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Bayesian Fusion Estimation via t Shrinkage

Author

Listed:
  • Qifan Song

    (Purdue University)

  • Guang Cheng

    (Purdue University)

Abstract

Shrinkage prior has gained great successes in many data analysis, however, its applications mostly focus on the Bayesian modeling of sparse parameters. In this work, we will apply Bayesian shrinkage to model high dimensional parameter that possesses an unknown blocking structure. We propose to impose heavy-tail shrinkage prior, e.g., t prior, on the differences of successive parameter entries, and such a fusion prior will shrink successive differences towards zero and hence induce posterior blocking. Comparing to conventional Bayesian fused LASSO which implements Laplace fusion prior, t fusion prior induces stronger shrinkage effect and enjoys a nice posterior consistency property. Simulation studies and real data analyses show that t fusion has superior performance to the frequentist fusion estimator and Bayesian Laplace fusion prior. This t fusion strategy is further developed to conduct a Bayesian clustering analysis, and our simulations show that the proposed algorithm compares favorably to classical Dirichlet process modeling.

Suggested Citation

  • Qifan Song & Guang Cheng, 2020. "Bayesian Fusion Estimation via t Shrinkage," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 353-385, August.
  • Handle: RePEc:spr:sankha:v:82:y:2020:i:2:d:10.1007_s13171-019-00177-0
    DOI: 10.1007/s13171-019-00177-0
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    References listed on IDEAS

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