Properties of the Bayesian Parameter Estimation of a Regression Based on Gaussian Processes
- 45 Downloads
We consider the regression approach based on Gaussian processes and outline our theoretical results about the properties of the posterior distribution of the corresponding covariance function’s parameter vector. We perform statistical experiments confirming that the obtained theoretical propositions are valid for a wide class of covariance functions commonly used in applied problems.
KeywordsPosterior Distribution Covariance Function Gaussian Process Kernel Density Estimate Hellinger Distance
Unable to display preview. Download preview PDF.
- 2.A. Ya. Chervonenkis, S. S. Chernova, and T. V. Zykova, “Applications of kernel ridge estimation to the problem of computing the aerodynamical characteristics of a passenger plane (in comparison with results obtained with artificial neural networks),” Autom. Remote Control, 72, No. 5, 1061–1067 (2011).CrossRefzbMATHGoogle Scholar
- 4.A. Forrester, A. Sobester, and A. Keane, Engineering Design via Surrogate Modelling: A Practical Guide, Wiley (2008).Google Scholar
- 7.S. Kok, “The asymptotic behaviour of the maximum likelihood function of Kriging approximations using the Gaussian correlation function,” in: EngOpt 2012 — Intern. Conf. on Engineering Optimization, Rio de Janeiro, Brazil, 1–5 July 2012 (2012).Google Scholar
- 13.V. Spokoiny, Bernstein–von Mises Theorem for Growing Parameter Dimension, arXiv:1302.3430 [math.ST] (2013).Google Scholar