This course covers the theoretical and applied foundations of Bayesian statistical analysis. It introduces the logic of Bayesian inference, the idea of regularization, the role of subjective priors, the likelihood, and the posterior distribution. We will discuss model checking and model comparison. Applied Bayesian models include Hierarchical models, factor analysis and item response theory models, treatment effect models, and generalized additive models. Throughout the course, we will focus on the flexible modeling of data arising in social/political science, as well as in public health. We will also pay close attention to the presentation and interpretation of substantive results.