@inproceedings{de69b6cc825e4caaaf1e43f7d96f7de6,
title = "Multi-fidelity No-U-Turn Sampling",
abstract = "Markov Chain Monte Carlo (MCMC) methods often take many iterations to converge for highly correlated or high-dimensional target density functions. Methods such as Hamiltonian Monte Carlo (HMC) or No-U-Turn Sampling (NUTS) use the first-order derivative of the density function to tackle the aforementioned issues. However, the calculation of the derivative represents a bottleneck for computationally expensive models. We propose to first build a multi-fidelity Gaussian Process (GP) surrogate. The building block of the multi-fidelity surrogate is a hierarchy of models of decreasing approximation error and increasing computational cost. Then the generated multi-fidelity surrogate is used to approximate the derivative. The majority of the computation is assigned to the cheap models thereby reducing the overall computational cost. The derivative of the multi-fidelity method is used to explore the target density function and generate proposals. We select or reject the proposals using the Metropolis Hasting criterion using the highest fidelity model which ensures that the proposed method is ergodic with respect to the highest fidelity density function. We apply the proposed method to three test cases including some well-known benchmarks to compare it with existing methods and show that multi-fidelity No-U-turn sampling outperforms other methods.",
keywords = "Bayesian inference, Gaussian process, Markov chain Monte Carlo, Multi-fidelity, No-U-Turn sampling",
author = "Kislaya Ravi and Tobias Neckel and Bungartz, {Hans Joachim}",
note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.; 15th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2022 ; Conference date: 17-07-2022 Through 22-07-2022",
year = "2024",
doi = "10.1007/978-3-031-59762-6_27",
language = "English",
isbn = "9783031597619",
series = "Springer Proceedings in Mathematics and Statistics",
publisher = "Springer",
pages = "543--560",
editor = "Aicke Hinrichs and Friedrich Pillichshammer and Peter Kritzer",
booktitle = "Monte Carlo and Quasi-Monte Carlo Methods - MCQMC 2022",
}