Introduction to Bayesian Statistics
Introduction to Bayesian Statistics
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DOI：
10.1002/047172212x
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发表时间：
2004-04
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影响因子：
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通讯作者：
W. M. Bolstad
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文献类型：
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作者：
W. M. Bolstad
前言。第一版序言。 1.统计科学概论。 1.1 科学方法：学习的过程。 1.2 统计在科学方法中的作用。 1.3 主要统计方法。 1.4 本文的目的和组织。 2. 科学数据收集。 2.1 从真实总体中抽样。 2.2 观察研究和设计实验。蒙特卡罗练习。 3. 显示和汇总数据。 3.1 以图形方式显示单个变量。 3.2 以图形方式比较两个样本。 3.3 位置测量。 3.4 传播的测量。 3.5 显示两个或多个变量之间的关系。 3.6 两个或多个变量的关联度量。练习。 4. 逻辑、概率和不确定性。 4.1 演绎逻辑和合理推理。 4.2 概率。 4.3 概率公理。 4.4 联合概率和独立事件。 4.5 条件概率。 4.6 贝叶斯定理。 4.7 分配概率。 4.8 优势比和贝叶斯因子。 4.9 击败庄家。练习。 5.离散随机变量。 5.1 离散随机变量。 5.2 离散随机变量的概率分布5.3 二项分布。 5.4 超几何分布。 5.5 泊松分布。 5.6 联合随机变量。 5.7 联合随机变量的条件概率练习。 6.离散随机变量的贝叶斯推理。 6.1 使用贝叶斯定理的两种等效方法。 6.2 具有离散先验的二项式贝叶斯定理。 6.3 贝叶斯定理的重要结论。 6.4 具有离散先验的泊松贝叶斯定理。练习。计算机练习。 7.连续随机变量。 7.1 概率密度函数。 7.2 一些连续分布。 7.3 联合连续随机变量。 7.4 联合连续和离散随机变量。练习。 8.二项式比例的贝叶斯推理。 8.1 使用统一先验。 8.2 使用 Beta 先验。 8.3 选择你的优先级。 8.4 总结后验分布8.5 估计比例。 8.6 贝叶斯可信区间。练习。计算机练习。 9. 比较贝叶斯和频率论的比例推论。 9.1 概率和参数的频率论解释。 9.2 点估计。 9.3 比较比例估计量。 9.4 区间估计。 9.5 假设检验。 9.6 检验片面假设9.7 检验双向假设练习。蒙特卡罗练习。 10.泊松的贝叶斯推理。 10.1 泊松的一些先验分布。 10.2 泊松参数的推论练习。计算机练习。 11.正态平均值的贝叶斯推断。 11.1 具有离散先验的正态均值的贝叶斯定理。 11.2 具有连续先验的正态均值的贝叶斯定理11.3 选择你的正常先验11.4 正态平均值的贝叶斯可信区间11.5 下一次观察的预测密度练习。计算机练习。 12. 比较贝叶斯和频率论的均值推论。 12.1 比较频率点估计器和贝叶斯点估计器。 12.2 比较平均值的置信区间和可信区间。 12.3 检验关于正态均值的片面假设。 12.4 检验关于正态均值的双向假设练习。 13. 均值差异的贝叶斯推理。 13.1 来自两个正态分布的独立随机样本。 13.2 情况1：方差相等。 13.3 情况2：不等方差。 13.4 使用正态近似对两个比例之间的差异进行贝叶斯推断13.5 配对实验的正态随机样本练习。 14.简单线性回归的贝叶斯推理。 14.1 最小二乘回归14.2 指数增长模型14.3 简单线性回归假设14.4 回归模型的贝叶斯定理14.5 未来观察的预测分布练习。计算机练习。 15.标准差的贝叶斯推理。 15.1 具有连续先验的正态方差的贝叶斯定理。 15.2 一些特定的先验分布和由此产生的后验分布15.3 正态标准差的贝叶斯推断。练习。计算机练习。 16.鲁棒贝叶斯方法。 16.1 错误指定先验的影响。 16.2 具有混合先验的贝叶斯定理练习。计算机练习。 A. 微积分简介。 B. 统计表格的使用。 C. 使用包含的 Minitab 宏。 D. 使用包含的 R 函数。 E. 选定练习的答案。参考。主题索引。
Preface. Preface to First Edition. 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 Events. 4.5 Conditional Probability. 4.6 Bayes' Theorem. 4.7 Assigning Probabilities. 4.8 Odds Ratios and Bayes Factor. 4.9 Beat the Dealer. 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 Poisson Distribution. 5.6 Joint Random Variables. 5.7 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. 6.4 Bayes' theorem for Poisson with Discrete Prior. 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 Poisson. 10.1 Some Prior Distributions for Poisson. 10.2 Inference for Poisson Parameter. Exercises. Computer Exercises. 11. Bayesian Inference for Normal Mean. 11.1 Bayes' Theorem for Normal Mean with a Discrete Prior. 11.2 Bayes' Theorem for Normal Mean with a Continuous Prior. 11.3 Choosing Your Normal Prior. 11.4 Bayesian Credible Interval for Normal Mean. 11.5 Predictive Density for Next Observation. Exercises. Computer Exercises. 12. Comparing Bayesian and Frequentist Inferences for Mean. 12.1 Comparing Frequentist and Bayesian Point Estimators. 12.2 Comparing Confidence and Credible Intervals for Mean. 12.3 Testing a OneSided Hypothesis about a Normal Mean. 12.4 Testing a TwoSided Hypothesis about a Normal Mean. Exercises. 13. Bayesian Inference for Difference between Means. 13.1 Independent Random Samples from Two Normal Distributions. 13.2 Case 1: Equal Variances. 13.3 Case 2: Unequal Variances. 13.4 Bayesian Inference for Difference Between Two Proportions Using Normal Approximation. 13.5 Normal Random Samples from Paired Experiments. Exercises. 14. Bayesian Inference for Simple Linear Regression. 14.1 Least Squares Regression. 14.2 Exponential Growth Model. 14.3 Simple Linear Regression Assumptions. 14.4 Bayes' Theorem for the Regression Model. 14.5 Predictive Distribution for Future Observation. Exercises. Computer Exercises. 15. Bayesian Inference for Standard Deviation. 15.1 Bayes' Theorem for Normal Variance with a Continuous Prior. 15.2 Some Specific Prior Distributions and The Resulting Posteriors. 15.3 Bayesian inference for normal standard deviation. Exercises. Computer Exercises. 16. Robust Bayesian Methods. 16.1 Effect of Misspecified Prior. 16.2 Bayes' Theorem with Mixture Priors. Exercises. Computer 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. Topic Index.