On the dangers of modelling through continuous distributions: A Bayesian perspective
AbstractWe point out that Bayesian inference on the basis of a given sample is not always possible with continuous sampling models, even under a proper prior. The reason for this paradoxical situation is explained, and linked to the fact that any dataset consisting of point observations has zero probability under a continuous sampling distribution. A number of examples, both with proper and improper priors, highlight the issues involved. A solution is proposed through the use of set observations, which take into account the precision with which the data were recorded. Use of a Gibbs sampler makes the solution practically feasible. The case of independent sampling from (possibly skewed) scale mixtures of Normals is analysed in detail for a location-scale model with a commonly used noninformative prior. For Student-t sampling with unrestricted degrees of freedom the usual inference, based on point observations, is shown to be precluded whenever the sample contains repeated observations. We show that Bayesian inference based on set observations, however, is possible and illustrate this by an application to a skewed dataset of stock returns.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Edinburgh School of Economics, University of Edinburgh in its series ESE Discussion Papers with number 22.
Date of creation: Oct 2004
Date of revision:
Location-scale model; Rounding; Scale Mixtures of Normals; Skewness; Student-T.;
Other versions of this item:
- Fernández, C. & Steel, M.F.J., 1997. "On the Dangers of Modelling through Continuous Distributions: A Bayesian Perspective," Discussion Paper 1997-05, Tilburg University, Center for Economic Research.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994.
"Multivariate Stochastic Variance Models,"
Review of Economic Studies,
Wiley Blackwell, vol. 61(2), pages 247-64, April.
- Tom Doan, . "RATS programs to estimate multivariate stochastic volatility models," Statistical Software Components RTZ00093, Boston College Department of Economics.
- Eric Jacquier & Nicholas G. Polson & Peter Rossi, .
"Stochastic Volatility: Univariate and Multivariate Extensions,"
Rodney L. White Center for Financial Research Working Papers
19-95, Wharton School Rodney L. White Center for Financial Research.
- Eric Jacquier & Nicholas G. Polson & Peter Rossi, 1999. "Stochastic Volatility: Univariate and Multivariate Extensions," Computing in Economics and Finance 1999 112, Society for Computational Economics.
- Éric Jacquier & Nicholas G. Polson & Peter E. Rossi, 1999. "Stochastic Volatility: Univariate and Multivariate Extensions," CIRANO Working Papers 99s-26, CIRANO.
- Hausman, Jerry A. & Lo, Andrew W. & MacKinlay, Archie Craig, 1955-, 1990.
"An ordered probit analysis of transaction stock prices,"
3234-90., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Hausman, Jerry A. & Lo, Andrew W. & MacKinlay, A. Craig, 1992. "An ordered probit analysis of transaction stock prices," Journal of Financial Economics, Elsevier, vol. 31(3), pages 319-379, June.
- Hausman, J.A. & Lo, A.W. & MacKinlay, A.C., 1991. "An Ordered Probit Analysis of Transaction Stock Prices," Weiss Center Working Papers 26-91, Wharton School - Weiss Center for International Financial Research.
- Jerry A. Hausman & Andrew W. Lo & A. Craig MacKinlay, 1991. "An Ordered Probit Analysis of Transaction Stock Prices," NBER Working Papers 3888, National Bureau of Economic Research, Inc.
- Ball, Clifford A, 1988. " Estimation Bias Induced by Discrete Security Prices," Journal of Finance, American Finance Association, vol. 43(4), pages 841-65, September.
- Fernández, C. & Steel, M.F.J., 1996. "On Bayesian Inference under Sampling from Scale Mixtures of Normals," Discussion Paper 1996-02, Tilburg University, Center for Economic Research.
- Roberts, G. O. & Smith, A. F. M., 1994. "Simple conditions for the convergence of the Gibbs sampler and Metropolis-Hastings algorithms," Stochastic Processes and their Applications, Elsevier, vol. 49(2), pages 207-216, February.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Gina Reddie).
If references are entirely missing, you can add them using this form.