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Objective Bayesian higher-order asymptotics in models with nuisance parameters

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  • Ventura, Laura
  • Sartori, Nicola
  • Racugno, Walter

Abstract

A higher-order approximation to the marginal posterior distribution for a scalar parameter of interest in the presence of nuisance parameters is proposed. The approximation is obtained using a matching prior. The procedure improves the normal first-order approximation and has several advantages. It does not require the elicitation on the nuisance parameters, neither numerical integration nor Monte Carlo simulation, and it enables us to perform accurate Bayesian inference even for small sample sizes. Numerical illustrations are given for models of practical interest, such as linear non-normal models and logistic regression. Finally, it is shown how the proposed approximation can routinely be applied in practice using results from likelihood asymptotics and the R package bundle hoa.

Suggested Citation

  • Ventura, Laura & Sartori, Nicola & Racugno, Walter, 2013. "Objective Bayesian higher-order asymptotics in models with nuisance parameters," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 90-96.
    • Handle: RePEc:eee:csdana:v:60:y:2013:i:c:p:90-96
    DOI: 10.1016/j.csda.2012.10.022
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    References listed on IDEAS

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    1. Ventura, Laura & Cabras, Stefano & Racugno, Walter, 2009. "Prior Distributions From Pseudo-Likelihoods in the Presence of Nuisance Parameters," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 768-774.
    2. Guolo, Annamaria & Brazzale, Alessandra R. & Salvan, Alessandra, 2006. "Improved inference on a scalar fixed effect of interest in nonlinear mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1602-1613, December.
    3. N. Sartori, 2003. "Modified profile likelihoods in models with stratum nuisance parameters," Biometrika, Biometrika Trust, vol. 90(3), pages 533-549, September.
    4. repec:dau:papers:123456789/1906 is not listed on IDEAS
    5. G. Datta & J. Ghosh, 1995. "Noninformative priors for maximal invariant parameter in group models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 4(1), pages 95-114, June.
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    Cited by:

    1. Erlis Ruli & Laura Ventura, 2021. "Can Bayesian, confidence distribution and frequentist inference agree?," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 359-373, March.
    2. Laura Ventura & Nancy Reid, 2014. "Approximate Bayesian computation with modified log-likelihood ratios," METRON, Springer;Sapienza Università di Roma, vol. 72(2), pages 231-245, August.
    3. Ventura, Laura & Ruli, Erlis & Racugno, Walter, 2013. "A note on approximate Bayesian credible sets based on modified loglikelihood ratios," Statistics & Probability Letters, Elsevier, vol. 83(11), pages 2467-2472.

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