An n-dimensional Rosenbrock Distribution for MCMC Testing
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Publication:139683
DOI10.48550/ARXIV.1903.09556arXiv1903.09556MaRDI QIDQ139683
Saralees Nadarajah, Martin Wiegand, Filippo Pagani
Publication date: 22 March 2019
Abstract: The Rosenbrock function is an ubiquitous benchmark problem for numerical optimisation, and variants have been proposed to test the performance of Markov Chain Monte Carlo algorithms. In this work we discuss the two-dimensional Rosenbrock density, its current -dimensional extensions, and their advantages and limitations. We then propose a new extension to arbitrary dimensions called the Hybrid Rosenbrock distribution, which is composed of conditional normal kernels arranged in such a way that preserves the key features of the original 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.
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