Bayesian inference for mixed effects models with heterogeneity

We are interested in Bayesian modelling of panel data using a mixed e ects model with heterogeneity in the individual random e ects. We compare two di erent approaches for modelling the heterogeneity using a mixture of Gaussians. In the rst model, we assume an in nite mixture model with a Dirichlet process prior, which is a non-parametric Bayesian model. In the second model, we assume an over-parametrised nite mixture model with a sparseness prior. Recent work indicates that the second model can be seen as an approximation of the former. In this paper, we investigate this claim and compare the estimates of the posteriors and the mixing obtained by Gibbs sampling in these two models. The results from using both synthetic and real-world data supports the claim that the estimates of the posterior from both models agree even when the data record is nite.