# Team : mistis

## Section: Scientific Foundations

Keywords : missing data, mixture of distributions, EM algorithm, stochastic algorithms, selection and combination of models, statistical pattern recognition, image analysis, hidden Markov field, Bayesian inference.

### Markovian models

Participants : Juliette Blanchet, Florence Forbes, Gersende Fort, Paulo Gonçalvès, Christian Lavergne, Mohammed Saidane, Matthieu Vignes.

Hidden Markov chains or hidden Markov fields correspond to cases where the
z_{i}'s are distributed according to a Markov chain or a Markov field.
These models are widely used in signal processing (speech recognition,
genome sequence analysis) and in image processing (remote sensing, MRI, etc.).
Markovian models are part of *graphical models*.
In these models, the variable organization can be
represented by a graph where the nodes represent the variables and the edges the statistical dependencies
between the variables. The graphs can be either
directed, e.g. Bayesian Networks, or undirected, e.g. Markov Random Fields.
The specificity of Markovian models is that the dependencies
between the nodes are limited to the nearest neighbor nodes. The
neighborhood definition can vary and be adapted to the problem of
interest. When parts of the variables (nodes) are not observed, we
refer to these models as Hidden Markov Models (HMM). Such models
are very flexible in practice and can naturally account for the
phenomena to be studied. They are very useful in modelling spatial
dependencies but these dependencies and the possible existence of
hidden variables are also responsible for a typically large amount
of computation. It follows that
the statistical analysis may not be straightforward
but we propose to use variational
approximations for estimation and model selection when exact calculations are
intractable. Many experiments have to be carried
out to assess the approximations quality and the associated
estimation
methods performance before addressing theoretical properties such as convergence and speed results.