Bayesian analysis of a linear mixed model with AR(p) errors via MCMC

Abstract

We develop Bayesian procedures to make inference about parameters of a statistical design with autocorrelated error terms. Modelling treatment effects can be complex in the presence of other factors such as time; for example in longitudinal data. In this paper, Markov chain Monte Carlo methods (MCMC), the Metropolis–Hastings algorithm and Gibbs sampler are used to facilitate the Bayesian analysis of real life data when the error structure can be expressed as an autoregressive model of order p. We illustrate our analysis with real data.

Keywords:

• Linear mixed model
• autoregressive process
• Metropolis–Hastings algorithm
• Gibbs sampling
• Bayesian statistics
• autocorrelation
• repeated measurement designs

Acknowledgements

The authors wish to thank Keith Knight for helpful discussions.