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.wil...@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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