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Marshall–Olkin 指数分布的贝叶斯估计AI 解读

SUMMARY Bayes estimators of the parameters of the Marshall–Olkin exponential distribution are obtained when random samples from series and parallel systems are available. The estimators are with respect to the quadratic loss function, and the prior distribution allows for prior dependence among the components of the parameter vector. Exact and approximate highest posterior density credible ellipsoids for the parameters are also obtained. In contrast with series sampling, the…

利用独立性结构改进列联表概率估计AI 解读

Estimation of the cell probabilities in a two-way contingency table is considered when it is plausible that the table might have an independence structure relating to the two traits. In a classical nonparametric setup, the unrestricted maximum likelihood estimators of the cell probabilities are the corresponding sample proportions; under the assumption of independence, the restricted estimators are the product of the respective row and column sample proportions. The latter…

利用独立结构改进列联表概率估计AI 解读

Estimation of the cell probabilities in a two-way contingency table is considered when it is plausible that the table might have an independence structure relating to the two traits. In a classical nonparametric setup, the unrestricted maximum likelihood estimators of the cell probabilities are the corresponding sample proportions; under the assumption of independence, the restricted estimators are the product of the respective row and column sample proportions. The latter…

二项数据的贝叶斯方法及其在无应答问题中的应用AI 解读

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AI 解读

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AI 解读

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…

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狄利克雷分布混合与列联表估计AI 解读

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.