统计数据分析简介

English | 2024 | ISBN: 978-3-031-66619-3 | 437 pages | PDF EPUB (True) | 39 MB

This graduate textbook on the statistical approach to data science describes the basic ideas, scientific principles and common techniques for the extraction of mathematical models from observed data. Aimed at young scientists, and motivated by their scientific prospects, it provides first principle derivations of various algorithms and procedures, thereby supplying a solid background for their future specialization to diverse fields and applications.

The beginning of the book presents the basics of statistical science, with an exposition on linear models. This is followed by an analysis of some numerical aspects and various regularization techniques, including LASSO, which are particularly important for large scale problems. Decision problems are studied both from the classical hypothesis testing perspective and, particularly, from a modern support-vector perspective, in the linear and non-linear context alike. Underlying the book is the Bayesian approach and the Bayesian interpretation of various algorithms and procedures. This is the key to principal components analysis and canonical correlation analysis, which are explained in detail. Following a chapter on nonlinear inference, including material on neural networks, the book concludes with a discussion on time series analysis and estimating their dynamic models.

Featuring examples and exercises partially motivated by engineering applications, this book is intended for graduate students in applied mathematics and engineering with a general background in probability and linear algebra.

这本研究生教材介绍了统计方法在数据科学中的应用，描述了从观察到的数据中提取数学模型的基本想法、科学原则和常用技术。这本书旨在为年轻的科学家提供指导，并激发他们对科学研究的兴趣。它提供了各种算法和程序的原理推导，从而为其未来专注于多样领域和应用奠定坚实的基础。 本书开始介绍了统计学的基本概念，重点讲解了线性模型。接着分析了一些数值方面的问题以及各种正则化技术，包括LASSO，在大规模问题中尤为重要。决策问题从经典的假设检验角度以及现代的支持向量视角进行了探讨，无论是在线性和非线性的背景下都有涉及。本书以贝叶斯方法为基础，并对各种算法和程序的贝叶斯解释进行详细说明。这是主成分分析和典型相关分析的关键所在，后者也被详尽地加以阐述。紧跟一章关于非线性推理内容之后，包括神经网络的相关材料，本书最后讨论了时间序列分析以及如何估计它们的动力学模型。 书中包含了一些部分受工程应用启发的例子和练习题，这本书旨在为概率论和线性代数有一般背景的应用数学和工程专业的研究生所准备。

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