  In the Bayesian community, an ongoing imperative is to develop efficient
algorithms. An appealing approach is to form a hybrid algorithm by combining
ideas from competing existing techniques. This paper addresses issues in
designing hybrid methods by considering selected case studies: the delayed
rejection algorithm, the pinball sampler, the Metropolis adjusted Langevin
algorithm, and the population Monte Carlo algorithm. We observe that even if
each component of a hybrid algorithm has individual strengths, they may not
contribute equally or even positively when they are combined. Moreover, even if
the statistical efficiency is improved, from a practical perspective there are
technical issues to be considered such as applicability and computational
workload. In order to optimize performance of the algorithm in real time, these
issues should be taken into account.
