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贝叶斯统计 （Bayesian Statistics）

应用于推论统计、统计决策、多元数据分析、序贯分析和抽样等领域。

研究生

UC-Berkley

Bayesian Statistics -- Statistics (STAT) 238 [4 units]

Description: Bayesian methods: conditional probability, one-parameter and multiparameter models, hierarchical models, predictive checking and sensitivity analysis, linear and generalized linear models, mixtures, time series, spatial models. Simulation of probability distributions. Experimental design. Case studies of applied modeling. Bayes theory; asymptotics, decision theory, randomization. The selection of topics may vary from year to year.

贝叶斯统计：贝叶斯方法：条件规律，单参数模型和多参数模型，分层模型，预测检验和敏感度分析，线性模型和广义线性模型，混合法，时间序列，空间模型。概率分布的模拟。试验设计。模型应用案例研究。贝叶斯理论；渐进性，决策论，随机性。

Statistics 220 (formerly Statistics 220r) . Bayesian Data Analysis

Begins with basic Bayesian models, whose answers often appear similar to classical answers, followed by more complicated hierarchical and mixture models with nonstandard solutions. Includes methods for monitoring adequacy of models and examining sensitivity of conclusions to change in models. Throughout, emphasis on drawing inferences via computer simulation rather than mathematical analysis.

贝叶斯数据分析：先介绍基本的贝叶斯模型，接着介绍更复杂的具有非标准解的分层模型和混合模型。模型充分性的监控方法，模型的敏感度检测方法。整个过程强调计算机模拟，而不是数学分析。

密歇根大学

Statistics 551: BAYESIAN INFERENCE

Prerequisite: Statistics 550, or Statistics 426 and permission. (3)

The foundations of Statistics, from the Bayesian point of view, followed by special topics in Bayesian inference and decision theory -- for example: the Bayesian view of the Stein paradox; Bayesian analysis of contingency tables; Bayesian analysis of nonparametric problems; the species sampling problems; and interesting recent articles.

贝叶斯推断：贝叶斯统计基础，贝叶斯推断和决策理论——如： Stein 悖论的贝叶斯观点 ，列联表的贝叶斯分析，非参数问题的贝叶斯分析；类别抽样问题；新近的文章。

Statistics 550 (SMS 603, IOE 560): BAYESIAN DECISION ANALYSIS

Prerequisite: Statistics 511, or permission. I. (3)

Axiomatic foundations; utility, subjective probability, decision functions; randomized acts; risk function; admissibility; completeness, Bayes and minimax rules; sufficiency; estimation problems, two-action problems, multiple decision procedures; preposterior analysis.

贝叶斯决策分析：公里基础；效用，主观规律，决策函数；随机化行为；风险函数；容许度；完整性，贝叶斯法则，极小极大法则；充分性；估计问题，两行动问题，多决策过程，先验分析。

北卡大学

195- BAYESIAN STATISTICS AND GENERALIZED LINEAR MODELS

Corequisites, Statistics 174 and Statistics 165, or permission of the instructor. Bayes factors; Empirical Bayes, formulation, Stein effect; Classical: EM, Laird-Ware; Hierarchical: prior, MCMC. GLM specific models: Binomial regression, polytomous regression, Cox proportional hazard, log linear. Spring. Ikstadt. (3)

贝叶斯统计与广义线性模型：贝叶斯因子；经验贝叶斯公式， Stein 效应。传统模型： EM方法，Laird-Ware方法； 层系模型：先验，MCMC. GLM。特殊模型：二项回归，多项回归， Cox 比例风险，对数线性模型。

华盛顿大学

STAT 544 Bayesian Statistical Methods (3)

Statistical methods based on the idea of a probability distribution over the parameter space. Coherence and utility. Subjective probability. Likelihood principle. Conjugate families. Structure of Bayesian inference. Limit theory for posterior distributions. Sequential experiments. Exchangeability. Bayesian nonparametrics. Empirical Bayes methods. Prerequisite: STAT 513 or permission of instructor. Offered: alternate years.

贝叶斯统计方法：基于参数空间概率分布思想的统计方法。一致性和效用。主观概率。似然法则。共轭分布族。贝叶斯推断的结构。后验分布的极限理论。序贯试验。可交换性。被叶斯非参数统计。经验贝叶斯方法。

STAT 564 Bayesian Statistics for the Social Sciences (4)

Statistical methods based on the idea of probability as a measure of uncertainty. Topics covered include subjective notion of probability, Bayes' Theorem, prior and posterior distributions, and data analysis techniques for statistical models. Prerequisite: introductory statistics. Offered: jointly with CS&SS 564.

社会科学贝叶斯统计：概率作为不确定性的测度的统计方法。包括：概率的主观定义，贝叶斯理论，先验和后验分布，统计模型的数据分析技术。

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决策论 （Decision Theory）

本科

哈佛大学

Statistics 185. Statistical Decision and Forecasting

The development of a Bayesian approach to the related problems of decision and forecasting. Decision topics will include utility, loss, decision rules, risk, admissibility of decision rules, and decision theoretic aspects of sequential analysis. Forecasting will be developed through the dynamic linear model and include topics such as sequential analysis and smoothing; models for polynomial trends, seasonal trends, and adjustment for covariates; and forecast intervention, monitoring, and error analysis. Theory and computational methods will be developed with a strong emphasis on applications to a variety of data sets.

Prerequisite: Statistics 110 or 139 or equivalent.

统计决策和预测：贝叶斯方法在决策和预测中的发展。决策包括效用、损失、决策法则、风险、决策法则的容许度，序贯分析的决策理论问题。预测通过动态线性模型讲授，包括：序贯分析与平滑、季节趋势模型、协变量的调整，预测的干预、监测、误差分析。强调在各种数据集中的应用。

宾夕法尼亚大学沃顿商学院

209. (STAT712) Decision Making under Uncertainty. (M) Stine. Prerequisite(s): STAT 102 or 112.

Analysis of managerial decision making under conditions of uncertainty and incomplete information. Modern theory of utility and statistical decision theory approaches. Case studies in managerial decision analysis.

不确定条件下的决策：分析信息不完全和不确定条件下的决策制定，现代效用理论和统计决策理论方法，管理决策分析案例研究。 ）

研究生

UC-Berkley

Advanced Topics in Learning and Decision-Making -- Statistics (STAT) 241B [3 units]

Description: Recent topics include: Graphical models and approximate inference algorithms. Markov chain Monte Carlo, mean field, and probability propagation methods. Model selection and stochastic realization. Bayesian, information-theoretic and structural risk minimization approaches. Markov decision processes and partially observable Markov decision processes. Reinforcement learning.

统计学习与统计决策高级专题：近期专题包括：图示模型和近似推断算法。MCMC法，均值域（mean field）和概率传播方法。模型选择与随机实现，贝叶斯统计、信息理论与结构风险最小化方法，马氏决策过程和部分可观测的马氏决策过程，增量学习。

Statistical Learning Theory -- Statistics (STAT) 241A [3 units]

Description: Classification, regression, clustering, dimensionality reduction, and density estimation. Mixture models, hierarchical models, factorial models, hidden Markov and state space models. Markov properties and recursive algorithms for general probabilistic inference. Nonparametric methods including decision trees, kernel methods, neural networks, and wavelets. Ensemble methods.

统计学习理论：分组、回归、聚类、降维（dimensionality reduction）、密度估计（density estimation），混合模型、分层模型、因子模型、藏匿的马氏状态空间模型，一般概率推断的马尔可夫性和递归（recursive）算法，包括决策树、核方法、神经网络和小波在内的非参数方法，总体方法（Ensemble methods）。

UCLA

202. Decision Theory. (4)

(Formerly numbered Mathematics 278C.) Lecture, three hours. Requisites: course 200B, Mathematics 131A. Bayes, admissible, and minimax decision rules. Invariant tests and estimates, best unbiased tests, locally best tests. Application to general linear model. Letter grading.

决策论：贝叶斯法则，课容许法则，极小极大法则。不变检验和估计，最优无偏检验，局部最优检验。在广义线性模型中的应用。

宾夕法尼亚大学沃顿商学院

927. Statistical Decision Theory. (M) Staff. Prerequisite(s): STAT 551.

A course in Bayesian statistical theory. Axiomatic developments of utility theory and subjective probability, and elements of Bayesian theory.

统计决策论：贝叶斯统计理论。效用理论和主观概率的发展，贝叶斯理论基础。

密歇根大学 贝叶斯决策分析、贝叶斯推断。（参见前文）

哈佛大学

[Statistics 290. Risk Analysis]

Rational decision-making under uncertainty, decision trees, subjective expected utility. Risk aversion, decreasing risk aversion, multiple risks. Risk sharing, insurance. Principals and agents. Rare events. Risks to life and health. Statistical models and assessment. Participants give talks and write papers on topics of their choice.

Note: Expected to be given in 2000–01.

Prerequisite: Statistics 111 or equivalent.

风险分析：不确定条件下的理性统计决策，决策树、期望效用，风险厌恶，风险厌恶递减，多重风险。风险分担、保险，统计模型与评估。