Introduction to Probability Simulation and Gibbs Sampling with R (Paperback)

Eric A. A. Suess

  • 出版商: Springer
  • 出版日期: 2010-06-15
  • 售價: $3,630
  • 貴賓價: 9.5$3,449
  • 語言: 英文
  • 頁數: 324
  • 裝訂: Paperback
  • ISBN: 038740273X
  • ISBN-13: 9780387402734
  • 相關分類: R 語言
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商品描述

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.

商品描述(中文翻譯)

本書的前七章使用R進行概率模擬和計算,包括隨機數生成、數值和蒙特卡羅積分,以及在離散和連續狀態下找到馬爾可夫鏈的極限分佈。應用包括二項信賴區間的覆蓋概率、從篩查測試中估計疾病患病率、提高系統可靠性的並行冗余,以及各種遺傳建模。這些初步章節可用於非貝葉斯課程中應用概率模型和馬爾可夫鏈的模擬。

第8至10章簡要介紹了貝葉斯估計,並演示了使用Gibbs抽樣器找到後驗分佈和區間估計的方法,包括一些傳統方法無法給出滿意結果的例子。介紹了WinBUGS軟件,詳細解釋了其界面並提供了使用Gibbs抽樣器進行貝葉斯估計的示例。

不需要具備使用R的經驗。附錄介紹了R,幾乎所有計算示例和問題都包含完整的R代碼(附有註釋和解釋)。本書的值得注意的特點包括其直觀的方法,通過生物統計學、可靠性和其他領域的例子來呈現思想;大量的圖表;以及非常多的問題(約佔頁數的三分之一),從簡單的練習到額外的主題介紹。許多問題提供了提示和答案。這些特點使本書非常適合高年級本科生和初級研究生的統計學學生。