References
- Efromovich S. Nonparametric curve estimation: methods, theory, and applications. Springer Series in Statistics. New York: Springer-Verlag; 1999.
- Fahrmeir L, Kneib T, Lang S, Marx B. Regression models, methods and applications. Heidelberg: Springer; 2013.
- Wakefield J. Bayesian and frequentist regression methods. New York: Springer Series in Statistics Springer; 2013.
- Lindley DV, Smith AFM. Bayes estimates for the linear model. J Roy Statist Soc Ser B. 1972;34:1–41.
- O'Hagan A, Forster J. Kendall's advanced theory of statistics. Vol. 2B. Bayesian inference. Chichester: John Wiley & Sons, Ltd.; 2004.
- Rasmussen CE, Williams CKI. Gaussian processes for machine learning. Massachusetts: The MIT Press; 2006.
- Shi JQ, Choi T. Gaussian process regression analysis for functional data. London: Monographs on Statistics and Applied Probability Chapman & Hall; 2011.
- Lenk PJ. Bayesian inference for semiparametric regression using a Fourier representation. J R Stat Soc Ser B Stat Methodol. 1999;61:863–879. doi: 10.1111/1467-9868.00207
- Choi T, Lee J, Roy A. A note on the Bayes factor in a semiparametric regression model. J Multivariate Anal. 2009;100:1316–1327. doi: 10.1016/j.jmva.2008.12.006
- Hart JD. Nonparametric smoothing and lack-of-fit tests. New York: Springer Series in Statistics Springer-Verlag; 1997.
- O'Hagan A. Bayes estimation of a convex quadratic. Biometrika. 1973;60:565–571. doi: 10.1093/biomet/60.3.565
- Geweke JF. Exact inference in the inequality constrained normal linear regression model. J Appl Econometrics. 1986;1:127–141. doi: 10.1002/jae.3950010203
- Geweke JF. Bayesian inference for linear models subject to linear inequality constraints. In: Johnson WO, Lee JC, Zellner A, editors. Modelling and prediction (Hsinchu, 1994). New York: Springer; 1996. p. 248–263.
- Shively TS, Sager TW, Walker SG. A Bayesian approach to non-parametric monotone function estimation. J R Stat Soc Ser B Stat Methodol. 2009;71:159–175. doi: 10.1111/j.1467-9868.2008.00677.x
- Meyer MC, Hackstadt AJ, Hoeting JA. Bayesian estimation and inference for generalised partial linear models using shape-restricted splines. J Nonparametr Stat. 2011;23:867–884. doi: 10.1080/10485252.2011.597852
- O'Hagan A, Leonard T. Bayes estimation subject to uncertainty about parameter constraints. Biometrika. 1976;63:201–203. doi: 10.1093/biomet/63.1.201
- Madi MT, Leonard T, Tsui KW. Bayesian inference for treatment effects with uncertain order constraints. Statist Probab Lett. 2000;49:277–283. doi: 10.1016/S0167-7152(00)00058-4
- Liseo B, Loperfido N. A Bayesian interpretation of the multivariate skew-normal distribution. Statist Probab Lett. 2003;61:395–401. doi: 10.1016/S0167-7152(02)00398-X
- Kim HJ. On a class of multivariate normal selection priors and its applications in Bayesian inference. J Korean Statist Soc. 2011;40:63–73. doi: 10.1016/j.jkss.2010.05.001
- Kim HJ, Choi T. On Bayesian estimation of regression models subject to uncertainty about functional constraints. J Korean Statist Soc. 2014;43:133–147. doi: 10.1016/j.jkss.2013.03.005
- Andrade JAA, O'Hagan A. Bayesian robustness modelling of location and scale parameters. Scand J Stat. 2011;38:691–711. doi: 10.1111/j.1467-9469.2011.00750.x
- Ferreira JTAS, Steel MFJ. A new class of skewed multivariate distributions with applications to regression analysis. Statist Sinica. 2007;17:505–529.
- Arellano-Valle RB, Castro LM, Genton MG, Gómez HW. Bayesian inference for shape mixtures of skewed distributions, with application to regression analysis. Bayesian Anal. 2008;3:513–539. doi: 10.1214/08-BA320
- Arellano-Valle RB, Genton MG, Loschi RH. Shape mixtures of multivariate skew-normal distributions. J Multivariate Anal. 2009;100:91–101. doi: 10.1016/j.jmva.2008.03.009
- Branco MD, Genton MG, Brunero L. Objective Bayesian analysis of skew-t distributions. Scand J Stat. 2013.
- Arellano-Valle RB, Branco MD, Genton MG. A unified view on skewed distributions arising from selections. Canad J Statist. 2006;34:581–601. doi: 10.1002/cjs.5550340403
- Kim HJ, Kim HM. A class of rectangle-screened multivariate normal distributions and its applications. Statistics. 2015;49:878–899. doi: 10.1080/02331888.2014.915841
- Branco MD, Dey DK. A general class of multivariate skew-elliptical distributions. J Multivariate Anal. 2001;79:99–113. doi: 10.1006/jmva.2000.1960
- Devroye L. Nonuniform random variate generation. New York: Springer-Verlag; 1986.
- Kotz S, Balakrishnan N, Johnson NL. Continuous multivariate distributions. Vol. 1: models and applications. 2nd ed. Wiley Series in Probability and statistics: applied probability and statistics. New York: Wiley-Interscience; 2000.
- Joe H. Approximations to multivariate normal rectangle probabilities based on conditional expectations. J Amer Statist Assoc. 1995;90:957–964. doi: 10.1080/01621459.1995.10476596
- Genz A, Bretz F. Computation of multivariate normal and t probabilities. Lecture Notes in Statistics. 2009;195. Available from: http://www.springer.com/us/book/9783642016882
- Box GEP, Tiao GC. Bayesian inference in statistical analysis. Reading (MA): Addison-Wesley Publishing Co.; 1973. Addison-Wesley series in behavioral science: quantitative methods.
- Press SJ. Applied multivariate analysis: using Bayesian and frequentist methods of inference. New York: Dover; 2005.
- Chib S, Greenberg E. Bayes inference in regression models with ARMA(p,q) errors. J Econometrics. 1994;64:183–206. doi: 10.1016/0304-4076(94)90063-9
- Chib S, Greenberg E. Understanding the Metropolis–Hastings algorithm. Amer Statist. 1995;49:327–335.
- Geweke J. Contemporary Bayesian econometrics and statistics. Hoboken (NJ): Wiley Series in Probability and Statistics Wiley-Interscience [John Wiley & Sons]; 2005.
- Judge GG, Hill RC, Griffiths WE, Lütkepohl H, Lee TC. Introduction to the theory and practice of econometrics. New York: Second John Wiley & Sons Inc.; 1988.
- Koop G, Poirier DJ, Tobias JL. Bayesian econometric methods. Cambridge: Cambridge University Press; 2007.
- Pindyck RS, Rubinfeld DL. Econometric models and economic forecasts. 2nd ed. New York: McGraw-Hill; 1981.
- Prado R, West M. Time series: modeling, computation, and inference. Boca Raton (FL): Texts in Statistical Science Series CRC Press; 2010.
- Roy A, Danaher M, Mumford SL, Chen Z. A Bayesian order-restricted model for hormonal dynamics during menstrual cycles of healthy women. Stat Med. 2012;31:2428–2440. doi: 10.1002/sim.4419
- Danaher MR, Roy A, Chen Z, Mumford SL, Schisterman EF. Minkowski–Weyl priors for models with parameter constraints: an analysis of the BioCycle study. J Amer Statist Assoc. 2012;107:1395–1409. doi: 10.1080/01621459.2012.712414
- Jylänki P, Vanhatalo J, Vehtari A. Robust Gaussian process regression with a Student-t likelihood. J Mach Learn Res. 2011;12:3227–3257.