The main theme of this thesis is the theoretical study of Gaussian processes as a tool in Bayesian nonparametric statistics. We are interested in the frequentist properties of Bayesian... Show moreThe main theme of this thesis is the theoretical study of Gaussian processes as a tool in Bayesian nonparametric statistics. We are interested in the frequentist properties of Bayesian nonparametric techniques in an asymptotic regime. We will be focusing specifically on consistency, convergence rates, uncertainty quantification and adaptation. These properties will be studied in the context of non-parametric problems, that is to say models with few modeling constraints. Moroever, the thesis will cover the topic of scalability of Bayesian techniques. Indeed, Bayesian methods are computation-hungry and rapidly become intractable as the number of observations grows. This issue led to the introduction of distributed Bayesian methods in order to decrease the computational complexity of the techniques. Show less
