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贝叶斯方法：面向统计学家与跨学科研究者的分析
1. Introductory statistical concepts 2. The discrete version of Bayes' theorem 3. Models with a single unknown parameter 4. The expected utility hypothesis and its alternatives 5. Models with several unknown parameters 6. Prior structures, posterior smoothing, and Bayes-Stein estimation Guide to worked examples Guide to self-study exercises.
二维列联表关联结构的贝叶斯检验与估计
In a two-way contingency table, one is interested in checking the goodness of fit of simple models such as independence, quasi-independence, symmetry, and constant association, and estimating parameters that describe the association structure of the table. In a large table, one may be interested in detecting a few outlying cells that deviate from the main association pattern in the table. Bayesian tests of these hypotheses are described using a prior defined on the set of…
二维列联表关联的贝叶斯检验与估计
In a two-way contingency table, one is interested in checking the goodness of fit of simple models such as independence, quasi-independence, symmetry, and constant association, and estimating parameters that describe the association structure of the table. In a large table, one may be interested in detecting a few outlying cells that deviate from the main association pattern in the table. Bayesian tests of these hypotheses are described using a prior defined on the set of…
二元与多类别响应数据的贝叶斯分析
A vast literature in statistics, biometrics, and econometrics is concerned with the analysis of binary and polychotomous response data. The classical approach fits a categorical response regression model using maximum likelihood, and inferences about the model are based on the associated asymptotic theory. The accuracy of classical confidence statements is questionable for small sample sizes. In this article, exact Bayesian methods for modeling categorical response data are…
均值与方差发生马尔可夫状态切换的自回归时间序列：Gibbs 抽样贝叶斯推断
The authors examine autoregressive time series models subject to regime switching. A Bayesian framework is develope d in which the unobserved.states, one for each time point, are treated as missing data and then analyzed using the Gibbs sampler. This approac h is straightforward because the conditional posterior distribution of the parameters given the states, and the conditional posterior distribution of the states given the parameters, are amenable to simulation. The…
二项数据的贝叶斯方法及其在无应答问题中的应用
In this article, Bayesian estimation methods for several binomial probabilities are studied by using a mixture of a product of beta prior distributions. Approximations to the posterior means and credible regions are derived. The results obtained are applied to a sample survey problem in which there is significant nonresponse.
利用先验信息估计列联表概率
SUMMARY Prior beliefs of association and independence in a two-way contingency table are discussed, and estimators of the cell probabilities are proposed which can incorporate this prior information. In the 2 × 2 table where the cell counts are assumed to have a multinomial distribution, estimators are developed which can incorporate prior beliefs about the correlation coefficient and the cross-product ratio. In the I × 2 table in which one set of marginal totals is fixed,…
利用狄利克雷混合分布估计二乘二列联表的贝叶斯方法
In the estimation of cell probabilities from a 2 × 2 table, a prior distribution is developed that can reflect prior beliefs about the cross-classification structure in the table. The posterior means using this prior shrink the classical estimates towards the association structure specified a priori by the user. Closed-form approximations to the posterior means and credible regions are developed in the special case where the two variables of the table are believed…
狄利克雷分布混合与列联表估计
Assuming a multinomial sampling model, prior distributions are developed which can accept prior information about symmetry and independence in a two-way contingency table. Bayesian estimates for the cell probabilities are obtained from the posterior distributions which are attractive alternatives to the usual classical estimates when vague prior information about symmetry or independence is available.