The three-state toric homogeneous Markov chain model has Markov degree two

@article{Norn2015TheTT,
  title={The three-state toric homogeneous Markov chain model has Markov degree two},
  author={Patrik Nor{\'e}n},
  journal={J. Symb. Comput.},
  year={2015},
  volume={68},
  pages={285-296}
}
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TLDR
A dynamic approach to explore the fiber of a model is presented, which is based on the combinatorics of hypergraphs arising from the toric algebra structure of log-linear models and allows for reciprocation effects.
Algebra & Number Theory

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We study the three state toric homogeneous Markov chain model and three special cases of it, namely: (i) when the initial state parameters are constant, (ii) without self-loops, and (iii) when both…
A Markov basis for two-state toric homogeneous Markov chain model without initial parameters
We derive a Markov basis consisting of moves of degree at most three for two-state toric homogeneous Markov chain model of arbitrary length without parameters for initial states. Our basis consists…
Markov degree of the three-state toric homogeneous Markov chain model
We consider the three-state toric homogeneous Markov chain model (THMC) without loops and initial parameters. At time $$T$$T, the size of the design matrix is $$6 \times 3\cdot 2^{T-1}$$6×3·2T-1 and…
Markov chain Monte Carlo test of toric homogeneous Markov chains
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