基于先验信息的统计预测方法及其应用研究
发布时间：2018-10-15 15:11
【摘要】：回归预测方法主要研究的是变量与变量之间的相互关系,应用回归分析根据一个或多个自变量的值,去预测因变量将要取得的值。 基于贝叶斯方法的线性回归模型,它与传统预测方法的不同之处在于其利用了来源经验和历史资料的先验信息,是一种以动态模型为研究对象的时间序列预测方法。先验分布反映了试验之前对总体参数分布的某种认识,在获得样本信息以后,对这个认识有了改变,其结果就反映在后验分布当中,也就是说后验分布综合了先验分布和样本的信息。贝叶斯统计以从经验中学习为目标,将历史信息与样本似然函数结合在一起,在统计预测模型中正在受到越来越广泛的应用。 本文总结了贝叶斯统计的基本思想方法,给出了有关先验分布的选取、参数估计以及假设检验的基本思想,讨论了基于贝叶斯方法的线性模型的基本理论及其特点,研究了基于贝叶斯方法的一元线性回归模型和多元线性回归模型,并就共轭先验分布的情形建立了动态线性预测模型,并将所建立的动态线性预测模型应用于三峡工程三期截流的水位预测和某省的用电量预测,得到的预测结果令人满意,说明该模型具有一定的优越性。
[Abstract]:The regression prediction method mainly studies the relationship between variables and variables. Regression analysis is used to predict the value of dependent variables according to the values of one or more independent variables. The linear regression model based on Bayesian method is different from the traditional prediction method in that it makes use of the prior information of source experience and historical data and is a time series prediction method based on dynamic model. The prior distribution reflects a certain understanding of the distribution of the total parameters before the experiment. After the sample information has been obtained, the understanding has changed, and the result is reflected in the posterior distribution. That is to say, the posterior distribution synthesizes the information of the prior distribution and the sample. Bayesian statistics, which aims at learning from experience and combines historical information with sample likelihood function, is being applied more and more widely in statistical prediction model. This paper summarizes the basic ideas and methods of Bayesian statistics, gives the basic ideas about the selection of prior distribution, parameter estimation and hypothesis test, and discusses the basic theory and characteristics of the linear model based on Bayesian method. The univariate linear regression model and multivariate linear regression model based on Bayesian method are studied, and the dynamic linear prediction model is established for the case of conjugate prior distribution. The dynamic linear prediction model has been applied to the water level prediction of the third phase closure of the three Gorges Project and the electricity consumption forecast of a certain province. The results are satisfactory, which shows that the model has some advantages.
【学位授予单位】：华北电力大学（北京）
【学位级别】：硕士
【学位授予年份】：2011
【分类号】：O212.1;C81
本文编号：2272932
[Abstract]:The regression prediction method mainly studies the relationship between variables and variables. Regression analysis is used to predict the value of dependent variables according to the values of one or more independent variables. The linear regression model based on Bayesian method is different from the traditional prediction method in that it makes use of the prior information of source experience and historical data and is a time series prediction method based on dynamic model. The prior distribution reflects a certain understanding of the distribution of the total parameters before the experiment. After the sample information has been obtained, the understanding has changed, and the result is reflected in the posterior distribution. That is to say, the posterior distribution synthesizes the information of the prior distribution and the sample. Bayesian statistics, which aims at learning from experience and combines historical information with sample likelihood function, is being applied more and more widely in statistical prediction model. This paper summarizes the basic ideas and methods of Bayesian statistics, gives the basic ideas about the selection of prior distribution, parameter estimation and hypothesis test, and discusses the basic theory and characteristics of the linear model based on Bayesian method. The univariate linear regression model and multivariate linear regression model based on Bayesian method are studied, and the dynamic linear prediction model is established for the case of conjugate prior distribution. The dynamic linear prediction model has been applied to the water level prediction of the third phase closure of the three Gorges Project and the electricity consumption forecast of a certain province. The results are satisfactory, which shows that the model has some advantages.
【学位授予单位】：华北电力大学（北京）
【学位级别】：硕士
【学位授予年份】：2011
【分类号】：O212.1;C81
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