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一般贝叶斯更新与损失似然自助法AI 解读

In this paper we revisit the weighted likelihood bootstrap, a method that generates samples from an approximate Bayesian posterior of a parametric model. We show that the same method can be derived, without approximation, under a Bayesian nonparametric model with the parameter of interest defined through minimizing an expected negative loglikelihood under an unknown sampling distribution. This interpretation enables us to extend the weighted likelihood bootstrap to posterior…

线性模型中的贝叶斯因子AI 解读

We show that the Bayes factor for testing whether a subset of coefficients are zero in the normal linear regression model gives the uniformly most powerful test amongst the class of invariant tests discussed in Lehmann & Romano (2005) if the prior distributions for the regression coefficients are in a specific class of distributions. The priors in this class can have any elliptical distribution, with a specific scale matrix, for the subset of coefficients that are being…