
AbstractThe Rosenbrock function is a ubiquitous benchmark problem in numerical optimization, and variants have been proposed to test the performance of Markov chain Monte Carlo algorithms on distributions with a curved and narrow shape. In this work we discuss the Rosenbrock distribution and the advantages and limitations of its current n‐dimensional extensions. We then propose a new extension to arbitrary dimensions called the Hybrid Rosenbrock distribution, which addresses all the limitations that affect the current extensions. The Hybrid Rosenbrock distribution is composed of conditional normal kernels arranged in such a way that preserves the key features of the original Rosenbrock kernel. Moreover, due to its structure, the Hybrid Rosenbrock distribution is analytically tractable, and possesses several desirable properties which make it an excellent test model for computational algorithms. We conclude with numerical experiments that show how commonly used Markov chain Monte Carlo algorithms may fail to explore densities with curved correlation structure, restating the importance of a reliable benchmark problem for this class of densities.
Markov chain Monte Carlo, algorithm testing, MCMC, Computational methods in Markov chains, 4901 Applied Mathematics, 49 Mathematical Sciences, benchmarking, Rosenbrock
Markov chain Monte Carlo, algorithm testing, MCMC, Computational methods in Markov chains, 4901 Applied Mathematics, 49 Mathematical Sciences, benchmarking, Rosenbrock
| selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 10 | |
| popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Top 10% | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Average | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Top 10% |
