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Probabilistic graphical models for statistical genetics and survival analysis. Application to the Lynch syndrome

Abstract : Probabilistic graphical models are omniscient in the study of complex systems involving latent variables. The sum-product algorithm exploits the graph structure for reducing the algorithmic complexity of an inference. In this thesis, we are interested in exact inference in Bayesian networks (BNs) and hidden Markov models (HMMs) and applications in survival analysis, genetics and segmentation. Two main themes are explored: - Extensions of the sum-product algorithm on the polynomial ring: inspired by versions of the algorithm over polynomial potentials to compute probability and moment generating functions, we develop a method for computing the exact derivatives of the likelihood up to a chosen order in BNs. Furthermore, we propose a method based on probability generating functions in constrained HMMs to relax the constraint on the prior for the segmentation space, in particular the number of homogeneous segments, in sequence segmentation. - Development of a BN for computing probabilities of genetic predisposition and cancer risks in the framework of the Lynch syndrome (LS). The LS is defined as a germline monoallelic pathogenic mutation in a gene of the mismatch repair system. BNs are particularly suited for studying familial genetics as they allow for modeling the structure dependency between genotypes (usually latent) and phenotypes (usually observed) of family members. As the Lynch spectrum is wide and multiple diagnoses for LS carriers not rare, personal histories of cancer are modeled in a multi-state survival model.
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https://tel.archives-ouvertes.fr/tel-03771227
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Submitted on : Wednesday, September 7, 2022 - 10:57:43 AM
Last modification on : Thursday, September 8, 2022 - 3:53:51 AM

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  • HAL Id : tel-03771227, version 1

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Alexandra Lefebvre. Probabilistic graphical models for statistical genetics and survival analysis. Application to the Lynch syndrome. Statistics [math.ST]. Sorbonne Université, 2022. English. ⟨NNT : 2022SORUS055⟩. ⟨tel-03771227⟩

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