A Shrinkage-Thresholding Metropolis Adjusted Langevin Algorithm for Bayesian Variable Selection

@article{Schreck2013ASM,
  title={A Shrinkage-Thresholding Metropolis Adjusted Langevin Algorithm for Bayesian Variable Selection},
  author={Amandine Schreck and Gersende Fort and Sylvain Le Corff and {\'E}ric Moulines},
  journal={IEEE Journal of Selected Topics in Signal Processing},
  year={2013},
  volume={10},
  pages={366-375}
}
This paper introduces a new Markov Chain Monte Carlo method for Bayesian variable selection in high dimensional settings. The algorithm is a Hastings-Metropolis sampler with a proposal mechanism which combines a Metropolis Adjusted Langevin (MALA) step to propose local moves associated with a shrinkage-thresholding step allowing to propose new models. The geometric ergodicity of this new trans-dimensional Markov Chain Monte Carlo sampler is established. An extensive numerical experiment, on… 

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