Section: New Results

Stochastic modeling

Spatial and spatio-temporal modeling

Participants: A. Gégout-Petit

External collaborators: Y. Cao, S. Li, L. Guerin-Dubrana (Inra Bordeaux)

In the framework of a collaboration with INRA Bordeaux about the esca-illness of vines, Anne Gégout-Petit with Shuxian Li developed different spatial models and spatio-temporal models for different purposes: (1) study the distribution and the dynamics of esca vines in order to tackle the aggregation and the potential spread of the illness (2) propose a spatio-temporal model in order to capture the dynamics of cases and measure the effects of environmental covariates. For purpose (1), we propose different test based on the join count statistics, a paper is accepted for publication [5]. We also developped a two-step centered autologistic model for the study of the dynamic of propagation. This work has been presented as invited paper in [20] and is in preparation for publication.

Modelisation of response to chemotherapy in gliomas

Participant: S. Wantz-Mézières

External collaborator: J.-M. Moureaux, Y. Gaudeau, M. Ben Abdallah, M. Ouqamra (CRAN, Université de Lorraine), L. Taillandier, M. Blonski (CHU Nancy)

The collaboration with neurologists (CHU Nancy) and automaticians (CRAN) has carried on this year and led to the PhD presentation of M. Ben Abdallah, on December 12, 2016 [17], [16]. We completed the modeling approach by a data analysis one. In the framework of a master 2 project, supervised and non supervised methods have confirmed our results on our local data base. This encourages us to continue our work in extending the data base via a collaboration with Montpellier CHU. Our perspectives are to validate multi-factor models, including biological and anatomopathological factors, and to design a decision-aid tool for praticians.

Time-changed extremal process as a random sup measure

Participant: Céline Lacaux

External collaborator: Gennady Samorodnistky

In extreme value theory, one of the major topics is the study of the limiting behavior of the partial maxima of a stationary sequence. When this sequence is i.i.d., the unique limiting process is well-known and called the extremal process. Considering a long memory stable sequence, the limiting process is obtained as a simple power time change extremal process. Céline Lacaux and Gennady Samorodnistky have proved that this limiting process can also be interpreted as a restriction of a self-affine random sup measure. In addition, they have established that this random measure arises as a limit of the partial maxima of the same long memory stable sequence, but in a different space. Their results open the way to propose new self-similar processes with stationary max-increments.

Fast and Exact synthesis of some operator scaling Gaussian random fields

Participant: Céline Lacaux

External collaborator: Hermine Biermé

Operator scaling Gaussian random fields, as anisotropic generalizations of self-similar fields, know an increasing interest in the literature. Up to now, such models were only defined through stochastic integrals, without knowing explicitly their covariance functions. In link with this misunderstanding, one of the drawbacks is that no exact method of simulation has been proposed. In view to fill this lack, Hermine Biermé and Céline Lacaux have recently exhibit explicit covariance functions, as anisotropic generalizations of fractional Brownian fields ones. This allows them to propose a fast and exact method to synthetise an operator scaling Gaussian random fields with such a covariance function. Their algorithm is based on the famous circulant embedding matrix method. This is a first piece of work to popularized operator scaling Gaussian random field in anisotropic spatial data modeling.

DNA sequences analysis

Participants: P. Vallois

External collaborators: A. Lagnoux and S. Mercier (Toulouse)

In an article accepted at Bioinformatics, the goal is to illustrate different results on the local score distribution assuming an i.i.d. model, especially the one based on the pair (local score,length) and the one on the local score position. We measure with statistical tests how different approximations of the local score distribution fit to simulated sequences. In particular, our simulations show that the popular Karlin & Altschul approximation is not accurate in a wide range of situations. We add to the local score the length of the segment that realises it and we study the induced changes with numerical simulations. We also study specificity and sensitivity for the different methods. We introduce a new one dimensional statistic which is a function of $H_n^{*}$ and $L_n^{*}$ and we test its distribution. Finally, we estimate the probability that $H_n^{*}=H_n$ in different settings.