With growing interest in data mining and its merits, including the incorporation of historical or experiential information into statistical analysis, Bayesian inference has become an important tool for analyzing complicated data and solving inverse problems in various fields such as artificial intelligence. This book introduces recent developments in Bayesian inference, and covers a variety of topics including robust Bayesian estimation, solving inverse problems via Bayesian theories, hierarchical Bayesian inference, and its applications for scattering experiments. We hope that this book will stimulate more extensive research on Bayesian fronts to include theories, methods, computational algorithms and applications in various fields such as data science, AI, machine learning, and causality analysis.