Bayesian modeling of joint and conditional distributions
In this paper, we study a Bayesian approach to flexible modeling of conditional distributions. The approach uses a flexible model for the joint distribution of the dependent and independent variables and then extracts the conditional distributions of interest from the estimated joint distribution. We use a finite mixture of multivariate normals (FMMN) to estimate the joint distribution. The conditional distributions can then be assessed analytically or through simulations. The discrete variables are handled through the use of latent variables. The estimation procedure employs an MCMC algorithm. We provide a characterization of the Kullback–Leibler closure of FMMN and show that the joint and conditional predictive densities implied by the FMMN model are consistent estimators for a large class of data generating processes with continuous and discrete observables. The method can be used as a robust regression model with discrete and continuous dependent and independent variables and as a Bayesian alternative to semi- and non-parametric models such as quantile and kernel regression. In experiments, the method compares favorably with classical nonparametric and alternative Bayesian methods.
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- De Iorio, Maria & Muller, Peter & Rosner, Gary L. & MacEachern, Steven N., 2004. "An ANOVA Model for Dependent Random Measures," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 205-215, January.
- John Geweke, 2004. "Getting It Right: Joint Distribution Tests of Posterior Simulators," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 799-804, January.
- Villani, Mattias & Kohn, Robert & Giordani, Paolo, 2009. "Regression density estimation using smooth adaptive Gaussian mixtures," Journal of Econometrics, Elsevier, vol. 153(2), pages 155-173, December.
- Geweke, John & Keane, Michael, 2007. "Smoothly mixing regressions," Journal of Econometrics, Elsevier, vol. 138(1), pages 252-290, May.
- Koenker,Roger, 2005.
Cambridge University Press, number 9780521845731, January.
- Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521608275, January.
- Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
- Norets, Andriy & Pelenis, Justinas, 2014. "Posterior Consistency In Conditional Density Estimation By Covariate Dependent Mixtures," Econometric Theory, Cambridge University Press, vol. 30(03), pages 606-646, June.
- Norets, Andriy & Pelenis, Justinas, 2011. "Posterior Consistency in Conditional Density Estimation by Covariate Dependent Mixtures," Economics Series 282, Institute for Advanced Studies.
- Sally A. Wood, 2002. "Bayesian mixture of splines for spatially adaptive nonparametric regression," Biometrika, Biometrika Trust, vol. 89(3), pages 513-528, August.
- Hayfield, Tristen & Racine, Jeffrey S., 2008. "Nonparametric Econometrics: The np Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i05).
- Jason Abrevaya, 2001. "The effects of demographics and maternal behavior on the distribution of birth outcomes," Empirical Economics, Springer, vol. 26(1), pages 247-257.
- Geweke, John, 2007. "Interpretation and inference in mixture models: Simple MCMC works," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3529-3550, April.
- Peter Hall & Jeff Racine & Qi Li, 2004. "Cross-Validation and the Estimation of Conditional Probability Densities," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1015-1026, December.
- Chung, Yeonseung & Dunson, David B., 2009. "Nonparametric Bayes Conditional Distribution Modeling With Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1646-1660.
- Gerfin, Michael, 1996. "Parametric and Semi-parametric Estimation of the Binary Response Model of Labor Market Participation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(3), pages 321-339, May-June.
- Michael Gerfin, 1993. "Parametric and Semiparametric Estimation of the Binary Response Model of Labor Market Participation," Diskussionsschriften dp9315, Universitaet Bern, Departement Volkswirtschaft.
- Li, Qi & Racine, Jeffrey S, 2008. "Nonparametric Estimation of Conditional CDF and Quantile Functions With Mixed Categorical and Continuous Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 423-434.
- Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355.
- Griffin, J.E. & Steel, M.F.J., 2006. "Order-Based Dependent Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 179-194, March.
- repec:dau:papers:123456789/3692 is not listed on IDEAS
- Taddy, Matthew A. & Kottas, Athanasios, 2010. "A Bayesian Nonparametric Approach to Inference for Quantile Regression," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(3), pages 357-369.
- David B. Dunson & Ju-Hyun Park, 2008. "Kernel stick-breaking processes," Biometrika, Biometrika Trust, vol. 95(2), pages 307-323. Full references (including those not matched with items on IDEAS)