Maximum Likelihood Markov Hypertrees

Maximum number of colors in hypertrees of bounded degree

The upper chromatic number χ(H) of a hypergraph H = (X, E) is the maximum number of colors that can occur in a vertex coloring φ : X → N such that no edge E ∈ E is completely multicolored. A hypertree (also called arboreal hypergraph) is a hypergraph whose edges induce subtrees on a fixed tree graph. It has been shown that on hypertrees it is algorithmically hard not only to determine exactly b...

Maximum Lilkelihood and Restricted Maximum Likelihood Estimation for a Class of Gaussian Markov Random Fields Maximum Likelihood and Restricted Maximum Likelihood Estimation for a Class of Gaussian Markov Random Fields

Statistical inference for discretely observed Markov jump processes

Likelihood inference for discretely observed Markov jump processes with finite state space is investigated. The existence and uniqueness of the maximum likelihood estimator of the intensity matrix are investigated. This topic is closely related to the imbedding problem for Markov chains. It is demonstrated that the maximum likelihood estimator can be found either by the EM algorithm or by a Mar...

Maximum-likelihood estimation for hidden Markov models

Hidden Markov models assume a sequence of random variables to be conditionally independent given a sequence of state variables which forms a Markov chain. Maximum-likelihood estimation for these models can be performed using the EM algorithm. In this paper the consistency of a sequence of maximum-likelihood estimators is proved. Also, the conclusion of the Shannon-McMillan-Breiman theorem on en...

Estimation of Hidden Markov Models with Nonparametric Simulated Maximum Likelihood

We propose a nonparametric simulated maximum likelihood estimation (NPSMLE) with built-in nonlinear …ltering. By recursively approximating the unknown conditional densities, our method enables a maximum likelihood estimation of general dynamic models with latent variables— including time-inhomogeneous and non-stationary processes. We establish the asymptotic properties of the NPSMLEs for hidden...