We consider Hidden Markov Chains obtained by passing a Markov Chain with rare transitions through a noisy memoryless channel. We obtain asymptotic estimates for the entropy of the resulting Hidden Markov Chain as the transition rate is reduced to zero. Let (Xn) be a Markov chain with finite state space S and transition matrix P (p) and let (Yn) be the Hidden Markov chain observed by passing (Xn...

This paper describes a method of enhancing speech corrupted by additive uncorrelated noise. The approach adopted is to use cepstral-domain hidden Markov models to determine statistics of the clean speech and noise processes. A compensated model of speech corrupted by noise is generated using parallel model combination. MMSE and linear non-homogeneous estimators of the clean speech signal are de...

In this paper, we propose a family of non-homogeneous Gauss-Markov fields with Potts region labels model for images to be used in a Bayesian estimation framework, in order to jointly restore and segment images degraded by a known point spread function and additive noise. The joint posterior law of all the unknowns ( the unknown image, its segmentation hidden variable and all the hyperparameters...

In this paper, we study large deviations of maximum likelihood and related estimators for hidden Markov models. A hidden Markov model consists of parameterized Markov chains in a Markovian random environment, with the underlying environmental Markov chain viewed as missing data. A difficulty with parameter estimation in this model is the non-additivity of the log-likelihood function. Based on a...

An overview of statistical and information-theoretic aspects of hidden Markov processes (HMPs) is presented. An HMP is a discrete-time finite-state homogeneous Markov chain observed through a discrete-time memoryless invariant channel. In recent years, the work of Baum and Petrie on finite-state finite-alphabet HMPs was expanded to HMPs with finite as well as continuous state spaces and a gener...

This paper proposes a short-term water demand forecasting method based on the use of the Markov chain. This method provides estimates of future demands by calculating probabilities that the future demand value will fall within pre-assigned intervals covering the expected total variability. More specifically, two models based on homogeneous and non-homogeneous Markov chains were developed and pr...