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Hierarchical models: Local proposal variances for RWM-within-Gibbs and MALA-within-Gibbs

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  • Bédard, Mylène

Abstract

The performance of RWM- and MALA-within-Gibbs algorithms for sampling from hierarchical models is studied. For the RWM-within-Gibbs, asymptotically optimal tunings for Gaussian proposal distributions featuring a diagonal covariance matrix are developed using existing scaling analyses. This leads to locally optimal proposal variances that depend on the mixing components of the hierarchical model and that correspond to the classical asymptotically optimal acceptance rate of 0.234. Ignoring the local character of the optimal scaling is possible, leading to an optimal proposal variance that remains fixed for the duration of the algorithm; the corresponding asymptotically optimal acceptance rate is then shown to be lower than 0.234. Similar ideas are applied to MALA-within-Gibbs samplers, leading to efficient yet computationally affordable algorithms. Simplifications for location and scale hierarchies are presented, and findings are illustrated through numerical studies. The local and fixed approaches for the RWM- and MALA-within-Gibbs are compared to competitive samplers in the literature.

Suggested Citation

  • Bédard, Mylène, 2017. "Hierarchical models: Local proposal variances for RWM-within-Gibbs and MALA-within-Gibbs," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 231-246.
    • Handle: RePEc:eee:csdana:v:109:y:2017:i:c:p:231-246
    DOI: 10.1016/j.csda.2016.12.007
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    References listed on IDEAS

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    1. Mylène Bédard & Randal Douc & Eric Moulines, 2014. "Scaling Analysis of Delayed Rejection MCMC Methods," Methodology and Computing in Applied Probability, Springer, vol. 16(4), pages 811-838, December.
    2. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
    3. G. O. Roberts & O. Stramer, 2002. "Langevin Diffusions and Metropolis-Hastings Algorithms," Methodology and Computing in Applied Probability, Springer, vol. 4(4), pages 337-357, December.
    4. Gareth O. Roberts & Jeffrey S. Rosenthal, 1998. "Optimal scaling of discrete approximations to Langevin diffusions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(1), pages 255-268.
    5. Xifara, T. & Sherlock, C. & Livingstone, S. & Byrne, S. & Girolami, M., 2014. "Langevin diffusions and the Metropolis-adjusted Langevin algorithm," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 14-19.
    6. Mark Girolami & Ben Calderhead, 2011. "Riemann manifold Langevin and Hamiltonian Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(2), pages 123-214, March.
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