Posterior inference in the random intercept model based on samples obtained with Markov chain Monte Carlo methods
The goal of this paper is to show the potential of Markov chain Monte Carlo (MCMC) methods. First of all it is demonstrated that posterior inference with respect to transformations and combinations of model parameters becomes rather easy if MCMC methods are applied. The author uses the random intercept model to introduce and illustrate properties of the augmented Gibbs sampler (AGS) as special case of MCMC approach. In such model \(y_{jk}=a_j+bx_{jk}+\varepsilon_{jk}\), where \(x_{jk}\) is the predictor, \(a_{j}\) is a random intercept, \(b\) denotes the regression coefficient, and the residual has \(N(0,\sigma^2)\) distribution. A short excursion to more general MCMC methods is also proposed. The paper focuses on the inferential possibilities offered by the availability of a sample from the posterior distribution. This sample can be used to compute posterior parameter estimations, standard deviations and credibility intervals. Using a simulation study, the frequency properties of some of these quantities are evaluated. The results of application of AGS to analysis of junior project data are presented.
scientific article; zbMATH DE number 2058937
scientific article