This classic textbook offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The first half of the book gives an exposition of real analysis: basic set theory, general topology, measure theory, integration, an introduction to functional analysis in Banach and Hilbert spaces, convex sets and functions and measure on topological spaces. The second half introduces probability based on measure theory, including laws of large numbers, ergodic theorems, the central limit theorem, conditional expectations and martingale's convergence. A chapter on stochastic processes introduces Brownian motion and the Brownian bridge. The edition has been made even more self-contained than before; it now includes a foundation of the real number system and the Stone-Weierstrass theorem on uniform approximation in algebras of functions. Several other sections have been revised and improved, and the comprehensive historical notes have been further amplified. A number of new exercises have been added, together with hints for solution.

This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The new edition begins with a short chapter on measure theory to orient readers new to the subject.

Highly useful text studies the logarithmic measures of information and their application to testing statistical hypotheses. Topics include introduction and definition of measures of information, their relationship to Fisher's information measure and sufficiency, fundamental inequalities of information theory, much more. Numerous worked examples and problems. References. Glossary. Appendix. 1968 2nd, revised edition.

The past decade has seen a dramatic increase in the use of Bayesian methods in marketing due, in part, to computational and modelling breakthroughs, making its implementation ideal for many marketing problems. Bayesian analyses can now be conducted over a wide range of marketing problems, from new product introduction to pricing, and with a wide variety of different data sources.
Bayesian Statistics and Marketing describes the basic advantages of the Bayesian approach, detailing the nature of the computational revolution. Examples contained include household and consumer panel data on product purchases and survey data, demand models based on micro-economic theory and random effect models used to pool data among respondents. The book also discusses the theory and practical use of MCMC methods.
Written by the leading experts in the field, this unique book:

Presents a unified treatment of Bayesian methods in marketing, with common notation and algorithms for estimating the models.
Provides a self-contained introduction to Bayesian methods.
Includes case studies drawn from the authors’ recent research to illustrate how Bayesian methods can be extended to apply to many important marketing problems.
Is accompanied by an R package, bayesm, which implements all of the models and methods in the book and includes many datasets. In addition the book’s website hosts datasets and R code for the case studies. Bayesian Statistics and Marketing provides a platform for researchers in marketing to analyse their data with state-of-the-art methods and develop new models of consumer behaviour. It provides a unified reference for cutting-edge marketing researchers, as well as an invaluable guide to this growing area for both graduate students and professors, alike.

The methodology used to construct tree structured rules is the focus of this monograph. Unlike many other statistical procedures, which moved from pencil and paper to calculators, this text's use of trees was unthinkable before computers. Both the practical and theoretical sides have been developed in the authors' study of tree methods. Classification and Regression Trees reflects these two sides, covering the use of trees as a data analysis method, and in a more mathematical framework, proving some of their fundamental properties.

Builds on classical probability theory and offers an extremely workable solution to the many problems of artificial intelligence, concentrating on the rapidly growing areas of fuzzy reasoning and neural computing. Contains a collection of previously unpublished articles by leading researchers in the field.

The last decade has brought dramatic changes in the way that researchers analyze economic and financial time series. This book synthesizes these recent advances and makes them accessible to first-year graduate students. James Hamilton provides the first adequate text-book treatments of important innovations such as vector autoregressions, generalized method of moments, the economic and statistical consequences of unit roots, time-varying variances, and nonlinear time series models. In addition, he presents basic tools for analyzing dynamic systems (including linear representations, autocovariance generating functions, spectral analysis, and the Kalman filter) in a way that integrates economic theory with the practical difficulties of analyzing and interpreting real-world data. "Time Series Analysis" fills an important need for a textbook that integrates economic theory, econometrics, and new results. The book is intended to provide students and researchers with a self-contained survey of time series analysis. It starts from first principles and should be readily accessible to any beginning graduate student, while it is also intended to serve as a reference book for researchers.

本书论述了自17世纪迄今数理统计学发展的简要历史。内容包括:概率基本概念的起源和发展,伯努利大数定律和狄莫旨二项概率正态逼近,贝叶斯关于统计推断的思想,最小二乘法与误差分布--高其正态分布的发现过程,社会统计学家对数理统计方法的主要贡献等。

Data measured as angles or two-dimensional orientations are found almost everywhere in science. They commonly arise in biology, geography, geophysics, medicine, meteorology and oceanography, and many other areas. Examples of such data include departure directions of birds from release points, fracture plane orientations, the directional movement of animals after stimulation, wind and ocean current directions, and biorhythms. Statistical methods for handling such data have developed rapidly in the last twenty years, particularly data display, correlation, regression and analysis of tempered or spatially structured data. Further, some of the exciting modern developments in general statistical methodology, particularly nonparametric smoothing methods and bootstrap-based methods, have contributed significantly to relatively intractable data analysis problems. This book provides a unified and up-to-date account of techniques for handling circular data.

因为精确预测以及在科技领域的广泛应用，量子力学被认为是最成功的科学理论之一，但也是最被误解的理论之一。在被创立后的近一个世纪，量子力学仍旧充满了争议。通过量子贝叶斯理论（QBism）解释量子理论中的悖论和谜题，本书为非专业的读者阐述了量子力学深远的含义、如何理解量子力学和量子力学如何与这个世界相互作用。QBism用对概率的全新理解去改造量子力学中的传统特征。贝叶斯概率与标准的“频率概率”不同的是，它是观察者对未来将要发生的一个事件或者一个命题的信任程度的数值测量。相比于频率主义，量子贝叶斯理论的优势在于它能够处理单个事件，它的概率估计可以根据获得的新信息去更新，并且可以包含“频率概率”的结果。但最重要的还是与量子理论相关的奇怪之处——如两个原子可以同时在不同的位置，信号可以传播得比光更快，以及薛定谔的猫可以同时处于死和活的状态的想法。
用直白的语言而不是方程，贝耶尔用一种通俗的方式，揭示了量子力学的意义，发现了认识物理学的新途径。

本书据Duxbury Press第5版译出。内容分为8个部分，共20章，分上下两册。各章均有大量习题。作者使用实例来引入主题，并把统计概念和实际问题联系在一起进行讲解，介绍了统计数据的收集和分析过程，讨论了如何解释数据分析的结果，并专门讲述了如何写数据分析报告。

在人工智能异常火热的今天，很多人认为我们生活在一个不可思议的历史时期，人工智能和大数据可能比工业革命更能改变人的一生。然而这种说法未免言过其实，我们的生活确实可能有所改变，但并非一定是朝好的方面发展。我们过于武断地认为计算机搜索和处理堆积如山的数据时不会出差错，但计算机只是擅长收集、储存和搜索数据，它们没有常识或智慧，不知道数字和词语的意思，无法评估数据库中内容的相关性和有效性，它们没有区分真数据、假数据和坏数据所需的人类判断力，没有分辨有理有据和虚假伪造的统计学模型所需的人类智能。
计算机挖掘大数据风行一时，但数据挖掘是人为而非智能，也是非常艰巨、危险的人工智能形式。数据挖掘先是通过大量的数据走势、相关关系来发现让我们内心愉悦却无实践价值的模型，然后创造理论来解释这些模型。作者通过“史密斯测试”和“得州神枪手谬误”等实例说明，如果你挖掘和拷问数据的时间够长、数量够大，你总能得到自己想要的结果，然而这是相关关系却并不是因果关系，只是自我选择偏好，并没有理论基础也没有实用价值。
在人工智能时代，我们对计算机的热爱不应该掩盖我们对其局限性的思考，真正的危险不是计算机比我们更聪明，而是我们认为计算机具有人类的智慧和常识，数据挖掘就是“知识发现”，从而信任计算机为我们做出重要决定。更多的计算能力和更多的数据并不意味着更多的智能，我们需要对人类的智慧有更多的信心。

This book offers a detailed history of parametric statistical inference. Covering the period between James Bernoulli and R.A. Fisher, it examines: binomial statistical inference; statistical inference by inverse probability; the central limit theorem and linear minimum variance estimation by Laplace and Gauss; error theory, skew distributions, correlation, sampling distributions; and the Fisherian Revolution. Lively biographical sketches of many of the main characters are featured throughout, including Laplace, Gauss, Edgeworth, Fisher, and Karl Pearson. Also examined are the roles played by DeMoivre, James Bernoulli, and Lagrange.