A Markov basis for two-state toric homogeneous Markov chain model without initial parameters

TL;DR

This paper derives a minimal Markov basis for a two-state toric homogeneous Markov chain model that excludes initial parameters, enabling more efficient statistical computations.

Contribution

It introduces a Markov basis with moves of degree up to three for the model without initial parameters, expanding the tools for algebraic statistical analysis.

Findings

Markov basis includes moves of degree one, two, and three

Basis applies to chains of arbitrary length

Enables efficient sampling for the model without initial parameters

Abstract

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 of moves of degree three and degree one, which alter the initial frequencies, in addition to moves of degree two and degree one for toric homogeneous Markov chain model with parameters for initial states.