A note on simulation methods for the Dirichlet-Laplace prior
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).
Cite
@article{arxiv.2508.11982,
title = {A note on simulation methods for the Dirichlet-Laplace prior},
author = {Luis Gruber and Gregor Kastner and Anirban Bhattacharya and Debdeep Pati and Natesh Pillai and David Dunson},
journal= {arXiv preprint arXiv:2508.11982},
year = {2025}
}
Comments
Correction: Bhattacharya, A., Pati, D., Pillai, N.S., and Dunson, D.B. (2015), "Dirichlet-Laplace Priors for Optimal Shrinkage," Journal of the American Statistical Association, 110, 1479-1490, DOI: 10.1080/01621459.2014.960967