Bayesian methods for tackling complex inferential problems in data science

Bayesian methods encompass a principled way of modeling, solving and analyzingvarious estimation and inference problems in data science. In this dissertation, weutilize a variety of Bayesian methods, such as posterior sampling, EM algorithm formixture models, subsampling for prior probability estimation, to tackle a wide rangeof inferential problems. These problems include hyperparameter tuning in regularizedlinear models in supervised learning, robust regression, frequency estimationfor dynamic/online datasets under global and local differential privacy frameworks.For each of these problems, we propose new algorithms that can compete with theexisting approaches in terms of estimation accuracy, while performing these tasksin a computationally more efficient way via utilizing sampling and subsampling.Along with each algorithm, we also provide both theoretical analyses and numericalexperiments that demonstrate their estimation performance.