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I have written three essays in the area of Bayesian inference and deep learning. The first essay uses the theory of normal variance-mean mixtures to derive a data augmentation scheme for models that include gamma functions. The second essay introduces and develops a weighted Bayesian bootstrap for machine learning and statistics. The last essay studies the characteristics-sorted factor model in empirical asset pricing and designs a nonreduced-form feedforward neural network with the non-arbitrage objective to minimize pricing errors.