Introducing myself
I got my PhD of mathematics in 2014 in the Université Lyon 1 (France). My supervisors were Jean Bérard and Anne-Laure Fougères.
For more information about me, you can check my blog and my LinkedIn/Viadeo profiles.
Thesis
My dissertation is available here (in French):
To download my defence presentation, click here.Abstract: This thesis is devoted to the inference of context-dependent evolutionary models of DNA sequences, and is specifically focused on the RN95+YPR class of stochastic models. This class of models is based on the reinforcement of some substitution rates depending on the local context, which introduces dependence phenomena between sites in the evolution of the DNA sequence. Because of these dependencies, the direct computation of the likelihood of the observed sequences involves high-dimensional matrices, and is usually infeasible.
Through encodings specific to the RN95+YpR class, we highlight new spatial dependence structures for these models, which are related to the evolution of DNA sequences throughout their evolutionary history. This enables the use of particle filter algorithms, developed in the context of hidden Markov models, in order to obtain consistent approximations of the likelihood. Another type of approximation of the likelihood, based on composite likelihoods, is also introduced.
These approximation methods for the likelihood are implemented in a C++ program. They are applied on simulated data to empirically investigate some of their properties, and on genomic data, especially for comparison of evolutionary models.