This chapter delves into the core principles and applications of Bayesian statistics, with a particular focus on Bayesian Credible Intervals and Bayes Factor. It begins by contrasting the Bayesian approach with frequentist methods, emphasizing the unique interpretation of probability and the integration of prior knowledge in Bayesian inference. The chapter comprehensively explores Bayesian Credible Intervals, discussing their definition, properties, computational aspects, and role in decision-making. It also examines the harmony and discrepancies between Credible Intervals and Bayes Factors, especially in light of recent findings that highlight conflicts in Bayesian statistics. The chapter concludes by reflecting on the coherence of Bayesian methods and their significance in modern statistical practice, underscoring the importance of thoughtful application and interpretation of these methods in research and decision-making.