Section: Overall Objectives

Overall Objectives

BIGS is a team labeled by Inria, by CNRS and by Université de Lorraine, via the Institut Élie Cartan of Nancy (UMR 7502 CNRS-Inria-UL). Our research is mainly focused on statistics and stochastic processes techniques aiming at a better understanding of biological systems. A special attention is devoted to online data analysis, local regression techniques and identification of complex biological systems. Our investigations encompass both theoretical aspects and concrete applications of the issues alluded to above. To be more specific, we focus on the following topics:

$•$ Online Factorial Analysis: High dimensional data are often obtained online, and cannot be stored integrally in a computer memory. One of the recent challenges in data analysis is then to be able to perform an accurate classification or clustering by taking advantage of the possibility of updating the information. This has to be done, of course, in a rather simple and efficient way, allowing real time analysis. To this aim, we use techniques based on some sophisticated tools coming from stochastic approximation.

$•$ Local Regression Techniques: The main issue here is the construction of a procedure allowing to assess, in quite a general framework, whether a given model fits a data set regarding most assumptions made in elaborating the model. This is based on a generalization of the Cramer-Von Mises statistics and involves a non parametric estimate of the conditional distribution of the response variable. A detailed analysis of the procedure, including rate of convergence and asymptotic properties, is being performed. The strategy is then implemented for a study concerning fetal biometry.

$•$ Photodynamic therapy: Since 1988, some control system scientists and biologists at the Centre de Recherche en Automatique de Nancy (CRAN in short) have worked together to develop the photodynamic therapy (PDT), an alternative treatment for cancer, by means of a model-based approach. The global aim in this direction is to use statistical as well as mechanistic models in order to (i) improve the response reproducibility, (ii) help biologists and chemists in the design of new photosensitizing agents and (iii) provide insight into complex phenomena associated with oncogenesis, tumor angiogenesis and interactions with the treatment. This heavily relies on the production of accurate and simple enough models involving various type of stochastic processes, such as Markov chains, branching processes and stochastic differential equations. The main questions here concern generally identification or estimation properties, but simulation issues can be important too.

$•$ Estimation for complex biological systems: Numerous biological systems are accurately described by multidimensional noisy differential equations driven by Gaussian processes (beyond the realm of Brownian motion) or by fractional fields, for which asymptotic properties and parameter estimation are fruitful informations. We are thus interested in studying this kind of systems, having in mind 3 specific applications of interest for us: (i) Bacteriophage systems (ii) Random fluctuation of nanoparticles. (iii) Automatic detection of osteoporosis.