Mathematical Sciences: Hidden Mark CV Models, Semi-parametric Models, and Sample Reuse Models

提案：DMS 95- 04955 PI: Peter Bickel机构：UC Berkeley题目：隐马尔可夫模型，半参数模型和样本重用模型摘要：本研究涉及隐马尔可夫模型推理方法的发展；半参数模型的模型拟合、诊断和检验；新型重采样方法的研究。在第一个领域，主要目标是将Baum和Petrie（1966）和研究者的工作扩展到潜在的连续状态和时间马尔可夫过程和马尔可夫随机场；并研究在不牺牲效率的情况下节省计算量的方法。在第二个领域，研究人员的目标是在生物统计学、计量经济学和其他领域产生的模型之间和模型内部产生一种统一的测试和模型选择方法。在第三个领域，我们的目标是研究n中的m，在有和没有替换引导的情况下，用于各种目的，包括在困难的测试情况下设置临界值。本研究的目标是在一些重要领域中自然出现的数据的某些类型的复杂模型中开发统计上合理和计算上可行的估计、测试和误差界限。隐马尔可夫模型的应用包括机器语音识别和基因组序列特征估计，在生物技术中具有重要意义。半参数模型的应用包括交通选择和民用基础设施研究的其他方面。可靠的重采样方法是我们研究的最后一个领域，对于计算我们正在开发的复杂程序的误差界限和阈值至关重要，实际上是整个程序的重要组成部分。它们的实现只有在我们这个计算速度越来越快的时代才有可能。

Proposal: DMS 95- 04955 PI: Peter Bickel Institution: UC Berkeley Title: Hidden Markov Models, Semi-Parametric Models, and Sample Reuse Models ABSTRACT This research involves development of methodology for inference in hidden Markov models; for model fitting, diagnostics and tests for semiparametric models; and studies of novel types of resampling methods. In the first area the main goals are to extend the work of Baum and Petrie (1966) and the investigators to underlying continuous state and time Markov processes and Markov random fields; and to study methods which achieve computational savings without sacrificing efficiency. In the second area, the goal of the investigators is to produce a unified approach to testing and model selection between and within models arising in biostatistics, econometric and elsewhere. In the third area, the goal is to study m out of n with and without replacement bootstraps for various purposes including setting critical values in difficult testing situations. The goal of this research is to develop statistically sound and computationally feasible estimates, tests, and error bounds in some types of complex models for data that arise, naturally in a number of important fields. Applications of hidden Markov models include speech recognition by machine and estimation of genomic sequence characteristics, of significance in biotechnology. Applications of semiparametric models include transportation choice and other aspects of civil infrastructure studies. Reliable resampling methods, our final area of study are essential for calculating error bounds and thresholds for the complex procedures we are developing and in fact are an essential part of the procedures as a whole. Their implementation is possible only in our age of ever more rapid computation.