Section: Overall Objectives
The mistis team aims at developing statistical methods for dealing with complex problems or data. Our applications relate mainly to image processing and spatial data problems with some applications in environment, biology and medicine. Our approach is based on the statement that complexity can be handled by working up from simple local assumptions in a coherent way, defining a structured model, and that is the key to modelling, computation, inference and interpretation. The methods we focus on involve mixture models, Markov models, and, more generally, hidden structure models identified by deterministic or stochastic algorithms on one hand, and semi and non-parametric methods on the other hand.
Hidden structure models are useful for taking into account heterogeneity in data. They concern many areas of statistical methodology (finite mixture analysis, hidden Markov models, random effect models, etc). Due to their missing data structure, they induce specific difficulties for both estimating the model parameters and assessing performance. The team focuses on research regarding both aspects. We design specific algorithms for estimating the parameters of missing structure models and we propose and study specific criteria for choosing the most relevant missing structure models in several contexts.
Semi- and non-parametric methods are relevant and useful when no appropriate parametric model exists for the data under study either because of data complexity, or because information is missing. The focus is on functions describing curves or surfaces or more generally manifolds rather than real valued parameters. This can be interesting in image processing for instance where it can be difficult to introduce parametric models that are general enough (e.g. for contours).