贝叶斯推断下部分线性模型中非参数部分的估计基于重构参数化方法

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中图分类号：0212.8 文献标志码：A

Estimation of the Nonparametric Component of Partial Linear Models under Bayesian Inference

Based on Reconstructed Parametric Methods

ZHAO Bo-han，YANG Jian-kui （School of Science，Beijing University of Posts and Telecommunications，Beijing lOo876，China）

Abstract： When dealing with the nonparametric component of partial linear models，traditional Gaussian process prior methods，while capable of estimating the nonparametric component，have low computational efficiency and are not suitable for handling high-dimensional data with large sample sizes. To address this issue，a reparameterized method was employed to interpolate and reconstruct the nonparametric component of partial linear models. New prior distributions were assigned to the parameters obtained after reconstruction. Based on these new priors，Bayesian inference was then utilized to derive the closed-form posterior distributions of the parameters. Numerical simulation results demonstrate that the method proposed in this article can effectively reduce computational costs andachieve satisfactoryinferential outcomes.

Keywords： partially linear model; Bayesian inference； Gaussian process; reconstruction parameterization

简单的线性模型往往不能很好地拟合各领域中的复杂数据，而非参数回归模型虽然可以较好地拟合数据但缺乏可解释性，因此在实际的应用中经常受阻。（剩余8807字）