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奇异模型的贝叶斯信息准则AI 解读

Summary We consider approximate Bayesian model choice for model selection problems that involve models whose Fisher information matrices may fail to be invertible along other competing submodels. Such singular models do not obey the regularity conditions underlying the derivation of Schwarz's Bayesian information criterion BIC and the penalty structure in BIC generally does not reflect the frequentist large sample behaviour of the marginal likelihood. Although large sample…

SUMMARY This paper discusses design issues in 'ecological studies' —epidemiological studies in which the relationship between disease and behavioural and environmental determinants is studied at the population rather than the individual level. The number of study populations has little relevance beyond a certain point, the power and precision being limited by the total number of disease events and by the size of the sample surveys used to estimate the distributions of…