Bayesian Analysis and Model Checking. Any Bayesian analysis requires you to create and apply a statistical model: a set of formulas for calculating posterior probabilities given prior probabilities, estimates of model parameters, and observed data. Model parameters are just the constant values that appear in model formulas. Because any model is just a rough approximation of reality, not the real thing, it is important to test whether the model is close enough to reality to trust predictions made using the model. One way to do this is to test whether substantive predictions made using a model agree with what you already know. For some Bayesian applications, model parameters are known before you being an analysis (a priori). This is not true for some other Bayesian applications such as record linkage and missing data imputation. For these more difficult cases, a statistical technique called Markov Chain Monte Carlo Data Augmentation can be applied. Essentially, parameter estimates are used to approximate the model and then the approximate model is used to re-estimate the parameters in an iterative process. So, posterior estimates of model parameters are really just predictions made by the model. You can compare these predictions to what you already know (your prior estimates) in order to test whether your model is close enough to reality.