零膨胀模型论文：零膨胀模型的若干问题研究.doc

零膨胀模型论文：零膨胀模型的若干问题研究【中文摘要】在相关应用科学研究领域,计数资料有时会表现出较大的变异性。当变量的方差远大于其均值时,便存在过离散现象。过离散的一种特殊情形就是零膨胀,是由于数据中含有大量的零值而造成方差和均值之间的差异,在建模时忽略这种现象,会导致参数的错误估计从而做出不合理的推论和预测。针对上述情形,国外学者们提出多个处理零膨胀现象的模型,比如零膨胀泊松模型、零膨胀负二项模型和零膨胀广义泊松模型。但在实践中,传统的零膨胀模型在小样本量的参数估计上出现较大的偏差。故本文在传统零膨胀模型的基础上,探讨了源于Beta-Binomial混合分布的零膨胀模型,并对新模型和上述三种模型做了模拟对比研究,结果显示在小样本、较低程度的过离散情形下,新模型比其它三个模型对参数和0概率的估计精度更高;另外,考虑到某些现实问题的复杂性,将空间和时间因素引入到零膨胀数据的建模之中,着重论述了具有时空效应的零膨胀模型及模型的MCMC实现,并通过实例分析表明时空效应-零膨胀泊松模型在对0概率预测优于传统零膨胀泊松模型,进一步说明了时空效应-零膨胀模型的可行性和有效性。【英文摘要】In the relevant field of applied science research,discrete data sometimes shows a bigger variability. When the variance of variable is far larger than its mean value, the over-dispersion phenomenon exists, especially when there is a great deal of zeros in the sample. If neglecting this kind of phenomenon, it will cause the mistake of parameter estimate to make a false reasoning and forecast.As is stated above, the foreign scholars proposed several models to deal with the problem, for example Zero-Inflated Poisson model, Zero-Inflated Negative Binomial model and Zero-Inflated General Poisson model. But in the practice, there is a certain deviation on parameter estimate when modeling with small samples using these models. Based on the current situation of traditional models, this paper investigates Zero-Inflated model with small samples which are from Beta-Binomial distribution and contrast the new model with the above three models under the simulation experiment. The results show the new model has better estimations on parameters and zero probability than other three models under the situation of small samples and lower over-dispersion. At the same time, considered the complexity of some practical problems, time-space effect is imported into the modeling of Zero-Inflated model. The Zero-Inflated model with time-space effect and the detailed MCMC implementation procedure are described in detail in the paper. And the analysis of the example shows the Zero-Inflated poisson model with time-space effect has more accurate estimation than Zero-Inflated poisson model on the forcast of zero probability which illuminates the feasibility and validity of the Zero-Inflated model with time-space effect.【关键词】零膨胀模型 混合分布模型 时空效应 MCMC方法【英文关键词】Zero-Inflated model mixture model time-space effect MCMC method【备注】索购全文在线加好友：1.3.9.9.3.8848 同时提供论文写作一对一指导和论文发表委托服务【目录】零膨胀模型的若干问题研究中文摘要4-5Abstract5第一章 序言7-91.1 零膨胀模型的概念与研究背景7-81.2 零膨胀模型(ZIM)国内外研究现状81.3 作者工作和本文结构8-9第二章 零膨胀模型的推广9-202.1 零膨胀泊松(ZIP)模型10-112.2 零膨胀泊松(ZIP)模型的推广11-142.2.1 零膨胀负二项分布(ZINB)模型11-122.2.2 零膨胀广义泊松(ZIGP)模型12-142.3 零膨胀 Beta-Binomial 模型14-162.4 零膨胀模型的模拟研究16-20第三章 时空效应-零膨胀模型20-303.1 时空效应-零膨胀模型原理与方法20-233.1.1 ZIP 模型的时空效应研究21-223.1.2