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A note on simulation methods for the Dirichlet-Laplace prior

Author

Listed:
  • Luis Gruber
  • Gregor Kastner
  • Anirban Bhattacharya
  • Debdeep Pati
  • Natesh Pillai
  • David Dunson

Abstract

Bhattacharya et al. (2015, Journal of the American Statistical Association 110(512): 1479-1490) introduce a novel prior, the Dirichlet-Laplace (DL) prior, and propose a Markov chain Monte Carlo (MCMC) method to simulate posterior draws under this prior in a conditionally Gaussian setting. The original algorithm samples from conditional distributions in the wrong order, i.e., it does not correctly sample from the joint posterior distribution of all latent variables. This note details the issue and provides two simple solutions: A correction to the original algorithm and a new algorithm based on an alternative, yet equivalent, formulation of the prior. This corrigendum does not affect the theoretical results in Bhattacharya et al. (2015).

Suggested Citation

  • Luis Gruber & Gregor Kastner & Anirban Bhattacharya & Debdeep Pati & Natesh Pillai & David Dunson, 2025. "A note on simulation methods for the Dirichlet-Laplace prior," Papers 2508.11982, arXiv.org.
    • Handle: RePEc:arx:papers:2508.11982
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    References listed on IDEAS

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    1. John Geweke, 2004. "Getting It Right: Joint Distribution Tests of Posterior Simulators," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 799-804, January.
    2. Florian Huber & Gregor Kastner & Michael Pfarrhofer, 2025. "Introducing shrinkage in heavy-tailed state space models to predict equity excess returns," Empirical Economics, Springer, vol. 68(2), pages 535-553, February.
    3. Anirban Bhattacharya & Debdeep Pati & Natesh S. Pillai & David B. Dunson, 2015. "Dirichlet--Laplace Priors for Optimal Shrinkage," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1479-1490, December.
    4. Marco Del Negro & Giorgio E. Primiceri, 2015. "Time Varying Structural Vector Autoregressions and Monetary Policy: A Corrigendum," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(4), pages 1342-1345.
    5. Marco Del Negro & Giorgio E. Primiceri, 2015. "Time Varying Structural Vector Autoregressions and Monetary Policy: A Corrigendum," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(4), pages 1342-1345.
    6. Gregor Kastner & Florian Huber, 2020. "Sparse Bayesian vector autoregressions in huge dimensions," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(7), pages 1142-1165, November.
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