Research on Sieve Approximations to Non and Semiparametric Models, Hidden Markov Models and Comparison of Phylogenetic Tree Biologies

-----------------------------------------------------------------------提案号：DMS-9802261 PI: Peter Bickel机构：项目：非参数和半参数模型，隐马尔可夫模型和系统发育树生物学比较的筛近似研究。摘要：对非参数和半参数模型下的“插入”性质进行了理论研究。研究人员的目的是表征非参数和半参数模型，其中适当拟合程序的结果可以安全地插入广泛的用途，以及当损失函数反映数据的某些特征的拟合目标而不是全局拟合时，模型选择标准的研究。该项目包括：*进一步发展在半或非参数环境下检验参数或半参数假设的理论。*隐马尔可夫模型推理理论的进一步发展。研究者提出了状态空间模型的扩展。*开发新程序和分析现有的估算程序固定效应和随机效应的预测使用半参数模型纵向和/或药代动力学数据。对系统发育树构建中随机模型选择敏感性的检验和诊断，如研究人员打算继续发展的半参数模型的测试和诊断，在许多领域都是有用的。例如，布莱克-斯科尔斯期权定价公式在金融领域被广泛使用。研究人员已经开发的一种方法表明，对于大数据集，公式是无效的，并指出了更合理的更现实的模型。系统发育树不仅用于表示物种之间的进化关系的动物和植物也如我们g oing研究中,蛋白质的重要家庭。研究导致合理进化树的模型类型也应该导致模式识别算法，这将有助于对蛋白质家族进行分类，从而将新蛋白质与已知性质的家族联系起来。这是在生物技术中寻找新的生物活性化合物的一项主要活动。

----------------------------------------------------------------------- Proposal Number: DMS-9802261 PI: Peter Bickel Institution: Project: Research on sieve approximations to non and semiparametric models, Hidden Markov models and comparison of phylogenetic tree biologies. Abstract: A theoretical investigation of the "plug in" property in the context of non and semiparametric models. The intention of the investigators is to characterize non and semiparametric models in which the outcomes of appropriate fitting procedures can be safely plugged in for a broad range of uses, and the study of model selection criteria when the loss function reflects the goal of fitting some features of the data well rather than a global fit. This project includes: *Further development of a theory for testing parametric or semiparametric hypotheses in a semi or non parametric context. *Further development of the theory of inference for Hidden Markov Models. The investigators propose extension to state space models. *Development of new procedures and analysis of existing procedures for estimating fixed effects and prediction of random effects using semiparametric models for longitudinal and/or "pharmacokinetic" data. *Further development of the theory and practice of selecting m in the m out of n bootstrap *An examination of the sensitivity to choice of stochastic model in the construction of phylogenetic trees Tests and diagnostics for semiparametric models such as those the investigators intend to continue to develop are useful in a number of areas. For instance, the Black Scholes option pricing formula is widely used in finance. One of the methods the investigators have already developed show the invalidity of the formula for large data set and points to plausible more realistic models. Phylogenetic trees are used not only for representing evolutionary relationships among species of animals and plants but also, as in the case we are g oing to study, important families of proteins. Studying the types of models that lead to plausible evolution trees should also lead to pattern recognition algorithms which will be useful in classifying protein families and hence to relating new proteins to families whose properties are known. This is a major activity in the search for new bioactive compounds in biotechnology.