针对混合非参数回归问题, 给出了一种基于贝叶斯框架的推断方法. 在该方法中对每一个非参数混合成分用一个随机过程的有限维分布族作为先验, 同时分别构造混合比例、随机误差的方差和非参数混合成分的贝叶斯估计, 并通过马尔科夫链蒙特卡洛(Markov chain Monte Carlo, MCMC) 法抽样来进行后验推断. 数值模拟分别从样本量、回归曲线的相对位置和多分类情况 3 个角度进行. 模拟结果表明, 相较于全局期望最大化(global expectation maximalization)算法, 混合非参数回归的贝叶斯推断方法能够有效利用先验信息来提高模型的拟合和预测能力. 最后将混合非参数回归的贝叶斯推断方法应用于蚜虫与受感染烟草植物的实验, 同时解决了数据的聚类与回归拟合问题, 其有效性和适用性得证.

For mixing nonparametric regression models, an inference method is proposed based on the Bayesian framework. In this method, a finite dimensional distribution family of the stochastic process is used as a prior distribution for each nonparametric component, and Bayesian estimators of mixture proportions, each random error's variance, and nonparametric components are constructed respectively. A Markov chain Monte Carlo (MCMC) method is used for posterior inference. The numerical simulations are performed from the perspectives of sample size, relative position of the regression curve, and multiclassification. The results show that, compared with the generalised expectation maximisation (GEM) algorithm, the Bayesian inference method of mixing nonparametric regression can effectively use the prior information to improve the ability of fitting and prediction. Finally, the Bayesian inference method is applied to the experimental data from aphids and infected tobacco plants and solved clustering and regression problems. This also demonstrates the effectiveness and applicability of the method.