关键词: 混合回归, 非参数回归, 贝叶斯估计, 有限维分布, MCMC 抽样

Abstract:

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.

Key words: mixture models, nonparametric regression, Bayesian estimation, finite dimensional distribution, Markov chain Monte Carlo (MCMC) sampling