G-prior

In statistics, the g-prior is an objective prior for the regression coefficients of a multiple regression. It was introduced by Arnold Zellner. It is a key tool in Bayes and empirical Bayes variable selection.

Consider a data set ${\displaystyle (x_{1},y_{1}),\ldots ,(x_{n},y_{n})}$, where the ${\displaystyle x_{i}}$ are Euclidean vectors and the ${\displaystyle y_{i}}$ are scalars. The multiple regression model is formulated as

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