Pairwise Markov Chains

Pairwise Markov Chains and Bayesian Unsupervised Fusion

Empirical Bayes Estimation in Nonstationary Markov chains

Estimation procedures for nonstationary Markov chains appear to be relatively sparse. This work introduces empirical  Bayes estimators  for the transition probability  matrix of a finite nonstationary  Markov chain. The data are assumed to be of  a panel study type in which each data set consists of a sequence of observations on N>=2 independent and identically dis...

The Rate of Rényi Entropy for Irreducible Markov Chains

In this paper, we obtain the Rényi entropy rate for irreducible-aperiodic Markov chains with countable state space, using the theory of countable nonnegative matrices. We also obtain the bound for the rate of Rényi entropy of an irreducible Markov chain. Finally, we show that the bound for the Rényi entropy rate is the Shannon entropy rate.

Switching Pairwise Markov Chains for Non Stationary Textured Images Segmentation

Hidden Markov chains (HMCs) have been extensively used to solve a wide range of problems related to computer vision, signal processing (Cappé, O., et al 2005) or bioinformatics (Koski, T., 2001). Such notoriety is due to their ability to recover the hidden data of interest using the entire observable signal thanks to some Bayesian techniques like MPM and MAP. HMCs have then been generalized to ...

Exit Time Tails From Pairwise Decorrelation in Hidden Markov Chains, With Applications to Dynamical Percolation

Consider a Markov process ωt at stationarity and some event C (a subset of the state-space of the process). A natural measure of correlations in the process is the pairwise correlation P[ω0,ωt∈C]−P[ω0∈C]2. A second natural measure is the probability of the continual occurrence event {ωs∈C,∀s∈[0,t]}. We show that for reversible Markov chains, and any event C, pairwise decorrelation of the event ...

SAR Image Segmentation using Generalized Pairwise Markov Chains

The efficiency of Markov models in the context of SAR image segmentation mainly relies on their spatial regularity constraint. However, a pixel may have a rather different visual aspect when it is located near a boundary or inside a large set of pixels of the same class. According to the classical hypothesis in Hidden Markov Chain (HMC) models, this fact can not be taken into consideration. Thi...