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辛普森悖论与贝叶斯因子AI 解读

Summary A counter-example presented by Lindley to Aitkin’s posterior Bayes factor is examined. The paradoxical feature of the counter-example is found to be a simple case of Simpson’s paradox.

后验贝叶斯因子AI 解读

SUMMARY A general procedure for computing Bayes factors for the comparison of arbitrary models is described, based on the use of the posterior mean of the likelihood under each model rather than the usual prior mean. The use of the posterior mean has several advantages, including reduced sensitivity to variations in the prior and the avoidance of the Lindley paradox in testing point null hypotheses. The frequency properties of the new procedure are evaluated in standard…

典范似然：处理干扰参数的新似然方法AI 解读

A new approach to the likelihood analysis of models with nuisance parameters is proposed, based on a singular value decomposition of the likelihood function, and is applied to several two-parameter models. The invariance of the approach under reparameterization is demonstrated, and the paper concludes with comments on multiparameter models.

典范似然：处理干扰参数的新似然方法AI 解读

A new approach to the likelihood analysis of models with nuisance parameters is proposed, based on a singular value decomposition of the likelihood function, and is applied to several two-parameter models. The invariance of the approach under reparameterization is demonstrated, and the paper concludes with comments on multiparameter models.

有限混合模型中的估计与假设检验AI 解读

SUMMARY Finite mixture models are a useful class of models for application to data. When sample sizes are not large and the number of underlying densities is in question, likelihood ratio tests based on joint maximum likelihood estimation of the mixing parameter, λ, and the parameter of the underlying densities, θ, are problematical. Our approach places a prior distribution on λ and estimates θ by maximizing the likelihood of the data given θ with λ integrated out.…

二元响应的方差成分模型：访员间变异AI 解读

SUMMARY Interviewer variability in a binary response is an example of a problem requiring variance component estimation in a non-normal family. The maximum likelihood estimation procedure is derived and used to examine some binary items on a large questionnaire. This raises some interesting questions about the use of unbalanced ANOVA methods with these data.