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Big Data in Omics and Imaging: Integrated Analysis and Causal Inference
Journal of the American Statistical Association ( IF 3.7 ) Pub Date : 2020-01-02 , DOI: 10.1080/01621459.2020.1721249
Oliver Y. Chén 1
Affiliation  

three areas mentioned in the book’s subtitle: Probability theory (including random variables and vectors but largely neglecting the matrices), stochastic processes (including stochastic integrals and differential equations) and (additionally) statistical inference. The author bases his book on the lecture notes of his classes at the University of Missouri, dedicating the book to graduate and PhD students and full-time academics in statistics or mathematics. Although this target group typically has some prior knowledge of probability theory, Chapter 1 of the book is a nonrigorous introduction to elementary probability theory under the title “rudimentary models.” Chapter 2 deals with statistical inference with a focus on Bayesian approaches, Micheas’ area of expertise. Being the only chapter on statistics, it feels like an excursion and is not directly relevant for the remainder of the book. The third chapter on measure theory establishes the basis for the rigorous introduction to probability theory presented in Chapters 4 and 5. The subsequent Chapters 6 and 7 on discreteand continuous-time stochastic processes cover Markov chains, martingales, the Poisson process, Brownian motion, general Markov processes, and conclude by defining stochastic integrals and stochastic differential equations with respect to Brownian motion. The book finishes with a very short treatise of stochastic partial differential equations at the end of Chapter 7 as promised on the book’s back cover. Every chapter in the book ends with a summary that provides useful references for the covered topics. Clearly, including such a vast array of subdisciplines into 336 pages (excluding appendix and bibliography) comes at a price and here the price is paid in terms of precision and depth of the presented material. With regard to precision, the “rudimentary models” in the first chapter lack accuracy, and slight mathematical inconsistencies appear at several places in the book (e.g., stochastic processes are introduced with general index set T, but properties like independent increments are formulated for T = [0, ∞) without specifying this). With regard to depth, various statements are listed without proof or with the proof left as an exercise for the reader (e.g., the standard central limit theorem for independent, identically distributed random variables is buried in an exercise in Chapter 2). Every chapter comes with a collection of exercises, and a solution manual for these is promised to be found at the book’s accompanying webpage. Unfortunately—to this day (January 2020)—the webpage only provides the solutions to the exercises of Chapter 1, an errata sheet, and the Matlab code used to generate the two figures of realized paths of Brownian motion on the book’s front cover. Navigation through the book is complicated as definitions and examples are more prominently highlighted than section titles. Neither the design nor the typesetting (which allows too many “orphans” and “widows,” dangling all alone at the bottoms or tops of pages) encourages the reader to use the book as a resource to create lectures or simply as a student textbook. To conclude, this book does not fulfill the expectations of a textbook since graduate students will have to consult secondary literature for a full understanding of the theory. Academic instructors may find it helpful as a source of possible topics to include in their own classes. Various potential lecture series based on the book’s materials are outlined by the author in the preface. Anita D. Behme Technische Universität Dresden Dresden, Germany anita.behme@tu-dresden.de

中文翻译:

组学和成像中的大数据:综合分析和因果推断

本书副标题中提到的三个领域:概率论(包括随机变量和向量,但在很大程度上忽略了矩阵)、随机过程(包括随机积分和微分方程)和(另外)统计推断。作者根据他在密苏里大学课堂的讲义编写这本书,将这本书献给研究生和博士生以及统计学或数学领域的全日制学者。尽管这个目标群体通常有一些概率论的先验知识,但本书的第 1 章以“基本模型”为标题对基本概率论进行了不严谨的介绍。第 2 章讨论统计推断,重点是贝叶斯方法,这是 Micheas 的专业领域。作为唯一关于统计的章节,这感觉就像一次短途旅行,与本书的其余部分没有直接关系。关于测度论的第三章为第 4 章和第 5 章中对概率论的严格介绍奠定了基础。随后关于离散和连续时间随机过程的第 6 章和第 7 章涵盖了马尔可夫链、鞅、泊松过程、布朗运动、一般马尔可夫过程,并通过定义关于布朗运动的随机积分和随机微分方程得出结论。正如本书封底所承诺的那样,本书在第 7 章末尾以一篇非常简短的随机偏微分方程论文结束。本书的每一章都以摘要结尾,为涵盖的主题提供有用的参考。清楚地,将如此大量的子学科纳入 336 页(不包括附录和参考书目)是有代价的,这里的代价是所呈现材料的精度和深度。在精度方面,第一章的“基本模型”缺乏准确性,书中多处出现轻微的数学不一致(例如,一般指标集T引入了随机过程,但为T制定了独立增量等性质= [0, ∞) 没有指定)。关于深度,列出了各种陈述而无需证明或将证明留给读者作为练习(例如,独立同分布随机变量的标准中心极限定理隐藏在第 2 章的练习中)。每章都附有习题合集,并且承诺在本书随附的网页上提供这些问题的解决方案手册。不幸的是,直到今天(2020 年 1 月),该网页仅提供了第 1 章练习、勘误表和用于生成本书封面上布朗运动的两个实现路径图的 Matlab 代码的解决方案。本书的导航很复杂,因为定义和示例比章节标题更突出。无论是设计还是排版(允许太多“孤儿”和“寡妇”,单独悬挂在页面底部或顶部)都鼓励读者将这本书用作创建讲座的资源或仅作为学生教科书。总结一下,这本书不能满足教科书的期望,因为研究生必须查阅中学文献才能充分理解该理论。学术教师可能会发现它作为可能包含在他们自己的课程中的主题的来源很有帮助。作者在序言中概述了基于本书材料的各种潜在系列讲座。Anita D. Behme Technische Universität Dresden 德国德累斯顿 anita.behme@tu-dresden.de
更新日期:2020-01-02
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