(特价书)贝叶斯方法（英文版）

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    数学书籍
“本书提供了有关最新现代贝叶斯统计方法的重要题材，文笔流畅，语言优美，其突出的特点是包括大量实际应用，涉及若干领域中AIC和BIC模型选择标准的运用和对比，通过效用理论以独特方式处理贝叶斯决策论，并论述了贝叶斯过程的频度特性，配备了可以扩展与加深书中内容的有趣和适中的自学练习。”
——Michael J．Evans，Mathematical Review
“以严密、纯熟的文笔介绍贝叶斯建模的基本原则，选材深思熟虑，按照研究生层次引入贝叶斯方法。”
——Journal of the American Statistical Association
贝叶斯“后验分布”或“预测分布”是对有关未知参或未来观测所需了解的每项事物的概括。本书以一种强有力和贴切的方式说明了如何运用贝叶斯统计技术，引导读者从具体数据中推测有关科学、医疗与社会问题的结论。本书解释了贝叶斯方法论所需的一些细微假设，并展示了如何运用这些假设去获取准确结论。本书所介绍的各种方法对计算机模拟的频度特性方面也非常适用。
本书生动地概述了有关费希尔方法(频度方法)，同时全面强调了似然性，适合作为主流统计学的教程。本书讲述了效用理论的进展以及时间序列和预测，从而也适合计量经济学的学生阅读。另外，本书还包括线性模型、范畴数据分析、生存竞争分析、随机效应模型和非线性平滑等内容。
本书提供了许多运行实例、自学练习和实际应用，可作为高年级本科生和研究生的教材，同时也可供其他交叉学科的研究人员阅读。

Thomas Leonard 于1973年在伦敦大学获得统计学博士学位。他曾在沃里克大学工作过，于1995年担任爱丁堡大学统计学系主席，还曾做过威斯康星—麦迪逊大学统计学教授。20世纪80年代，他最早将拉普拉斯算子引入到贝叶斯方法中。他发表了多篇有关统计学应用方面的论文，并作为统计学专家参与过多个美国法律诉讼案件。
John S．J．Hsu 加州大学圣芭芭拉分校统计学与应用概率论副教授、统计实验室主任，擅长研究应用问题，还建立了贝叶斯理论研究计划。由于在log—线性模型分析方面的贡献，他获得了爱丁堡大学的名誉职位。在Thomas Leonard和Kam—Wah Tsui的指导下，他于1990年在威斯康星—麦迪逊大学获得统计学博士学位。

Preface
1 Introductory Statistical Concepts
1.0 Preliminaries and Overview
1.1 Sampling Models and Likelihoods
1.2 Practical Examples
1.3 Large Sample Properties of Likelihood Procedures
1.4 Practical Examples
1.5 Some Further Properties of Likelihood
1.6 Practical Examples
1.7 The Midcontinental Rift
1.8 A Model for Genetic Traits in Dairy Science
1.9 Least Squares Regression with Serially Correlated Errors
1.10 Annual World Crude Oil Production (1880-1972)
2 The Discrete Version of Bayes' Theorem
2.0 Preliminaries and Overview
2.1 Bayes' Theorem
2.2 Estimating a Discrete-Valued Parameter
2.3 Applications to Model Selection
2.4 Practical Examples
2.5 Logistic Discrimination and the Construction of Neural Nets

　　Statistics uses theoretical models and techniques to help applied researchers to extract,and infer, real-life, scientific, medical, and social conclusions from numerical data, which are subject to random uncertainty. For any particular study, it is important to combine theoretical and computational resources, together with applied skills, and an ability to interact with experts with knowledge relating to the background and usefulness of the data.
　　 Many studies and data sets are nonstandard, and it is not always possible to provide a completely convincing analysis based upon preexisting techniques. Therefore, statisticians frequently need to develop new techniques, on line, for a particular practical study. Furthermore, the statistical state of the art is continuously evolving, and it is therefore important for researchers to continue to develop the available statistical methodology. Finally, when existing methodology is available, it is important that this should be applied with specific knowledge of the subtleties of the assumptions involved, together with their consequences.
　　 There are nowadays two main streams of statistical thought. We will refer to these as
　　the "Fisherian" and the "Bayesian" philosophies. The Fisherian philosophy is named after Sir Ronald Fisher and combines the "frequency approach" (unbiased estimators, hypothesis tests, and confidence intervals) with likelihood methods. The Fisherian philosophy also includes the "fiducial approach," an incomplete method, suggested by Fisher, which attempts to achieve some of the advantages of the Bayesian approach (e.g., good conditional inference, given the observed values of the data, combined with appealing frequency properties when repeating the experiment a number of times under identical conditions), but without the assumption of a "prior distribution"
　　 The Bayesian philosophy is named after the Reverend Thomas Bayes and refers
　　to such concepts as "prior and posterior knowledge," "prior, posterior, and predictive distributions" and "Bayes decision roles and estimators" The Bayesian approach possesses many advantages, even when viewed from a Fisherian viewpoint, in particular its inherent long-run frequency properties. In practical terms, this means that if computer simulations are used to compare the mean squared error, prediction error, coverage probability, or power of different procedures, then Bayesian methods can perform remarkably well. This validation is an essential ingredient, when combined with the construction of statistical techniques, and provides just one substantial justification of the Bayesian paradigm. Other advantages are summarized by Berger (1985) and Bemardo and Smith (1994), and in our introductions to Chapters 2, 3, 5, and 6 of the current text.
　　 Chapter 1 describes a number of Fisherian procedures, which comprise important background to the Bayesian approach. It is, for example, essential for the reader to be able to construct and understand likelihood functions before attempting Bayesian techniques. The reader should also understand basic data analysis.
　　 Chapter 2 provides an easy introduction to Bayesian ideas and utilizes easy forms of
　　B ayes' theorem when the parameter space is discrete. These are of particular importance in medical and legal applications.
　　 Chapter 3 develops the Bayesian paradigm when there is a single unknown parame-
　　ter. In such cases, a univariate probability distribution readily summarizes the posterior information. Frequency properties of related estimators and decision rules are developed.
　　 Chapter 4 provides a break to some of the technicalities and considers the "expected
　　utility hypothesis" and its role in financial decision making. Some extensions to the expected utility hypothesis are considered.
　　 Chapter 5 extends the ideas of Chapter 3 to statistical models with several parameters. Approaches to the linear statistical model, categorical data analysis, and time-series analysis are included.
　　 Chapter 6 provides advanced studies of prior structures, posterior smoothing, and Bayes-Stein estimation. Many of the techniques again achieve appealing frequency properties. Computational techniques, already mentioned in Chapter 5, for approximating or simulating high-dimensional numerical integrations, for example, for providing adequate finite sample size analyses of nonlinear models, are developed further. These include Laplacian methods, importance sampling, and Markov Chain Monte Carlo Methods (MCMC).
　　 The text contains 49 worked examples and 148 self-study exercises, which relate to special cases of methodology more broadly explained in the main body of the text. The reader is thereby provided with layers of knowledge, which can be studied at different levels. The volume progressively develops a number of special themes in a possibly unique manner. A large number of further practical examples are described throughout the text.
　　 The bibliography integrates Bayesian statistics with other statistical methodologies
　　and with interdisciplinary research. While the Bayesian references represent the last four decades of research, they do not provide an exhaustive reference list for the Bayesian literature.
　　 Much of the material in this text has been previously taught to graduate students in statistics, economics, and business attending a Bayesian Decisions course at the Uni-versity of Wisconsin-Madison, and to graduate students attending a Bayesian Inference course at the University of California at Santa Barbara. The text is also appropriate for the following readerships:
　　 · Students attending a statistics course with a mixture of Fisherian and Bayesian philosophies, at final-year undergraduate or at Master's-degree level. In this case, the instructors should concentrate on the easier parts of Chapter 1, together with Chapters 2 and 3, and the easier parts of Chapter 5. If the course is taught within an economics graduate program, then Chapter 4 and Sections 5.3-5.7 will also be of interest, together with the simulation procedures of Chapter 6.