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Geometry of Higher-Order Markov Chains

Journal Name:

  • Journal of Algebraic Statistics

Publication Year:

  • 2012

Key Words:

Author NameUniversity of Author

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Abstract (2. Language): 
We determine an explicit Grobner basis, consisting of linear forms and determinantal quadrics, for the prime ideal of Raftery's mixture transition distribution model for Markov chains. When the states are binary, the corresponding projective variety is a linear space, the model itself consists of two simplices in a cross-polytope, and the likelihood function typically has two local maxima. In the general non-binary case, the model corresponds to a cone over a Segre variety.
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REFERENCES

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