  Our article is concerned with adaptive sampling schemes for Bayesian
inference that update the proposal densities using previous iterates. We
introduce a copula based proposal density which is made more efficient by
combining it with antithetic variable sampling. We compare the copula based
proposal to an adaptive proposal density based on a multivariate mixture of
normals and an adaptive random walk Metropolis proposal. We also introduce a
refinement of the random walk proposal which performs better for multimodal
target distributions. We compare the sampling schemes using challenging but
realistic models and priors applied to real data examples. The results show
that for the examples studied, the adaptive independent \MH{} proposals are
much more efficient than the adaptive random walk proposals and that in general
the copula based proposal has the best acceptance rates and lowest
inefficiencies.
