Synthetic response data; effect of sparsity restriction and range of prior strength parameter. Results reported in Figure3, for the empirical Bayes approach, were obtained by exact model averaging with the number of predictors included in a model restricted to not exceed d
= 4. Posterior inclusion probabilities for 50 simulated datasets from Simulation 1 were compared with results obtained by exact model averaging with an increased maximum number of included predictors of d
= 5 (left) and using Markov chain Monte Carlo-based model averaging with no sparsity restriction (centre). Sensitivity to the range of prior strength parameter values considered by empirical Bayes was also assessed by comparing the posterior inclusion probabilities obtained with to those obtained with an increased range of.