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Fast Monte Carlo Markov chains for Bayesian shrinkage models with random effects

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  • Abrahamsen, Tavis
  • Hobert, James P.

Abstract

When performing Bayesian data analysis using a general linear mixed model, the resulting posterior density is almost always analytically intractable. However, if proper conditionally conjugate priors are used, there is a simple two-block Gibbs sampler that is geometrically ergodic in nearly all practical settings, including situations where p>n (Abrahamsen and Hobert, 2017). Unfortunately, the (conditionally conjugate) multivariate Gaussian prior on β does not perform well in the high-dimensional setting where p≫n. In this paper, we consider an alternative model in which the multivariate Gaussian prior is replaced by the normal-gamma shrinkage prior developed by Griffin and Brown (2010). This change leads to a much more complex posterior density, and we develop a simple MCMC algorithm for exploring it. This algorithm, which has both deterministic and random scan components, is easier to analyze than the more obvious three-step Gibbs sampler. Indeed, we prove that the new algorithm is geometrically ergodic in most practical settings.

Suggested Citation

  • Abrahamsen, Tavis & Hobert, James P., 2019. "Fast Monte Carlo Markov chains for Bayesian shrinkage models with random effects," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 61-80.
    • Handle: RePEc:eee:jmvana:v:169:y:2019:i:c:p:61-80
    DOI: 10.1016/j.jmva.2018.08.014
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    References listed on IDEAS

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    1. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    2. 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.
    3. Johnson, Alicia A. & Jones, Galin L., 2015. "Geometric ergodicity of random scan Gibbs samplers for hierarchical one-way random effects models," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 325-342.
    4. Xiang Zhou & Peter Carbonetto & Matthew Stephens, 2013. "Polygenic Modeling with Bayesian Sparse Linear Mixed Models," PLOS Genetics, Public Library of Science, vol. 9(2), pages 1-14, February.
    5. Jürg Schelldorfer & Peter Bühlmann & Sara Van De Geer, 2011. "Estimation for High‐Dimensional Linear Mixed‐Effects Models Using ℓ 1 ‐Penalization," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(2), pages 197-214, June.
    6. Rohart, Florian & San Cristobal, Magali & Laurent, Béatrice, 2014. "Selection of fixed effects in high dimensional linear mixed models using a multicycle ECM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 209-222.
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