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The three-state toric homogeneous Markov chain model has Markov degree two
three-state toric Markov chain model Markov degree two Statistics Theory
2012/7/9
We prove that the three-state toric homogenous Markov chain model has Markov degree two. In algebraic terminology, that a certain class of toric ideals are generated by quadratic binomials. This was c...
On nonlinear Markov chain Monte Carlo
Foster–Lyapunov condition interacting Markov chains nonlinear Markov kernels Poisson equation
2011/9/9
Abstract: Let $\mathscr{P}(E)$ be the space of probability measures on a measurable space $(E,\mathcal{E})$. In this paper we introduce a class of nonlinear Markov chain Monte Carlo (MCMC) methods for...
A simple variance inequality for U-statistics of a Markov chain with applications
U-statistics Markov chains Inequalities Limit theorems Law of large numbers
2011/9/5
Abstract: We establish a simple variance inequality for U-statistics whose underlying sequence of random variables is an ergodic Markov Chain. The constants in this inequality are explicit and depend ...