前七章使用R进行概率模拟和计算,包括随机数生成、数值积分和蒙特卡罗积分,以及寻找具有离散和连续状态的马尔可夫链的极限分布。应用包括二项式置信区间的覆盖概率、通过筛查测试估计疾病流行率、提高系统可靠性的并行冗余,以及各种遗传建模。
这些最初的章节可用于模拟应用概率模型和马尔可夫链的非贝叶斯课程。第8章到第10章简要介绍了贝叶斯估计,并举例说明了如何使用吉布斯采样器来寻找后验分布和区间估计,包括一些传统方法无法给出满意结果的例子。文中介绍了WinBUGS软件,详细解释了其接口,并举例说明了它在贝叶斯估计的Gibbs抽样中的应用。没有使用R的经验是必需的。附录介绍了R,几乎所有计算示例和问题都包含完整的R代码(以及注释和解释)。这本书值得注意的特点是其直观的方法,用来自生物统计学、可靠性和其他领域的例子展示想法;数量庞大;它的问题非常多(约占页面的三分之一),从简单的练习到其他主题的展示。为许多问题提供了提示和答案。这些特点使这本书成为高年级本科生和研究生初级阶段统计学学生的理想选择。埃里克·A·苏斯(Eric A.Suess)是统计学和生物统计学的主席兼教授,布鲁斯·E·特朗博(Bruce E.Trumbo)是统计学和数学的名誉教授,两人都在东湾加利福尼亚州立大学(California State University,East Bay)。Suess教授在将贝叶斯方法和Gibbs抽样应用于流行病学方面经验丰富。特朗博教授是美国统计协会和数理统计研究所的研究员,他是ASA创始人奖和IMS卡弗奖章的获得者。
Introduction to Probability Simulation and Gibbs Sampling with R (Use R!)
The first seven chapters use R for probability simulation and computation, including random number generation, numerical and Monte Carlo integration, and finding limiting distributions of Markov Chains with both discrete and continuous states. Applications include coverage probabilities of binomial confidence intervals, estimation of disease prevalence from screening tests, parallel redundancy for improved reliability of systems, and various kinds of genetic modeling.
These initial chapters can be used for a non-Bayesian course in the simulation of applied probability models and Markov Chains. Chapters 8 through 10 give a brief introduction to Bayesian estimation and illustrate the use of Gibbs samplers to find posterior distributions and interval estimates, including some examples in which traditional methods do not give satisfactory results. WinBUGS software is introduced with a detailed explanation of its interface and examples of its use for Gibbs sampling for Bayesian estimation. No previous experience using R is required. An appendix introduces R, and complete R code is included for almost all computational examples and problems (along with comments and explanations). Noteworthy features of the book are its intuitive approach, presenting ideas with examples from biostatistics, reliability, and other fields; its large number of figures; and its extraordinarily large number of problems (about a third of the pages), ranging from simple drill to presentation of additional topics. Hints and answers are provided for many of the problems. These features make the book ideal for students of statistics at the senior undergraduate and at the beginning graduate levels. Eric A. Suess is Chair and Professor of Statistics and Biostatistics and Bruce E. Trumbo is Professor Emeritus of Statistics and Mathematics, both at California State University, East Bay. Professor Suess is experienced in applications of Bayesian methods and Gibbs sampling to epidemiology. Professor Trumbo is a fellow of the American Statistical Association and the Institute of Mathematical Statistics, and he is a recipient of the ASA Founders Award and the IMS Carver Medallion.
OR