This work gives an overview of statistical analysis for some models multivariate discrete-valued (MDV) time series. We present observation-driven and based on higher-order Markov chains. Several extensions are highlighted including non-stationarity, network autoregressions, conditional non-linear autoregressive models, robust estimation, random fields spatio-temporal models.

In a Bayesian approach for solving linear inverse problems one needs to specify the prior laws for calculation of the posterior law. A cost function can also be defined in order to have a common tool for various Bayesian estimators which depend on the data and the hyperparameters. The Gaussian case excepted, these estimators are not linear and so depend on the scale of the measurements. In this...

In a Bayesian approach for solving linear inverse problems one needs to specify the prior laws for calculation of the posterior law. A cost function can also be deened in order to have a common tool for various Bayesian estimators which depend on the data and the hyperparameters. The Gaussian case excepted, these estimators are not linear and so depend on the scale of the measurements. In this ...

Wireless communication systems based on multiple-input multiple-output (MIMO) technology and orthogonal frequency division multiplexing (OFDM) have the potential to achieve enormous increase in the capacity and link reliability. In order to realize such systems, channel estimation is crucial. In this paper, an adaptive channel estimation and tracking scheme based on recursive least squares (RLS...

We use the Markov Random Field (MRF) model in order to segment sonar images, i.e. to localize the sea bottom areas and the projected shadow areas corresponding to objects lying on seaaoor. This model requires on one hand knowledges about the statistical distributions relative to the diierent zones and on the other hand the estimation of the law parameters. The Kolmogorov criterion or the 2 crit...

Hidden Markov models (HMM) are successfully applied in various elds of time series analysis. Colored noise, e.g. due to ltering, violates basic assumptions of the model. While it is well-known how to consider auto-regressive (AR) ltering, there is no algorithm to take into account moving-average (MA) ltering in parameter estimation exactly. We present an approximate likelihood estimator for MA-...

Most statistical analyses of fMRI data assume that the nature, timing and duration of the psychological processes being studied are known. However, in many areas of psychological inquiry, it is hard to specify this information a priori. Examples include studies of drug uptake, emotional states or experiments with a sustained stimulus. In this paper we assume that the timing of a subject's activ...

The estimation of quality for real time services over telecommunication networks requires realistic models in order to generate impairments and failures during transmission. Starting with the classical Gilbert-Elliot model, we derive the second order statistics over arbitrary time scales and fit the parameters to match the packet loss pattern of traffic traces. The results show that simple Mark...

We study the entropy rate of a hidden Markov process, defined by observing the output of a symmetric channel whose input is a first order Markov process. Although this definition is very simple, obtaining the exact amount of entropy rate in calculation is an open problem. We introduce some probability matrices based on Markov chain's and channel's parameters. Then, we try to obtain an estimate ...

We use an exact Bayesian calculation to design classifiers that distinguish whether a finite sequence drawn from a finite alphabet is a sample path of a Markov chain of order k = 0 or of order k > 0. Three exact Bayes (EB) classifiers are derived, each corresponding to a different prior. We also include a classifier based on the Bayesian Information Criterion (BIC), a popular technique for Mark...