>
> Second (more important): what would be the best way of visualizing the
> 3x3 mean and standard deviation matrices? For the mean, I thought of a
> barplot where the layers add up to 1, but I have no experience with
> visualization of statistical data (at least, reading this list I
> learned that I should avoid circles, pie-charts and their ilk).

Gosh, a 3x3 transition matrix has only two non-trivial eigenvectors,
one of which corresponds to the limiting distribution, so I would
simply plot 2 x 200 = 400 points in 3 dimensions, and look at the
matrices themselves, rather than at a mean and standard deviation.

-  tom blackwell  -  u michigan medical school  -  ann arbor  -

> Thanks,
> Tamas
>
> [1] You could ask why I don't just estimate the trans. prob. matrix
> just once from the whole dataset. The problem is that the process is
> meant to model (real) interest rates with only three levels, and
> involves many peculiar assumptions. By the way, many thanks to Kjetil
> Brinchmann Halvorsen, Rolf Turner, Ted Harding, Patrick Burns and
> Martin Maechler for giving detailed and helpful replies to my earlier
> question about Markov chains in R.
> --
> Tamás K. Papp
> E-mail: tpapp at axelero.hu (preferred, especially for large messages)
>         tpapp at westel900.net
>