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Modélisation stochastique et analyse statistique de la pulsatilité en neuroendocrinologie

Abstract : The aim of this thesis is to propose several models representing neuronal calcic activity and unsderstand its applicatition in the secretion of GnRH hormone. This work relies on experience realised in INRA Centre Val de Loire. Chapter 1 proposes a continuous model, in which we examine a Markov process of shot-noise type. Chapter 2 studies a discrete model type AR(1), based on a discretization of the model from Chapter 1 and proposes a first estimation of the parameters. Chapter 3 proposes another dicrete model, type AR(1), in which the innovations are the sum of a Bernouilli variable and a Gaussian variable representing a noise, and taking into account a linear drift . Estimations of the parameters are given in order to detect spikes in neuronal paths. Chapter 4 studies a biological experience involving 33 neurons. With the modelisation of Chapter 3, we detect synchronization instants (simultaneous spkike of a high proportion of neurons of the experience) and then, using simulations, we test the quality of the method that we used and we compare it to an experimental approach.
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Camille Constant. Modélisation stochastique et analyse statistique de la pulsatilité en neuroendocrinologie. Probabilités [math.PR]. Université de Poitiers, 2019. Français. ⟨NNT : 2019POIT2330⟩. ⟨tel-02529299⟩

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