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一般线性假设下系数估计与模型选择的后验一致性AI 解读

Berk (1970), LeCam (1953) and others have given conditions for the consistency of posterior distributions from a sequence of random variables. They have required that the sequence be i.i.d. We show that their results, Berk's in particular, may be extended to the general linear hypothesis with normal errors model (where the sequence of observations of the dependent variable need not be i.i.d.). We do not assume that the distribution governing the sequence of dependent…

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节点数量未知时的贝叶斯样条回归AI 解读

Summary The problem of selecting the model and coefficients for a spline regression curve with normal errors is considered. The locations of all possible knots are assumed to be known; which subset of these is the set of actual knots is unknown. Each subset forms a model. Priors of the form of a marginal distribution on the index of the model and a conditional distribution for each model on the coefficients and variance are allowed. The posterior distribution is explicitly…