Publications [#257855] of David B. Dunson

Papers Published

  1. Zhu, B; Dunson, DB, Locally Adaptive Bayes Nonparametric Regression via Nested Gaussian Processes., Journal of the American Statistical Association, vol. 108 no. 504 (January, 2013), ISSN 0162-1459
    (last updated on 2019/06/18)

    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 mth-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.