A non-iterative posterior sampling algorithm for Laplace linear regression model

ABSTRACT

In this article, a non-iterative sampling algorithm is developed to obtain an independently and identically distributed samples approximately from the posterior distribution of parameters in Laplace linear regression model. By combining the inverse Bayes formulae, sampling/importance resampling, and expectation maximum algorithm, the algorithm eliminates the diagnosis of convergence in the iterative Gibbs sampling and the samples generated from it can be used for inferences immediately. Simulations are conducted to illustrate the robustness and effectiveness of the algorithm. Finally, real data are studied to show the usefulness of the proposed methodology.

KEYWORDS:

• EM algorithm
• Gibbs sampling
• Inverse Bayes formulae
• Laplace linear regression
• Sampling/important resampling

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F15
• 62J05
• 62D99
• 65C60

Acknowledgments

The authors gratefully acknowledge the editor and referees for their valuable comments and suggestions. The authors declare that there is no conflict of interests regarding the publication of this article.

Funding

This research is supported by The National Science Foundation of China Grants 11371227.

Conflict of interest

The authors declare there is no conflict of interest.