137
Views
4
CrossRef citations to date
0
Altmetric
Articles

Bayesian linear regression models with flexible error distributions

ORCID Icon, ORCID Icon & ORCID Icon
Pages 2571-2591 | Received 05 Jan 2019, Accepted 12 Jun 2020, Published online: 02 Jul 2020

References

  • Frühwirth-Schnatter S. Finite mixture and markov switching models: modeling and applications to random processes. New York: Springer Science & Business Media; 2006.
  • McLachlan GJ, Peel D. Finite mixture models. New York: John Wiley & Sons; 2000.
  • Lange KL, Little RJ, Taylor JM. Robust statistical modeling using the t distribution. J Am Stat Assoc. 1989;84(408):881–896.
  • Bartolucci F, Scaccia L. The use of mixtures for dealing with non-normal regression errors. Comput Stat Data Anal. 2005;48(4):821–834.
  • Soffritti G, Galimberti G. Multivariate linear regression with non-normal errors: a solution based on mixture models. Stat Comput. 2011;21(4):523–536.
  • Galimberti G, Soffritti G. A multivariate linear regression analysis using finite mixtures of t distributions. Comput Stat Data Anal. 2014;71:138–150.
  • Fernandez C, Steel MFJ. Multivariate student-t regression models: pitfalls and inference. Biometrika. 1999;86(1):153–167.
  • Fonseca TC, Ferreira MAR, Migon HS. Objective bayesian analysis for the student-t regression model. Biometrika. 2008;95(2):325–333.
  • Villa C, Walker SG. Objective prior for the number of degrees of freedom of a t distribution. Bayesian Anal. 2014;9(1):197–220.
  • Benites L, Maehara R, Lachos VH, et al. Linear regression models using finite mixtures of skew heavy-tailed distributions. Chil J Stat. 2019;10(1):21–41.
  • Andrews DF, Mallows CL. Scale mixtures of normal distributions. J R Stat Soc Ser B Stat Methodol. 1974;36(1):99–102.
  • Peel D, McLachlan GJ. Robust mixture modelling using the t distribution. Stat Comput. 2000;10(4):339–348.
  • Kullback S, Leibler RA. On information and sufficiency. Ann Math Statist. 1951;22(1):79–86.
  • da Silva NB. Modelagem bayesiana semi-paramétrica via misturas [dissertation]. Universidade Federal de Minas Gerais; 2017.
  • Gonçalves FB, Prates MO, Lachos VH. Robust bayesian model selection for heavy-tailed linear regression using finite mixtures. Braz J Probab Stat. 2020;34(1):51–70.
  • Simpson D, Rue H, Riebler A, et al. Penalising model component complexity: a principled, practical approach to constructing priors. Stat Sci. 2017;32(1):1–28.
  • Prates MO, Lachos VH, Cabral C. mixsmsn: fitting finite mixture of scale mixture of skew-normal distributions. J Stat Softw. 2013;54(12):1–20.
  • R Core Team. R: a language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing; 2017. Available from: https://www.R-project.org/.
  • Spiegelhalter DJ, Best NG, Carlin BP, et al. Bayesian measures of model complexity and fit. J R Stat Soc Ser B Stat Methodol. 2002;64(4):583–639.
  • Watanabe S. Asymptotic equivalence of bayes cross validation and widely applicable information criterion in singular learning theory. J Mach Learn Res. 2010;11:3571–3594.
  • Ripley B, Venables B, Bates DM, et al. Package mass. 2013.
  • Carlin BP, Chib S. Bayesian model choice via markov chain monte carlo methods. J R Stat Soc Ser B Stat Methodol. 1995;57:473–484.
  • Richardson S, Green P. On Bayesian analysis of mixtures with an unknown number of components. J R Stat Soc Ser B Stat Methodol. 1997;59(4):731–792.
  • Stephens M. Bayesian methods for mixtures of normal distributions [dissertation]. University of Oxford; 1997.
  • Pruim R. Nhanes: data from the us national health and nutrition examination study; 2015. R package version 2.1.0; Available from: https://CRAN.R-project.org/package=NHANES.
  • Lin T, Lee J, Hsieh W. Robust mixture modeling using the skew-t distribution. Stat Comput. 2007;17(2):81–92.
  • Cabral CB, Bolfarine H, Pereira JRG. Bayesian density estimation using skew student-t-normal mixtures. Comput Stat Data Anal. 2008;52(12):5075–5090.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.