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Posterior simulation via the exponentially tilted signed root log-likelihood ratio

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  • Samer A. Kharroubi

    (American University of Beirut)

Abstract

We explore the use of importance sampling based on exponentially tilted signed root log-likelihood ratios for Bayesian computation. Approximations based on exponentially tilted signed root log-likelihood ratios are used in two distinct ways; firstly, to define an importance function with antithetic variates and, secondly, to define suitable control variates for variance reduction. These considerations give rise to alternative simulation-consistent schemes to other importance sampling techniques (for example, conventional and/or adaptive importance sampling) for Bayesian computation in moderately parameterized regular problems. The schemes based on control variates can also be viewed as usefully supplementing computations based on asymptotic approximations by supplying external estimates of error. The methods are illustrated by a censored regression model and a more challenging 12-parameter nonlinear repeated measures model for bacterial clearance.

Suggested Citation

  • Samer A. Kharroubi, 2018. "Posterior simulation via the exponentially tilted signed root log-likelihood ratio," Computational Statistics, Springer, vol. 33(1), pages 213-234, March.
    • Handle: RePEc:spr:compst:v:33:y:2018:i:1:d:10.1007_s00180-017-0772-9
    DOI: 10.1007/s00180-017-0772-9
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    References listed on IDEAS

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    5. Cerquetti, Annalisa, 2007. "A note on Bayesian nonparametric priors derived from exponentially tilted Poisson-Kingman models," Statistics & Probability Letters, Elsevier, vol. 77(18), pages 1705-1711, December.
    6. Susanne M. Schennach, 2005. "Bayesian exponentially tilted empirical likelihood," Biometrika, Biometrika Trust, vol. 92(1), pages 31-46, March.
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