Integrating Out Nuisance Parameters for Computationally More Efficient Bayesian Estimation: An Illustration and Tutorial

Bayesian estimation has become very popular. However, run time of Bayesian models is often unsatisfactorily high. In this illustration, we show how to reduce run time by (a) integrating out nuisance model parameters and by (b) reformulating the model based on covariances and means. The core concept is to use the sample scatter matrix which is in our case Wishart distributed with the model-implied covariance matrix as the scale matrix. To illustrate this approach, we choose the popular multi-level null (intercept-only) model, provide a step-by-step instruction on how to implement this model in a multi-purpose Bayesian software, and show how structural equation modeling techniques can be employed to bypass mathematically challenging derivations. A simulation study showed that run time is considerably reduced and an empirical example illustrates our approach. Further, we show how the JAGS sampling progress can be monitored and stopped automatically when convergence and precision criteria are reached.