Issues in designing hybrid algorithms

TL;DR

This paper discusses challenges in designing hybrid algorithms in Bayesian computation, emphasizing that combining methods requires careful consideration of their individual strengths, practical applicability, and computational costs.

Contribution

It highlights key issues in hybrid algorithm design through case studies, providing insights into their practical implementation and efficiency considerations.

Findings

Component strengths may not always synergize in hybrids.

Technical issues like applicability and workload impact performance.

Efficiency gains must be balanced with practical constraints.

Abstract

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.