Estimating Parameters in Spike-convolution Models and Mixture Models

估计尖峰卷积模型和混合模型中的参数

• 批准号: 9971698
• 负责人: Lei Li
• 金额: $ 7.99万
• 依托单位: Florida State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-06-15 至 2002-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9971698&HistoricalAwards=false
• 关键词: Estimating; Parameters; Spike; convolution; Models

9971698This research links the parametric deconvolution problem in the spike-convolution model with the estimation problem in finite mixture models. It aims to weave together good results on algorithms and asymptotics from both sides, and develop new methodologies, which are implementable in computation and efficient in theory. The first object of this research, the spike-convolution model, is introduced as part of the models proposed for DNA sequencing by the PI and his collaborators. The current sequencing scheme named after Sanger combines three techniques: enzymatic reactions, gel or capillary electrophoresis and fluorescence-based detection. This biochemical procedure produces a four-component vector time series for each DNA fragment. The task of DNA base-calling is to recover the underlying DNA sequence from the above time series. Most of the base-calling errors are caused by the diffusion effect of electrophoresis. It is found that this diffusion effect can be well described by the so-called spike-convolution model. It arises when a sparse Dirac spike train is convolved with a fixed point spread function, and additive noise or measurement error is superimposed. In this model, deconvolution is nothing but a standard parameter estimation problem, where the parameters include the number, locations and heights of the underlying spikes, the baseline and the measurement error variance. The second object of this research, the finite mixture model, is the framework of many statistical analyses like robustness checking, clustering, estimating density functions, etc. However, the estimation of the parameters in mixture models can be very troublesome, especially when many components are involved. It is believed that a broad class of finite mixture models is closely related to the spike-convolution model. No simple solution exists to the estimation problems in these two models because of the complexity. This research proposes to combine the method of trigonometric moments with a two-stage model selection procedure, Gauss-Newton algorithm, or EM algorithm depending on the situations. The numerical and statistical aspects of the new methods and their variants are examined and compared with those of existing methods. The Toeplitz forms constructed from trigonometric moments and their statistical properties play a key role in the proposed methods, and are investigated in full detail.This research studies the newly proposed spike-convolution model and the long-standing finite mixture models from a unified perspective. The former is motivated by the large scale and high throughput DNA sequencing, which is one of the most important aspects of the ongoing Human Genome Project and other genome projects. The lack of satisfactory deconvolution techniques and statistical models has made DNA base-calling---the data analysis part of sequencing---a bottle neck of these projects. An effective deconvolution technique, a target of this research, is a fundamental prerequisite for rapid and reliable DNA base-calling. In fact, similar deconvolution problems arise in many other scientific disciplines like geophysics, spectroscopy, and chromatography. The research results are also expected to enrich the understanding and methodologies of finite mixture models, which have applications to a diversity of fields such as physics, medicine, and biology.

9971698这项研究将尖峰卷积模型中的参数反卷积问题与有限混合模型中的估计问题联系起来。 它的目标是将双方在算法和渐近学方面的良好成果编织在一起，开发出计算上可实现且理论上高效的新方法。 本研究的第一个对象是尖峰卷积模型，作为 PI 及其合作者提出的 DNA 测序模型的一部分引入。 当前以桑格命名的测序方案结合了三种技术：酶促反应、凝胶或毛细管电泳以及基于荧光的检测。 该生化过程为每个 DNA 片段生成一个四分量向量时间序列。 DNA 碱基调用的任务是从上述时间序列中恢复潜在的 DNA 序列。 大多数碱基识别错误是由电泳的扩散效应引起的。 发现这种扩散效应可以通过所谓的尖峰卷积模型很好地描述。 当稀疏狄拉克尖峰序列与定点扩展函数卷积并且叠加加性噪声或测量误差时，就会出现这种情况。 在这个模型中，反卷积只不过是一个标准的参数估计问题，其中参数包括底层尖峰的数量、位置和高度、基线和测量误差方差。 本研究的第二个对象，有限混合模型，是鲁棒性检查、聚类、估计密度函数等许多统计分析的框架。然而，混合模型中参数的估计可能非常麻烦，特别是当涉及许多组件时。 据信，一大类有限混合模型与尖峰卷积模型密切相关。 由于这两个模型的估计问题非常复杂，因此不存在简单的解决方案。 本研究建议根据情况将三角矩方法与两阶段模型选择程序、高斯-牛顿算法或 EM 算法相结合。 对新方法及其变体的数值和统计方面进行了检查，并与现有方法进行了比较。 由三角矩构造的托普利茨形式及其统计特性在所提出的方法中发挥着关键作用，并对其进行了全面详细的研究。本研究从统一的角度研究了新提出的尖峰卷积模型和长期存在的有限混合模型。 前者的动机是大规模、高通量的 DNA 测序，这是正在进行的人类基因组计划和其他基因组计划最重要的方面之一。 由于缺乏令人满意的反卷积技术和统计模型，DNA 碱基识别（测序的数据分析部分）成为这些项目的瓶颈。 有效的反卷积技术是本研究的目标，它是快速可靠的 DNA 碱基识别的基本先决条件。 事实上，类似的反卷积问题也出现在许多其他科学学科中，例如地球物理学、光谱学和色谱法。 研究结果还有望丰富有限混合模型的理解和方法，这些模型可应用于物理、医学和生物学等多个领域。