Introduction to Bayesian Statistics
暫譯: 貝葉斯統計學導論
William M. Bolstad
- 出版商: Wiley
- 出版日期: 2004-04-26
- 售價: $1,400
- 貴賓價: 9.8 折 $1,372
- 語言: 英文
- 頁數: 376
- 裝訂: Hardcover
- ISBN: 0471270202
- ISBN-13: 9780471270201
-
相關分類:
機率統計學 Probability-and-statistics
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商品描述
Description:
There is a strong upsurge in the use of Bayesian methods in applied statistical analysis, yet most introductory statistics texts only present frequentist methods. In Bayesian statistics the rules of probability are used to make inferences about the parameter. Prior information about the parameter and sample information from the data are combined using Bayes theorem. Bayesian statistics has many important advantages that students should learn about if they are going into fields where statistics will be used. This book uniquely covers the topics usually found in a typical introductory statistics book but from a Bayesian perspective.
Table of Contents:
Preface.
1. Introduction to Statistical Science.
1.1 The Scientific Method: A Process for Learning.
1.2 The Role of Statistics in the Scientific Method.
1.3 Main Approaches to Statistics.
1.4 Purpose and Organization of This Text.
2. Scientific Data Gathering.
2.1 Sampling from a Real Population.
2.2 Observational Studies and Designed Experiments.
Monte Carlo Exercises.
3. Displaying and Summarizing Data.
3.1 Graphically Displaying a Single Variable.
3.2 Graphically Comparing Two Samples.
3.3 Measures of Location.
3.4 Measures of Spread.
3.5 Displaying Relationships Between Two or More Variables.
3.6 Measures of Association for Two or More Variables.
Exercises.
4. Logic, Probability, and Uncertainty.
4.1 Deductive Logic and Plausible Reasoning.
4.2 Probability.
4.3 Axioms of Probability.
4.4 Joint Probability and Independent Event s.
4.5 Conditional Probability.
4.6 Bayes’ Theorem.
4.7 Assigning Probabilities.
4.8 Odds Ratios and Bayes Factor.
Exercises.
5. Discrete Random Variables.
5.1 Discrete Random Variables.
5.2 Probability Distribution of a Discrete Random Variable.
5.3 Binomial Distribution.
5.4 Hypergeometric Distribution.
5.5 Joint Random Variables.
5.6 Conditional Probability for Joint Random Variables.
Exercises.
6. Bayesian Inference for Discrete Random Variables.
6.1 Two Equivalent Ways of Using Bayes’ Theorem.
6.2 Bayes’ Theorem for Binomial with Discrete Prior.
6.3 Important Consequences of Bayes’ Theorem.
Exercises.
Computer Exercises.
7. Continuous Random Variables.
7.1 Probability Density Function.
7.2 Some Continuous Distributions.
7.3 Joint Continuous Random Variables.
7.4 Joint Continuous and Discrete Random Variables.
Exercises.
8. Bayesian Inference for Binomial Proportion.
8.1 Using a Uniform Prior.
8.2 Using a Beta Prior.
8.3 Choosing Your Prior.
8.4 Summarizing the Posterior Distribution.
8.5 Estimating the Proportion.
8.6 Bayesian Credible Interval.
Exercises.
Computer Exercises.
9. Comparing Bayesian and Frequentist Inferences for Proportion.
9.1 Frequentist Interpretation of Probability and Parameters.
9.2 Point Estimation.
9.3 Comparing Estimators for Proportion.
9.4 Interval Estimation.
9.5 Hypothesis Testing.
9.6 Testing a OneSided Hypothesis.
9.7 Testing a TwoSided Hypothesis.
Exercises.
Monte Carlo Exercises.
10. Bayesian Inference for Normal Mean.
10.1 Bayes’ Theorem for Normal Mean with a Discrete Prior.
10.2 Bayes’ Theorem for Normal Mean with a Continuous Prior.
10.3 Choosing Your Normal Prior.
10.4 Bayesian Credible Interval for Normal Mean.
10.5 Predictive Density for Next Observation.
Exercises.
Computer Exercises.
11. Comparing Bayesian and Frequentist Inferences for Mean.
11.1 Comparing Frequentist and Bayesian Point Estimators.
11.2 Comparing Confidence and Credible Intervals for Mean.
11.3 Testing a OneSided Hypothesis about a Normal Mean.
11.4 Testing a TwoSided Hypothesis about a Normal Mean.
Exercises.
12. Bayesian Inference for Difference between Means.
12.1 Independent Random Samples from Two Normal Distributions.
12.2 Case 1: Equal Variances.
12.3 Case 2: Unequal Variances.
12.4 Bayesian Inference for Difference Between Two Proportions Using Normal Approximation.
12.5 Normal Random Samples from Paired Experiments.
Exercises.
13. Bayesian Inference for Simple Linear Regression.
13.1 Least Squares Regression.
13.2 Exponential Growth Model.
13.3 Simple Linear Regression Assumptions.
13.4 Bayes’ Theorem for the Regression Model.
13.5 Predictive Distribution for Future Observation.
Exercises.
14. Robust Bayesian Methods.
14.1 Effect of Misspecified Prior.
14.2 Bayes’ Theorem with Mixture Priors.
Exercises.
A. Introduction to Calculus.
B. Use of Statistical Tables.
C. Using the Included Minitab Macros.
D. Using the Included R Functions.
E. Answers to Selected Exercises.
References.
Index.
商品描述(中文翻譯)
描述：在應用統計分析中，貝葉斯方法的使用正在強勁上升，然而大多數入門統計學教材僅介紹頻率主義方法。在貝葉斯統計中，概率規則用於對參數進行推斷。先前對參數的資訊和來自數據的樣本資訊通過貝葉斯定理進行結合。貝葉斯統計有許多重要的優勢，學生應該了解這些優勢，尤其是當他們進入需要使用統計的領域時。本書獨特地從貝葉斯的角度涵蓋了通常在典型入門統計書中找到的主題。
目錄：
前言。
1. 統計科學導論。
1.1 科學方法：學習的過程。
1.2 統計在科學方法中的角色。
1.3 統計的主要方法。
1.4 本書的目的和組織。
2. 科學數據收集。
2.1 從真實人口中抽樣。
2.2 觀察性研究和設計實驗。
蒙地卡羅練習。
3. 數據的顯示和總結。
3.1 單一變量的圖形顯示。
3.2 比較兩個樣本的圖形顯示。
3.3 位置的度量。
3.4 散佈的度量。
3.5 顯示兩個或多個變量之間的關係。
3.6 兩個或多個變量的關聯度量。
練習。
4. 邏輯、概率和不確定性。
4.1 演繹邏輯和合理推理。
4.2 概率。
4.3 概率公理。
4.4 聯合概率和獨立事件。
4.5 條件概率。
4.6 貝葉斯定理。
4.7 分配概率。
4.8 機率比和貝葉斯因子。
練習。
5. 離散隨機變量。
5.1 離散隨機變量。
5.2 離散隨機變量的概率分佈。
5.3 二項分佈。
5.4 超幾何分佈。
5.5 聯合隨機變量。
5.6 聯合隨機變量的條件概率。
練習。
6. 離散隨機變量的貝葉斯推斷。
6.1 使用貝葉斯定理的兩種等效方法。
6.2 對於具有離散先驗的二項分佈的貝葉斯定理。
6.3 貝葉斯定理的重要後果。
練習。
計算機練習。
7. 連續隨機變量。
7.1 概率密度函數。
7.2 一些連續分佈。
7.3 聯合連續隨機變量。
7.4 聯合連續和離散隨機變量。
練習。
8. 二項比例的貝葉斯推斷。
8.1 使用均勻先驗。
8.2 使用貝塔先驗。
8.3 選擇你的先驗。
8.4 總結後驗分佈。
8.5 估計比例。
8.6 貝葉斯可信區間。
練習。
計算機練習。
9. 比較貝葉斯和頻率推斷的比例。
9.1 頻率主義對概率和參數的解釋。
9.2 點估計。
9.3 比較比例的估計量。
9.4 區間估計。
9.5 假設檢驗。
9.6 測試單側假設。
9.7 測試雙側假設。
練習。
蒙地卡羅練習。
10. 正態均值的貝葉斯推斷。
10.1 對於具有離散先驗的正態均值的貝葉斯定理。
10.2 對於具有連續先驗的正態均值的貝葉斯定理。
10.3 選擇你的正態先驗。
10.4 正態均值的貝葉斯可信區間。
10.5 下一次觀察的預測密度。
練習。
計算機練習。
11. 比較貝葉斯和頻率推斷的均值。
11.1 比較頻率和貝葉斯點估計量。
11.2 比較均值的置信區間和可信區間。
11.3 測試正態均值的單側假設。
11.4 測試正態均值的雙側假設。
練習。
12. 均值差異的貝葉斯推斷。
12.1 來自兩個正態分佈的獨立隨機樣本。
12.2 案例1：方差相等。
12.3 案例2：方差不等。
12.4 使用正態近似的兩個比例之間的貝葉斯推斷。
12.5 來自配對實驗的正態隨機樣本。
練習。
13. 簡單線性回歸的貝葉斯推斷。
13.1 最小二乘回歸。
13.2 指數增長模型。
13.3 簡單線性回歸假設。
13.4 回歸模型的貝葉斯定理。
13.5 未來觀察的預測分佈。
練習。
14. 穩健的貝葉斯方法。
14.1 錯誤指定先驗的影響。
14.2 混合先驗的貝葉斯定理。
練習。
A. 微積分導論。
B. 統計表的使用。
C. 使用附帶的 Minitab 巨集。
D. 使用附帶的 R 函數。
E. 選定練習的答案。
參考文獻。
索引。
