Bayesian statistical modeling is essential in ecological and environmental science, but most users of these approaches are limited to implementing Bayesian models with automated software. This book presents details and algorithms for fully Bayesian computation, primarily for students and practitioners in the ecological and environmental sciences. It empowers the reader to extend and enhance statistical models for such data without software limitations. It teaches fundamental aspects of how to connect statistical models to computer algorithms so that they can implement their own models that are specific their problem of interest without limitation.