 Locally Adaptive Bayes Nonparametric Regression via Nested Gaussian ProcessesBin Zhu and David B. Dunson Journal of the American Statistical Association, 2013, vol. 108, issue 504, 1445-1456 Abstract: We propose a nested Gaussian process (nGP) as a locally adaptive prior for Bayesian nonparametric regression. Specified through a set of stochastic differential equations (SDEs), the nGP imposes a Gaussian process prior for the function's m th-order derivative. The nesting comes in through including a local instantaneous mean function, which is drawn from another Gaussian process inducing adaptivity to locally varying smoothness. We discuss the support of the nGP prior in terms of the closure of a reproducing kernel Hilbert space, and consider theoretical properties of the posterior. The posterior mean under the nGP prior is shown to be equivalent to the minimizer of a nested penalized sum-of-squares involving penalties for both the global and local roughness of the function. Using highly efficient Markov chain Monte Carlo for posterior inference, the proposed method performs well in simulation studies compared to several alternatives, and is scalable to massive data, illustrated through a proteomics application. Date: 2013 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:taf:jnlasa:v:108:y:2013:i:504:p:1445-1456 Ordering information: This journal article can be ordered from DOI: 10.1080/01621459.2013.838568 Access Statistics for this article Journal of the American Statistical Association is currently edited by Xuming He, Jun Liu, Joseph Ibrahim and Alyson Wilson More articles in Journal of the American Statistical Association from Taylor & Francis Journals |
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