Development and Application of Graphical Modeling techniques for Assesshrg the Joint Risks of Contaminants

复杂因果关系的图形化建模技术是在多元正态分布的假设下发展起来的。因此，它们仅限于对线性因果关系进行建模。“为了消除这一限制，我们在这个项目中开发了基于等级相关矩阵的图形建模技术。该方法被用于研究二恶英、多氯联苯和杀虫剂等环境污染物的联合风险，测量了120名妇女母乳中这些化学物质的含量，并测量了这些母亲所生婴儿的甲状腺和免疫激素状况。该方法发现甲状腺功能与二恶英的比值比为1.65 (p=0.29)，校正PCB后为7.15 （p=0.02）。我们进一步开发了一种使用潜在结构模型的图形化建模技术，并探索了处理时间序列数据的方法。对上述方法进行了理论研究；即(i)通过分层调整混杂变量，制定了比较两个负二项分布的估计和检验方法。发展了一种非参数归算方法。发展一种理论，利用各种基函数对数据建模，从高维数据中提取资料；建立了贝叶斯信息准则来选择模型；不仅将其应用于图形建模，还将其应用于其他统计方法，如DNA数据的判别分析等。为1至K倍比较设置中的重复测量数据制定了图形建模理论，并为所涉及的参数制定了近似置信区间。(v)提出了估计小扩散扩散过程的未知漂移参数和扩散参数的理论，并证明了它们的一致性和渐近正态性。

The graphical modeling techniques which have been proposed for the analysis of complex causal relationship are developed under the assumption of multivariate normal distribution. Thus they are limited for modeling only linear cause-effect relationships. 'lb remove this restriction we developed in this project graphical modeling techniques based on rank correlation matrix. The method was applied for studying joint risks of environmental contaminants such as Dioxin, PCB and pesticides measuring the amount of these chemicals in breast milks of 120 women and also measuring the thyroid and immune hormone status of infants from those mothers. It was discovered by the method that the odds ratios of thyroid function and Dioxin was 1.65 (p=0.29), but was 7.15 (p=0.02) when adjusted for PCB.We further developed a method of graphical modeling technique that used latent structure models, and also explored the method that may deal with time series data.Theoretical studies were conducted to develop those methods mentioned above ; namely(i)Developed estimation and testing method for comparing two negative binomial distributions by adjusting for confounding variables by stratification.(ii)Developed a method of nonparametric imputation.(iii) Developed a theory to extract information from high dimensional data by modeling the data using various base functions ; developed a Bayes Information criteria to select the models; applied it to not only the graphical modeling but also other statistical methods such as disiminant analysis for DNA data and others.(iv)Developed a theory of graphical modeling for repeated measurements data in one to K multiple comparison setting and developed an approximate confidence intervals for the parameters involved.(v)Developed theory for estimating unknown drift parameter and diffusion parameter of the diffusion process with small diffusion and proved their consisitency and asymptotic normality.