The performance of three versions of the Gibbs sampling algorithm, and of two versions of the Langevin-Hastings algorithm were studied in a specific application involving an analysis of a reaction norm model. Two datasets were simulated using different sets of parameters. The results vary somewhat between sets of parameters and across datasets. For variance components, the single-site Gibbs algorithm outperformed the bivariate and the block-updating versions when total computing cost was taken into account. However the block-updating version performed best for genetic random effects. The Langevin-Hastings algorithms led to higher autocorrelations among samples of the chain and to higher computing cost per sample. The results indicate it may be difficult to provide advice in terms of a given strategy that holds broadly across a range of target distributions.

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