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MCMC Convergence for Global-Local Shrinkage Priors

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  • Kshitij Khare

    (University of Florida)

  • Malay Ghosh

    (University of Florida)

Abstract

Global-local continuous shrinkage priors have emerged as effective and computationally scalable tools for Bayesian sparsity-based regularization in modern high-dimensional settings. These priors have been successfully deployed in various scientific fields, including econometrics. Markov chain Monte Carlo (MCMC) methods are critical for exploring the resulting intractable posterior distributions. In this paper we review the convergence analyses of the corresponding Markov chains, as these analyses are crucial to help understand the quality of the MCMC based approximations of desired posterior quantities. In particular, we discuss unique features of some of these priors which translate into unique and novel choices for the respective convergence analyses. We also describe how these specific examples have served as catalysts for the development of new general techniques for Markov chain convergence analysis.

Suggested Citation

  • Kshitij Khare & Malay Ghosh, 2022. "MCMC Convergence for Global-Local Shrinkage Priors," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(1), pages 211-234, September.
    • Handle: RePEc:spr:jqecon:v:20:y:2022:i:1:d:10.1007_s40953-022-00311-0
    DOI: 10.1007/s40953-022-00311-0
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    References listed on IDEAS

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