This paper proposes the use of the Bernstein–Dirichlet process prior for a new nonparametric approach to estimating the link function in the single-index model (SIM). The Bernstein–Dirichlet process prior has so far mainly been used for nonparametric density estimation. Here we modify this approach to allow for an approximation of the unknown link function. Instead of the usual Gaussian distribution, the error term is assumed to be asymmetric Laplace distributed which increases the flexibility and robustness of the SIM. To automatically identify truly active predictors, spike-and-slab priors are used for Bayesian variable selection. Posterior computations are performed via a Metropolis-Hastings-within-Gibbs sampler using a truncation-based algorithm for stick-breaking priors. We compare the efficiency of the proposed approach with well-established techniques in an extensive simulation study and illustrate its practical performance by an application to nonparametric modelling of the power consumption in a sewage treatment plant. 相似文献
To maximize the ecological services of urban forests, a better understanding of the effects of urbanization on urban forest characteristics, landscape metrics, and their associations is needed for landscape-related regulations in space-limited green infrastructure of metropolitan regions. In this study, Harbin, a typical fast-growing provincial-capital city in Northeast China, is used as a case study. Based on remote sensing images, field surveys, and correlation and variation partitioning analyses, we conclude that landscape characteristics and forest attributes have large variations among different urbanization intensity (UI) regions. Forest patch density (PD), landscape shape index, woody plants species richness, and the Shannon–Wiener index (H′) increased linearly, while stem section area and tree height decreased linearly with the increasing of UIs. UI had a greater influence on tree size and forest community attributes than the forest landscape pattern. Accordingly, any landscape regulation on forest attributes should be implemented according to UIs. In addition, Euclidean nearest neighbor distance(ENN-MN), mean perimeter-area ratio (PARA-MN), fractal dimension index(FRAC-MN), and PD could probably indicate forest attributes the most, e.g., the increase of PARA-MN may be accompanied with taller trees in low and heavy UI regions, but lower woody plants species evenness in low and medium UI regions. More diversified woody plants species, and afforested areas should be advocated in a low UI region, while in a heavy UI region, the conservation of large trees should be implemented. Our results highlight that the implementation of urban forest management should vary according to different urbanization regions to maximize ecological services.
