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An n-dimensional Rosenbrock distribution for Markov chain Monte Carlo testing

Published version
Peer-reviewed

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Abstract

jats:titleAbstract</jats:title>jats:pThe 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 jats:italicn</jats:italic>‐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.</jats:p>

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Keywords

algorithm testing, benchmarking, Markov chain Monte Carlo, MCMC, Rosenbrock

Journal Title

Scandinavian Journal of Statistics

Conference Name

Journal ISSN

0303-6898
1467-9469

Volume Title

Publisher

Wiley
Sponsorship
Engineering and Physical Sciences Research Council (EP/R018561/1)