【摘要】：回歸預(yù)測方法主要研究的是變量與變量之間的相互關(guān)系,應(yīng)用回歸分析根據(jù)一個或多個自變量的值,去預(yù)測因變量將要取得的值。 基于貝葉斯方法的線性回歸模型,它與傳統(tǒng)預(yù)測方法的不同之處在于其利用了來源經(jīng)驗和歷史資料的先驗信息,是一種以動態(tài)模型為研究對象的時間序列預(yù)測方法。先驗分布反映了試驗之前對總體參數(shù)分布的某種認(rèn)識,在獲得樣本信息以后,對這個認(rèn)識有了改變,其結(jié)果就反映在后驗分布當(dāng)中,也就是說后驗分布綜合了先驗分布和樣本的信息。貝葉斯統(tǒng)計以從經(jīng)驗中學(xué)習(xí)為目標(biāo),將歷史信息與樣本似然函數(shù)結(jié)合在一起,在統(tǒng)計預(yù)測模型中正在受到越來越廣泛的應(yīng)用。 本文總結(jié)了貝葉斯統(tǒng)計的基本思想方法,給出了有關(guān)先驗分布的選取、參數(shù)估計以及假設(shè)檢驗的基本思想,討論了基于貝葉斯方法的線性模型的基本理論及其特點,研究了基于貝葉斯方法的一元線性回歸模型和多元線性回歸模型,并就共軛先驗分布的情形建立了動態(tài)線性預(yù)測模型,并將所建立的動態(tài)線性預(yù)測模型應(yīng)用于三峽工程三期截流的水位預(yù)測和某省的用電量預(yù)測,得到的預(yù)測結(jié)果令人滿意,說明該模型具有一定的優(yōu)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.
【學(xué)位授予單位】：華北電力大學(xué)（北京）
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2011
【分類號】：O212.1;C81

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