ABSTRACT
This chapter presents the fundamental to the theory and application of Bayesian statistics at the intermediate and advanced levels. Advances in computational methods have made it fairly straightforward to apply Bayesian methods in many scientific contexts. The chapter emphasizes the importance of incorporating scientifically relevant information into priors when it is available. Jeffreys proposed a class of non-subjective priors for Bayesian problems that can often be termed reference priors. The chapter discusses the informative priors and the key assumption of prior independence between parameters. It discusses a number of examples that illustrate the type of priors that we advocate in the absence of substantive scientific information. The chapter discusses “diffuse” priors that are expected to have little impact on the posterior.
