Likelihood, credible and confidence intervals for parameters in complex models

Murray Aitkin1
1School of Mathematics and Statistics, University of Melbourne, Melbourne, Australia

Tóm tắt

Recent papers have discussed general procedures with complex models to obtain confidence interval statements for a parameter of interest in the presence of nuisance parameters. This paper discusses the role of the likelihood in these procedures, and points out the simplicity of the Bayesian credible interval approach to the same models.

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Tài liệu tham khảo

Aitkin, M.: Profile likelihood. In: Encyclopedia of Biostatistics, pp. 3534–3536. Wiley, New York (1998) Aitkin, M.: Bayesian bootstrap analysis of regression in finite population survey data with stratification and clustering. J. Off. Stat. 24, 21–51 (2008) Aitkin, M.: Statistical inference: an integrated Bayesian/likelihood approach. CRC Press, Boca Raton (2010) Angus, J.E.: Bootstrapping a universal pivot when nuisance parameters are estimated. Am. Stat. 70(1), 100–107 (2016) Berger, J.O., Bernardo, J.M.: On the development of reference priors (with discussion). In Bayesian statistics, vol. 4, pp. 35–60. Oxford University Press, London (1992) Cox, D.R.: Principles of statistical inference. Cambridge University Press, Cambridge (2016) Datta, G.S., Sweeting, T.J.: Probability matching priors. In: Dey, D.K., Rao, C.R. (eds.) Handbook of statistics, 25: Bayesian thinking: modeling computation, pp. 91–114. Elsevier, Amsterdam (2005) Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A., Rubin, D.B.: Bayesian Data Analysis, 3rd edn. CRC Press, Boca Raton (2014) Lunn, D., Jackson, C., Best, N., Thomas, A., Spiegelhalter, D.: The BUGS Book. CRC Press, Boca Raton (2013) Ohlsson, U.: Confidence intervals for the mean of a lognormal distribution. Journal of Statistics Education 13. (2005) http://ww2.amstat.org/publications/jse/v13n1/olsson.html. Accessed 1 Sept 2018 Rolke, W.A., López, A.M., Conrad, J.: Limits and confidence intervals in the presence of nuisance parameters. Nucl. Instrum. Meth. A 551, 493–503 (2005) Schweder, T., Hjort, N.L.: Confidence, likelihood, probability. Cambridge University Press, Cambridge (2016) Sen, B., Walker, M., Woodroofe, M.: On the unified method with nuisance parameters. Stat. Sinica 19, 301–314 (2009) Tanner, M.A.: Tools for statistical inference: methods for the exploration of posterior distributions and likelihood functions, 3rd edn. Springer, New York (1993) Tanner, M.A., Wong, W.H.: The calculation of posterior distributions by data augmentation (with discussion). J Am Stat. Assoc. 82, 528–550 (1987) Welch, B.L.: On confidence limits and sufficiency with particular reference to parameters of location. Ann. Math. Stat. 10, 58–69 (1939)