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arXiv · 1503.06370

Bayesian Variable Selection for Linear Regression with the $\kappa$-$G$ Priors

Zichen Ma·Ernest Fokoué
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Abstract

In this paper, we introduce a new methodology for Bayesian variable selection in linear regression that is independent of the traditional indicator method. A diagonal matrix $\mathbf{G}$ is introduced to the prior of the coefficient vector $\boldsymbol{\beta}$, with each of the $g_j$'s, bounded between $0$ and $1$, on the diagonal serves as a stabilizer of the corresponding $\beta_j$. Mathematically, a promising variable has a $g_j$ value that is close to $0$, whereas the value of $g_j$ corresponding to an unpromising variable is close to $1$. This property is proven in this paper under orthogonality together with other asymptotic properties. Computationally, the sample path of each $g_j$ is obtained through Metropolis-within-Gibbs sampling method. Also, in this paper we give two simulations to verify the capability of this methodology in variable selection.

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Zichen Ma, Ernest Fokoué. 2015-03-22. Bayesian Variable Selection for Linear Regression with the $\kappa$-$G$ Priors. https://arxiv.org/abs/1503.06370

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