The transition matrix is a collection of conditional distributions.
it would seem natural to compute the entropy of the stationary
distribution.
albyn
Quoting "Wilson, Andrew" <a.wilson at lancaster.ac.uk>:
> Does anyone have any "R" code for computing the entropy of a
simple
> first or second order Markov chain, given a transition matrix something
> like the following (or the symbol vector from which it is computed)?
>
> AGRe ARIe CSRe DIRe DSCe eos
> HRMe SPTe TOBe
> AGRe 0.0000000 0.0000000 0.0000000 0.0000000 1.0000000 0.0000000
> 0.0000000 0.0000000 0.0000000
> ARIe 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 1.0000000
> 0.0000000 0.0000000 0.0000000
> CSRe 0.0000000 0.0000000 0.0000000 0.0000000 1.0000000 0.0000000
> 0.0000000 0.0000000 0.0000000
> DIRe 0.0000000 0.0000000 0.0000000 0.0000000 1.0000000 0.0000000
> 0.0000000 0.0000000 0.0000000
> DSCe 0.1666667 0.1666667 0.0000000 0.0000000 0.1666667 0.0000000
> 0.1666667 0.1666667 0.1666667
> eos 0.0000000 0.0000000 0.0000000 0.0000000 1.0000000 0.0000000
> 0.0000000 0.0000000 0.0000000
> HRMe 0.0000000 0.0000000 0.0000000 1.0000000 0.0000000 0.0000000
> 0.0000000 0.0000000 0.0000000
> NMSe 0.0000000 0.0000000 0.0000000 0.0000000 1.0000000 0.0000000
> 0.0000000 0.0000000 0.0000000
> TOBe 0.0000000 0.0000000 1.0000000 0.0000000 0.0000000 0.0000000
> 0.0000000 0.0000000 0.0000000
>
> [The second order matrix would have column names incorporating both
> prior states - e.g. "SPTe.TOBe".]
>
> I looked around at the various simple entropy functions but couldn't
> find anything for this specific problem - they seem mostly to assume a
> single numerical vector as input.
>
> Many thanks in advance for any help,
>
> Andrew Wilson
>
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