Abstract
The normal linear model, with sign or other linear inequality constraints on its coefficients, arises very commonly in many scientific applications. Given inequality constraints Bayesian inference is much simpler than lassical inference, but standard Bayesian computational methods become impractical when the posterior probability of the inequality constraints (under a diffuse prior) is small. This paper shows how the Gibbs sampling algorithm can provide an alternative, attractive approach to inference subject to linear inequality constraints in this situation, and how the GHK probability simulator may be used to assess the posterior probability of the constraints.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bails, D. G., and L. C. Peppers (1982), Business fluctuations. Englewood Cliffs: Prentice-Hall
Bernardo, J. M., and A. F. M. Smith (1994), Bayesian Theory. New York: Wiley
Chamberlain, G., and E. Learner (1976), Matrix weighted averages and posterior bounds, Journal of the Royal Statistical Society, Series B, 38, 73–84
Davis, W. W. (1978), Bayesian analysis of the linear model subject to linear inequality constraints, Journal of the American Statistical Association 73, 573–79
Gelfand, A. E., and A. F. M. Smith (1990), Sampling based approaches to calculating marginal densities, Journal of the American Statistical Association 85, 398–409
Geweke, J. (1986), Exact inference in the inequality constrained normal linear regulation model, Journal of Applied Econometrics 1, 127–41
Geweke, J. (1991), Efficient simulation from the multivariate normal and student- t distributions subject to linear constraints. In E. M. Keramidas (ed.), Computing Science and Statistics: Proceedings of the 23rd Symposium on the Interface, pp. 571 – 78. Fairfax, VA: Interface Foundation of North America
Geweke, J. (1992), Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In J. O. Berger et al. (eds.), Proceedings of the Fourth Valencia International Meeting on Bayesian Statistics. Oxford: Oxford University Press
Geweke, J. (1993), Bayesian treatment of the student-t linear model, Journal of Applied Econometrics 8, S19–S40
Geweke, J (1995), Variable selection and model comparison in regression. Forthcoming in JO Berger, JM Bernardo, AP Dawid, and AFM Smith (eds.), Proceedings of the Fifth Valencia International Meeting on Bayesian Statistics. Also, Research Department Working Paper 539, Federal Reserve Bank of Minneapolis, (1994)
Geweke, J., M. Keane, and D. Runkle (1995), Recursively simulating multinomial multiperiod probit probabilities, American Statistical Association 1994 Proceedings of the Business and Economic Statistics Section, forthcoming
Gourieroux, C., A. Holly, and A. Monfort (1982), Likelihood ratio test, Wald test, and Kuhn-Tucker test in linear models with inequality constraints on the regression parameters, Econometrica 50, 63–80
Hajivassiliou, V., and D. McFadden (1990), The method of simulated scores for the estimation of LDV models with an application to external debt crises. Cowles Foundation Discussion Paper 967, Yale University.
Hajivassiliou, V., D. McFadden, and P. Ruud (1995), Simulation of multivariate normal orthant probabilities: Methods and programs, Journal of Econometrics, forthcoming
Judge, G. G., and T. Takayama (1966), Inequality restrictions in regression analysis, Journal of the American Statistical Association 61, 166–81
Keane, M. (1990), Four essays in empirical macro and labor economics. Ph.D. dissertation, Brown University
Keane, M. (1993), A computationally practical simulation estimator for panel data, Econometrica 62, 95–116
Keane, M. (1994), Simulation estimation for panel data models with limited dependent variables. In G. S. Maddala, C. R. Rao, and H. D. Vinod (eds.), Handbook of Statistics vol. 11, pp. 545–71. Amsterdam: Elsevier Science Publishers
Learner, E., and G. Chamberlain (1976), A Bayesian interpretation of pretesting, Journal of the Royal Statistical Society, Series B, 38, 85–94
Lindley, D. V. (1957), A statistical paradox, Biometrika 44, 187–92
Lovell, M. C., and E. Prescott (1970), Multiple regression with inequality constraints: pretesting bias, hypothesis testing, and efficiency, Journal of the American Statistical Association 65, 913–25
Pindyck, R. S., and D. L. Rubinfeld (1981), Econometric models and economic forecasts. New York: McGraw-Hill
Press, S. J. (1989), Bayesian statistics: Principles, models, and applications. New York: John Wiley
Rao, C.R. (1965), Linear statistical inference and its applications. New York: Wiley
Tierney, L., (1994), Markov chains for exploring posterior distributions, (with discussion and rejoinder), Annals of Statistics, 22: 1701–1762. (Also, School of Statistics Technical Report 560, University of Minnesota, (1991)
Wolak, F. A. (1987), An exact test for multiple inequality and equality constraints in the linear regression model, Journal of the American Statistical Association 82, 782–93
Zellner, A. (1971), An introduction to Bayesian analysis in econometrics. New York: Wiley
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer Science+Business Media New York
About this chapter
Cite this chapter
Geweke, J.F. (1996). Bayesian Inference for Linear Models Subject to Linear Inequality Constraints. In: Lee, J.C., Johnson, W.O., Zellner, A. (eds) Modelling and Prediction Honoring Seymour Geisser. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2414-3_15
Download citation
DOI: https://doi.org/10.1007/978-1-4612-2414-3_15
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7529-9
Online ISBN: 978-1-4612-2414-3
eBook Packages: Springer Book Archive