298
Views
2
CrossRef citations to date
0
Altmetric
Bayesian and Latent Variable Models

Bayesian Semiparametric Analysis of Multivariate Continuous Responses, With Variable Selection

&
Pages 896-909 | Received 14 May 2019, Accepted 02 Mar 2020, Published online: 14 Apr 2020

References

  • Barnard, J., McCulloch, R., and Meng, X.-L. (2000), “Modeling Covariance Matrices in Terms of Standard Deviations and Correlations, With Application to Shrinkage,” Statistica Sinica, 10, 1281–1311.
  • Chan, D., Kohn, R., Nott, D., and Kirby, C. (2006), “Locally Adaptive Semiparametric Estimation of the Mean and Variance Functions in Regression Models,” Journal of Computational and Graphical Statistics, 15, 915–936. DOI: 10.1198/106186006X157441.
  • Chen, Z., and Dunson, D. B. (2003), “Random Effects Selection in Linear Mixed Models,” Biometrics, 59, 762–769. DOI: 10.1111/j.0006-341X.2003.00089.x.
  • Chiu, T. Y. M., Leonard, T., and Tsui, K.-W. (1996), “The Matrix-Logarithmic Covariance Model,” Journal of the American Statistical Association, 91, 198–210. DOI: 10.1080/01621459.1996.10476677.
  • Daniels, M. J., and Kass, R. E. (1999), “Nonconjugate Bayesian Estimation of Covariance Matrices and Its Use in Hierarchical Models,” Journal of the American Statistical Association, 94, 1254–1263. DOI: 10.1080/01621459.1999.10473878.
  • Ferguson, T. S. (1973), “A Bayesian Analysis of Some Nonparametric Problems,” The Annals of Statistics, 1, 209–230. DOI: 10.1214/aos/1176342360.
  • Gamerman, D. (1997), “Sampling From the Posterior Distribution in Generalized Linear Mixed Models,” Statistics and Computing, 7, 57–68.
  • George, E. I., and McCulloch, R. E. (1993), “Variable Selection via Gibbs Sampling,” Journal of the American Statistical Association, 88, 881–889. DOI: 10.1080/01621459.1993.10476353.
  • Johnson, R., and Wichern, D. (2014), Applied Multivariate Statistical Analysis, Essex: Pearson.
  • Klein, N., and Kneib, T. (2016), “Simultaneous Inference in Structured Additive Conditional Copula Regression Models: A Unifying Bayesian Approach,” Statistics and Computing, 26, 841–860. DOI: 10.1007/s11222-015-9573-6.
  • Klein, N., Kneib, T., Klasen, S., and Lang, S. (2015), “Bayesian Structured Additive Distributional Regression for Multivariate Responses,” Journal of the Royal Statistical Society, Series C, 64, 569–591. DOI: 10.1111/rssc.12090.
  • Liang, F., Paulo, R., Molina, G., Clyde, M. A., and Berger, J. O. (2008), “Mixtures of g Priors for Bayesian Variable Selection,” Journal of the American Statistical Association, 103, 410–423. DOI: 10.1198/016214507000001337.
  • Liechty, J. C., Liechty, M. W., and Müller, P. (2004), “Bayesian Correlation Estimation,” Biometrika, 91, 1–14. DOI: 10.1093/biomet/91.1.1.
  • Liechty, J. C., Liechty, M. W., and Müller, P. (2009), “The Shadow Prior,” Journal of Computational and Graphical Statistics, 18, 368–383.
  • Liu, X., and Daniels, M. J. (2006), “A New Algorithm for Simulating a Correlation Matrix Based on Parameter Expansion and Reparameterization,” Journal of Computational and Graphical Statistics, 15, 897–914. DOI: 10.1198/106186006X160681.
  • Mardia, K., Kent, J., and Bibby, J. (1979), Multivariate Analysis, Probability and Mathematical Statistics, London: Academic Press.
  • Müller, P., and Mitra, R. (2013), “Bayesian Nonparametric Inference—Why and How,” Bayesian Analysis, 8, 269–302. DOI: 10.1214/13-BA811.
  • O’Hara, R. B., and Sillanpää, M. J. (2009), “A Review of Bayesian Variable Selection Methods: What, How and Which,” Bayesian Analysis, 4, 85–117. DOI: 10.1214/09-BA403.
  • Papageorgiou, G. (2018), “BNSP: An R Package for Fitting Bayesian Semiparametric Regression Models and Variable Selection,” The R Journal, 10, 526–548. DOI: 10.32614/RJ-2018-069.
  • Papageorgiou, G. (2019), “BNSP: Bayesian Non- and Semi-Parametric Model Fitting,” R Package Version 2.1.1.
  • Pinheiro, J. C., and Bates, D. M. (1996), “Unconstrained Parametrizations for Variance-Covariance Matrices,” Statistics and Computing, 6, 289–296. DOI: 10.1007/BF00140873.
  • Pourahmadi, M. (1999), “Joint Mean-Covariance Models With Applications to Longitudinal Data: Unconstrained Parameterisation,” Biometrika, 86, 677–690. DOI: 10.1093/biomet/86.3.677.
  • Pourahmadi, M. (2007), “Cholesky Decompositions and Estimation of a Covariance Matrix: Orthogonality of Variance-Correlation Parameters,” Biometrika, 94, 1006–1013.
  • Rigby, R. A., and Stasinopoulos, D. M. (2005), “Generalized Additive Models for Location, Scale and Shape” (with discussion), Journal of the Royal Statistical Society, Series C, 54, 507–554. DOI: 10.1111/j.1467-9876.2005.00510.x.
  • Roberts, G. O., and Rosenthal, J. S. (2001), “Optimal Scaling for Various Metropolis-Hastings Algorithms,” Statistical Science, 16, 351–367. DOI: 10.1214/ss/1015346320.
  • Roberts, G. O., and Rosenthal, J. S. (2009), “Examples of Adaptive MCMC,” Journal of Computational and Graphical Statistics, 18, 349–367.
  • Rothman, A. J. (2017), “MRCE: Multivariate Regression With Covariance Estimation,” R Package Version 2.1.
  • Rothman, A. J., Levina, E., and Zhu, J. (2010), “Sparse Multivariate Regression With Covariance Estimation,” Journal of Computational and Graphical Statistics, 19, 947–962. DOI: 10.1198/jcgs.2010.09188.
  • Scheipl, F., Fahrmeir, L., and Kneib, T. (2012), “Spike-and-Slab Priors for Function Selection in Structured Additive Regression Models,” Journal of the American Statistical Association, 107, 1518–1532. DOI: 10.1080/01621459.2012.737742.
  • Sethuraman, J. (1994), “A Constructive Definition of Dirichlet Priors,” Statistica Sinica, 4, 639–650.
  • Smith, M., and Kohn, R. (2000), “Nonparametric Seemingly Unrelated Regression,” Journal of Econometrics, 98, 257–281. DOI: 10.1016/S0304-4076(00)00018-X.
  • Tsay, R. S., and Pourahmadi, M. (2017), “Modelling Structured Correlation Matrices,” Biometrika, 104, 237–242.
  • Umlauf, N., Klein, N., and Zeileis, A. (2018), “BAMLSS: Bayesian Additive Models for Location, Scale, and Shape (and Beyond),” Journal of Computational and Graphical Statistics, 27, 612–627. DOI: 10.1080/10618600.2017.1407325.
  • Whittaker, J. (2009), Graphical Models in Applied Multivariate Statistics, New York: Wiley.
  • Yu, P. L. H., Li, W. K., and Ng, F. C. (2014), “Formulating Hypothetical Scenarios in Correlation Stress Testing via a Bayesian Framework,” The North American Journal of Economics and Finance, 27, 17–33. DOI: 10.1016/j.najef.2013.10.002.
  • Zellner, A. (1962), “An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias,” Journal of the American Statistical Association, 57, 348–368. DOI: 10.1080/01621459.1962.10480664.
  • Zellner, A. (1986), “On Assessing Prior Distributions and Bayesian Regression Analysis With g-Prior Distributions,” in Bayesian Inference and Decision Techniques: Essays in Honor of Bruno de Finetti, eds. P. Goel and A. Zellner, New York: Elsevier Science Publishers, pp. 233–243.
  • Zhang, X., Boscardin, J. W., and Belin, T. R. (2006), “Sampling Correlation Matrices in Bayesian Models With Correlated Latent Variables,” Journal of Computational and Graphical Statistics, 15, 880–896. DOI: 10.1198/106186006X160050.

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.