Universiteit Leiden

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Bayes and Networks

Promotor: A.W. van der Vaart

F. Gao
23 mei 2017
Thesis in Leiden Repository

The dissertation consists of research in three subjects in two themes—Bayes and networks: The first studies the posterior contraction rates for the Dirichlet-Laplace mixtures in a deconvolution setting (Chapter 1). The second subject regards the statistical inference in preferential attachment networks, in three different but related settings: for the general sublinear preferential attachment functions, we develop the empirical estimation (Chapter 3); in the case of affine preferential attachment model with random initial degrees, we employ the maximum likelihood estimation on the affine parameter with results on the estimator's asymptotic normality (Chapter 4); and for the parametric sublinear preferential attachment functions, we apply again the maximum likelihood estimation (Chapter 5). The last subject is about the modeling and inference of the movie-actor network with preferential attachment models (Chapter 6), and based on the data made publicly available by the internet movie database.