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。 它的目的是将双方的算法和渐近学算法结合在一起，并开发新方法，这些方法在计算中是可以实现的，并且在理论上有效。 这项研究的第一个对象是Spike-Convolution模型，是PI及其合作者为DNA测序提出的模型的一部分。 当前的测序方案以Sanger命名，结合了三种技术：酶促反应，凝胶或毛细管电泳和基于荧光的检测。 该生化程序为每个DNA片段产生一个四分量矢量时间序列。 DNA基呼叫的任务是从上述时间序列中恢复潜在的DNA序列。 大多数基本呼叫误差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。 当稀疏的Dirac Spike Train用固定点扩散功能卷曲时，会产生它，并叠加添加噪声或测量误差。 在此模型中，反卷积不过是一个标准参数估计问题，其中参数包括基线尖峰的数字，位置和高度，基线和测量误差方差。 这项研究的第二个对象是有限的混合模型，是许多统计分析的框架，例如鲁棒性检查，聚类，估计密度功能等。但是，混合模型中参数的估计可能非常麻烦，尤其是当许多组件时参与。 据认为，广泛的有限混合模型与尖峰 - 横线模型密切相关。 由于复杂性，这两个模型中没有简单的解决方案。 这项研究建议将三角矩的方法与两阶段模型选择程序，高斯 - 纽顿算法或EM算法相结合，具体取决于情况。 研究了新方法及其变体的数值和统计方面，并将其与现有方法的数字方面进行了比较。 由三角学矩及其统计特性构成的Toeplitz形式在提议的方法中起着关键作用，并进行了全面研究。这项研究从统一的角度来看，新提出的Spike-Convolution模型和长期有限的混合模型。 前者是由大规模和高吞吐量DNA测序的动机，这是正在进行的人类基因组项目和其他基因组项目的最重要方面之一。 缺乏令人满意的反卷积技术和统计模型使DNA基底话 - - 测序的数据分析部分 - 这些项目的瓶颈。 这项研究的一种有效的反向卷积技术是快速可靠的DNA基呼叫的基本先决条件。 实际上，在许多其他科学学科（例如地球物理，光谱和色谱法）等许多其他科学学科中也出现了类似的反向卷积问题。 预计研究结果还将丰富对有限混合模型的理解和方法，这些模型对物理，医学和生物学等各种领域都有应用。