BAMLSS: Bayesian Additive Models for Location, Scale, and Shape (and Beyond)

References

• Belitz, C., Brezger, A., Kneib, T., Lang, S., and Umlauf, N. (2017), BayesX – Software for Bayesian Inference in Structured Additive Regression Models, Version 3.0.2, available at http://BayesX.org.
   Google Scholar
• Belitz, C., and Lang, S. (2008), “Simultaneous Selection of Variables and Smoothing Parameters in Structured Additive Regression Models,” Computational Statistics & Data Analysis, 53, 61–81.
   Web of Science ®Google Scholar
• Carpenter, B., Gelman, A., Hoffman, M. D., Lee, D., Goodrich, B., Betancourt, M., Brubaker, M., Guo, J., Li, P., and Riddell, A. (2017), “Stan: A Probabilistic Programming Language,” Journal of Statistical Software, 76(1), 1–32.
   PubMed Web of Science ®Google Scholar
• Carter, C. K., and Kohn, R. (1994), “On Gibbs Sampling for State Space Models,” Biometrika, 81, 541–553.
   Web of Science ®Google Scholar
• Chambers, J. M., and Hastie, T. J. (eds.) (1992), Statistical Models in S, London: Chapman & Hall.
   Google Scholar
• Fahrmeir, L., Kneib, T., and Lang, S. (2004), “Penalized Structured Additive Regression for Space Time Data: A Bayesian Perspective,” Statistica Sinica, 14, 731–761.
   Web of Science ®Google Scholar
• Fahrmeir, L., Kneib, T., Lang, S., and Marx, B. (2013), Regression – Models, Methods and Applications, Berlin: Springer-Verlag.
   Google Scholar
• Gamerman, D. (1997), “Sampling From the Posterior Distribution in Generalized Linear Mixed Models,” Statistics and Computing, 7, 57–68.
   Web of Science ®Google Scholar
• Gelman, A. (2006), “Prior Distributions for Variance Parameters in Hierarchical Models,” (Comment on Article by Browne and Draper), Bayesian Analysis, 1, 515–534.
   Google Scholar
• Hastie, T., and Tibshirani, R. (1990), Generalized Additive Models, Boca Raton, FL: Chapman & Hall/CRC.
   Google Scholar
• Hofner, B. (2008), “Variable Selection and Model Choice in Survival Models with Time-Varying Effects,” Ph.D. dissertation, Institut für Statistik.
   Google Scholar
• Klein, N., and Kneib, T. (2016), “Scale-Dependent Priors for Variance Parameters in Structured Additive Distributional Regression,” Bayesian Analysis, 11, 1071–1106.
   Web of Science ®Google Scholar
• Klein, N., Kneib, T., Klasen, S., and Lang, S. (2015a), “Bayesian Structured Additive Distributional Regression for Multivariate Responses,” Journal of the Royal Statistical Society, Series C, 64, 569–591.
   Google Scholar
• Klein, N., Kneib, T., and Lang, S. (2015), “Bayesian Generalized Additive Models for Location, Scale and Shape for Zero-Inflated and Overdispersed Count Data,” Journal of the American Statistical Association, 110, 405–419.
   Web of Science ®Google Scholar
• Klein, N., Kneib, T., Lang, S., and Sohn, A. (2015b), “Bayesian Structured Additive Distributional Regression with an Application to Regional Income Inequality in Germany,” Annals of Applied Statistics, 9, 1024–1052.
   Web of Science ®Google Scholar
• Kneib, T., and Fahrmeir, L. (2007), “A Mixed Model Approach for Geoadditive Hazard Regression,” Scandinavian Journal of Statistics, 34, 207–228.
   Web of Science ®Google Scholar
• Köhler, M., Umlauf, N., Beyerlein, A., Winkler, C., Ziegler, A.-G., and Greven, S. (2017), “Flexible Bayesian Additive Joint Models With an Application to Type 1 Diabetes Research,” Biometrical Journal, 59, 1144–1165.
   Google Scholar
• Krige, D. G. (1951), “A Statistical Approach to Some Basic Mine Valuation Problems on the Witwatersrand,” Journal of the Chemical, Metallurgical and Mining Society of South Africa, 52, 119–139.
   Google Scholar
• Lang, S., Umlauf, N., Wechselberger, P., Harttgen, K., and Kneib, T. (2014), “Multilevel Structured Additive Regression,” Statistics and Computing, 24, 223–238.
   Web of Science ®Google Scholar
• Lunn, D. J., Spiegelhalter, D., Thomas, A., and Best, N. (2009), “The BUGS Project: Evolution, Critique and Future Directions,” Statistics in Medicine, 28, 3049–3082.
   PubMed Web of Science ®Google Scholar
• Lunn, D. J., Thomas, A., Best, N., and Spiegelhalter, D. (2000), “WinBUGS – A Bayesian Modelling Framework: Concepts, Structure, and Extensibility,” Statistics and Computing, 10, 325–337.
   Web of Science ®Google Scholar
• Neal, R. M. (2003), “Slice Sampling,” The Annals of Statistics, 31(3), 705–767.
   Web of Science ®Google Scholar
• Nemec, J., Chimani, B., Gruber, C., and Auer, I. (2011), “Ein Neuer Datensatz Homogenisierter Tagesdaten,” ÖGM Bulletin, 2011, 19–20.
   Google Scholar
• Nemec, J., Gruber, C., Chimani, B., and Auer, I. (2013), “Trends in Extreme Temperature Indices in Austria Based on a New Homogenised Dataset,” International Journal of Climatology, 33, 1538–1550.
   Web of Science ®Google Scholar
• Paciorek, C. (2007), “Bayesian Smoothing With Gaussian Processes Using Fourier Basis Functions in the spectralGP Package,” Journal of Statistical Software, 19, 1–38.
   PubMed Web of Science ®Google Scholar
• Plummer, M. (2003), “JAGS: A Program for Analysis of Bayesian Graphical Models Using Gibbs Sampling,” in Proceedings of the 3rd International Workshop on Distributed Statistical Computing, Vienna, Austria, eds, K. Hornik, F. Leisch, and A. Zeileis, available at http://www.ci.tuwien.ac.at/Conferences/DSC-2003/Proceedings/.
   Google Scholar
• Polson, N. G., and Scott, J. G. (2012), “On the Half-Cauchy Prior for a Global Scale Parameter,” Bayesian Analysis, 7, 887–902.
   Web of Science ®Google Scholar
• R Core Team (2016), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing.
   Google Scholar
• Rigby, R. A., and Stasinopoulos, D. M. (2005), “Generalized Additive Models for Location, Scale and Shape,” Journal of the Royal Statistical Society, Series C, 54, 507–554.
   Google Scholar
• Rue, H., Martino, S., and Chopin, N. (2009), “Approximate Bayesian Inference for Latent Gaussian Models by Using Integrated Nested Laplace Approximations,” Journal of the Royal Statistical Society, Series B, 71, 319–392.
   Google Scholar
• Ruppert, D., Wand, M. P., and Carrol, R. J. (2003), Semiparametric Regression, New York: Cambridge University Press.
   Google Scholar
• Silverman, B. W. (1985), “Some Aspects of the Spline Smoothing Approach to Non-Parametric Regression Curve Fitting,” Journal of the Royal Statistical Society, Series B, 47, 1–52.
   Google Scholar
• Simpson, D., Rue, H., Riebler, A., Martins, T. G., and Sørbye, S. H. (2017), “Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors,” Statistical Science, 32, 1–28.
   Google Scholar
• Smyth, G. (1996), “Partitioned Algorithms for Maximum Likelihood and Other Non-Linear Estimation,” Statistics and Computing, 6, 201–216.
   Web of Science ®Google Scholar
• Stauffer, R., Mayr, G. J., Messner, J. W., Umlauf, N., and Zeileis, A. (2017), “Spatio-Temporal Precipitation Climatology over Complex Terrain Using a Censored Additive Regression Model,” International Journal of Climatology, 37, 3264–3275.
   Google Scholar
• Taylor, B. M. (in press), “Spatial Modelling of Emergency Service Response Times,” Journal of the Royal Statistical Society, Series A, 180, 433–453.
   Google Scholar
• Umlauf, N., Adler, D., Kneib, T., Lang, S., and Zeileis, A. (2015), “Structured Additive Regression Models: An R Interface to BayesX,” Journal of Statistical Software, 63(1), 1–46.
   Google Scholar
• Umlauf, N., Klein, N., Zeileis, A., and Köhler, M. (2017), bamlss: Bayesian Additive Models for Location Scale and Shape (and Beyond), R Package Version 1.0-0, available at https://CRAN.R-project.org/package=bamlss.
   Google Scholar
• Umlauf, N., Mayr, G., Messner, J., and Zeileis, A. (2012), “Why Does It Always Rain on Me? A Spatio-Temporal Analysis of Precipitation in Austria,” Austrian Journal of Statistics, 41, 81–92.
   Google Scholar
• Waldmann, E., Taylor-Robinson, D., Klein, N., Kneib, T., Pressler, T., Schmid, M., and Mayr, A. (2017), “Boosting Joint Models for Longitudinal and Time-to-Event Data,” Biometrical Journal, 59, 1104–1121.
   Google Scholar
• Wilkinson, G. N., and Rogers, C. E. (1973), “Symbolic Description of Factorial Models for Analysis of Variance,” Journal of the Royal Statistical Society, Series C, 22, 392–399.
   Google Scholar
• Wood, S. N. (2004), “Stable and Efficient Multiple Smoothing Parameter Estimation for Generalized Additive Models,” Journal of the American Statistical Association, 99, 673–686.
   Web of Science ®Google Scholar
• ——— (2016), “Just Another Gibbs Additive Modeler: Interfacing JAGS and mgcv,” Journal of Statistical Software, 75(7), 1–15.
   PubMed Web of Science ®Google Scholar
• Zeileis, A., and Croissant, Y. (2010), “Extended Model Formulas in R: Multiple Parts and Multiple Responses,” Journal of Statistical Software, 34(1), 1–13.
   Web of Science ®Google Scholar