* Correspondence: [email protected] Faculty of Science, Jiangsu University, Zhenjiang, 212013, China Full list of author information is available at the end of the article Abstract In this paper, we study a convergence theorem for a finite second-order Markov chain indexed by a general infinite tree with uniformly bounded degree. Meanwhile, the strong law of large numbers (LLN) and Shannon-...

A recent dual-tree wavelet shrinkage method to suppress sand ripples in sonar imagery is extended with a Markov random field framework. Markov chain Monte Carlo sampling is used to estimate the posterior marginal ripple state in the wavelet domain. Ripple suppression is realised by multiplying the dual-tree wavelet coefficients by the conditional probabilities of the non-ripple state. Tests on ...

In this paper we show that an arbitrary tree structured QBD Markov chain can be embedded in a tree-like QBD process with a special structure. Moreover, we present an algebraic proof that applying the natural fixed point iteration (FPI) to the nonlinear matrix equation V = B + ∑d s=1 Us(I − V )Ds that solves the tree-like QBD process, is equivalent to the more complicated iterative algorithm pre...

Assessing the Convergence of Markov Chain Monte Carlo Methods for Bayesian Inference of Phylogenetic Trees In biology, it is commonly of interest to investigate the ancestral pattern that gave rise to a currently existing group of individuals, such as genes or species. This ancestral pattern is frequently represented pictorially by a phylogenetic tree. Due to the growing popularity of Bayesian ...

Algorithms are presented that allow the calculation of the probability of a set of sequences related by a binary tree that have evolved according to the Thorne-Kishino-Felsenstein model for a fixed set of parameters. The algorithms are based on a Markov chain generating sequences and their alignment at nodes in a tree. Depending on whether the complete realization of this Markov chain is decomp...

Weiru Liu, Xin Hong, and Kenny Adamson School of Computing and Mathematics, University of Ulster at Jordanstown, UK [email protected] Abstract. Binary join trees have been a popular structure to compute the impact of multiple belief functions initially assigned to nodes of trees or networks. Shenoy has proposed two alternative methods to transform a qualitative Markov tree into a binary tree. ...

We introduce two models for multi-type random trees motivated by studies of trait dependence in the evolution of species. Our discrete time model, the multi-type ERM tree, is a generalization of Markov propagation models on a random tree generated by a binary search or ‘equal rates Markov’ mechanism. Our continuous time model, the multi-type Yule tree with mutations, is a multi-type generalizat...

An algorithm is presented that allows the calculation of the probability of a set of sequences related by a binary tree that has evolved according to the Thorne-Kishino-Felsenstein model (1991) for a fixed set of parameters. There are two ideas underlying this algorithm. Firstly, a markov chain is defined that generates ancestral sequences and their alignment at two neighboring nodes in a tree....

This paper provides some new guidance in the construction of region graphs for Generalized Belief Propagation (GBP). We connect the problem of choosing the outer regions of a LoopStructured Region Graph (SRG) to that of finding a fundamental cycle basis of the corresponding Markov network. We also define a new class of tree-robust Loop-SRG for which GBP on any induced (spanning) tree of the Mar...