本文關(guān)鍵詞：基于零膨脹計數(shù)數(shù)據(jù)回歸模型的貝葉斯分析　出處：《昆明理工大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 零膨脹 貝葉斯 Probit 偏斜正態(tài)分布 層次回歸模型

【摘要】：計數(shù)數(shù)據(jù)廣泛的存在于生物醫(yī)學(xué)、金融保險、公共健康以及風(fēng)險控制等領(lǐng)域,零點膨脹是該數(shù)據(jù)所呈現(xiàn)出的特征之一。所謂零點膨脹,即零觀測的比例遠超過了擬合分布所允許的范圍,也即在零處發(fā)生了膨脹。零點膨脹泊松回歸模型是擬合上述數(shù)據(jù)的一般選擇。此外,計數(shù)數(shù)據(jù)還常常會呈現(xiàn)出散度偏大的特征,若數(shù)據(jù)方差的變化大于其均值,則稱該數(shù)據(jù)是散度偏大的。較傳統(tǒng)的零點膨脹泊松回歸模型而言,零點膨脹下的負二項(ZINB)回歸模型更能夠解釋數(shù)據(jù)中散度偏大的結(jié)構(gòu),是分析散度偏大計數(shù)數(shù)據(jù)的有力工具。從已有的研究成果來看,現(xiàn)有的方法和理論大都集中于計數(shù)數(shù)據(jù)的似然分析方面,相比之下,對于現(xiàn)實生活中廣泛存在的計數(shù)數(shù)據(jù)的貝葉斯分析仍存在較大的研究空間,特別是對散度偏大計數(shù)數(shù)據(jù)下的層次回歸模型的貝葉斯統(tǒng)計推斷研究仍有待進一步完善。與極大似然方法相比,貝葉斯方法綜合了樣本中的先驗信息,對于某些分布的建模又具有較靈活的特點,特別是對于缺失數(shù)據(jù)與復(fù)雜模型的研究,貝葉斯方法尤其具有計算的可行性、有效性等方面的優(yōu)勢。因此,本論文將從貝葉斯分析的角度入手,對具有零點膨脹和散度偏大的計數(shù)數(shù)據(jù)進行深入研究。論文首先針對計數(shù)數(shù)據(jù)的零膨脹問題,建立與Probit模型相結(jié)合的零膨脹泊松回歸模型,同時建立起了結(jié)合Gibbs抽樣與M-H算法的MCMC技術(shù)以獲得模型參數(shù)的貝葉斯估計,在此基礎(chǔ)上,論文采用了DIC信息準(zhǔn)則以進行模型之間的比較和選擇并進一步考慮了偏后驗預(yù)測p值以合理評估模型的擬合優(yōu)度。此外,由于抽樣程序及問卷設(shè)計的需要,計數(shù)數(shù)據(jù)往往會呈現(xiàn)出組內(nèi)相關(guān)與組間獨立的特征,經(jīng)典的縱向計數(shù)數(shù)據(jù)分析理論總是對隨機效應(yīng)及隨機誤差均考慮正態(tài)分布的情形,然而在實際應(yīng)用中,這樣的假設(shè)缺乏統(tǒng)計上的穩(wěn)健性與建模的靈活性,特別是對于具有尖峰厚尾以及非對稱的“非正態(tài)型”數(shù)據(jù)而言,這樣的假設(shè)會導(dǎo)致有偏甚至無效的統(tǒng)計推斷結(jié)論。為此,本論文重點考慮了偏斜正態(tài)分析下的ZINB層次回歸模型的貝葉斯分析問題。具體的,建立起了關(guān)于零點膨脹計數(shù)數(shù)據(jù)的ZINB層次回歸模型并對隨機誤差及隨機效應(yīng)考慮偏斜正態(tài)分布,在貝葉斯后驗推斷方面,基于數(shù)據(jù)添加思想及偏斜正態(tài)分布的隨機表示理論,建立起了三層次的貝葉斯分析模型并最終得到模型的后驗分布。實際例子表明,該論文提出的方法是有效的。
[Abstract]:Counting data is widely distributed in biomedicine, finance and insurance, public health and risk control. Zero expansion is one of the characteristics of the data. The so-called zero point expansion, that is, the proportion of zero observation is far beyond the range allowed by the fitting distribution, that is, the expansion at zero. The zero inflated Poisson regression model is a general choice for fitting the above data. In addition, the number of data is often characterized by large divergence, and if the variance of the data is larger than the mean value, it is called a large divergence. Compared with the traditional zero inflated Poisson regression model, the negative two item (ZINB) regression model with zero expansion can explain the larger dispersion structure in data, and it is a powerful tool to analyze the scattered count data. From the existing research results, and likelihood method and the existing theory focused on the analysis of count data compared to the larger research space still exists in Bias analysis of count data exists for in real life, especially the further improvement of partial plans according to the estimation of divergence count Bias statistical regression model under the level still. Compared with the maximum likelihood method and Bayesian method is integrated in the sample prior information, and has the characteristics of flexible modeling for some distribution, especially for the lack of research data and complex models, especially has the advantages of Bayesian method calculation is feasible and effective. Therefore, from the point of view of Bias analysis, this paper will make a thorough study of the counting data with zero point expansion and greater divergence. Firstly, according to the problem of zero inflated count data, a combination of Probit model and zero inflated Poisson regression model, and established the Bayesian estimation to obtain model parameters with Gibbs sampling and M-H algorithm of MCMC technology, on this basis, this paper uses the DIC information criterion to compare and choose between models and the partial posterior predictive value of P to evaluate the goodness of fit for the model. In addition, due to the sampling procedures and the design of the questionnaire, count data often shows characteristics of group related groups of independent, longitudinal count data analysis theory of the classic is always on the random effects and random error are considered normal distributions, but in practical application, the assumption of lack of robustness and statistical modeling the flexibility, especially for leptokurtic and non symmetric "non normal" data, this assumption will lead to biased statistical inference even invalid conclusion. To this end, this paper focuses on the Bias analysis of the ZINB hierarchical regression model under skew normal analysis. Specifically, to establish a zero inflated count data ZINB level regression model and the random error and the random effects considering skewed normal distribution in Bias, posterior inference, data adding method and skew normal distribution stochastic representation theory based on established Bias analysis model of three levels and get the final model posterior distribution. The practical example shows that the method proposed in this paper is effective.
【學(xué)位授予單位】：昆明理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O212.8

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相關(guān)碩士學(xué)位論文 前1條

1 汪鐵豐;Probit模型的發(fā)展和演變[D];東北師范大學(xué);2008年

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本文編號：1341086