Due to great applications in various fields, such as social science, biomedicine, genomics, and signal processing, and the improvement of computing ability, Bayesian inference has made substantial developments for analyzing complicated data. This book introduces key ideas of Bayesian sampling methods, Bayesian estimation, and selection of the prior. It is structured around topics on the impact of the choice of the prior on Bayesian statistics, some advances on Bayesian sampling methods, and Bayesian inference for complicated data including breast cancer data, cloud-based healthcare data, gene network data, and longitudinal data. This volume is designed for statisticians, engineers, doctors, and machine learning researchers.