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We propose a new importance sampling algorithm for producing a posterior sample for quantities of interest in a Bayesian implementation of the logistic model when the prior distribution on the \(\beta \) coefficients belongs to a large class of scale mixtures of Gaussian densities, including the Student-t, the variance gamma distribution, and the logistic density with independent components. We also show that the proposed algorithm provides an easy way to compute the marginal density of the data, which facilitates model selection procedures through the Bayes factor. We claim that the proposed algorithm – which completely avoids the adoption of MCMC techniques – works satisfactorily at least when the sample size is less than 500.

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An Importance Sampling Algorithm for Bayesian Logistic Regression with Scale Mixture of Gaussian Priors

  • 会议论文

  • 发表日期：

    2026年

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  • Paolo Onorati,
  • Brunero Liseo

摘要

We propose a new importance sampling algorithm for producing a posterior sample for quantities of interest in a Bayesian implementation of the logistic model when the prior distribution on the \(\beta \) coefficients belongs to a large class of scale mixtures of Gaussian densities, including the Student-t, the variance gamma distribution, and the logistic density with independent components. We also show that the proposed algorithm provides an easy way to compute the marginal density of the data, which facilitates model selection procedures through the Bayes factor. We claim that the proposed algorithm – which completely avoids the adoption of MCMC techniques – works satisfactorily at least when the sample size is less than 500.