On the dangers of modelling through continuous distributions: A Bayesian perspective
We 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.
|Date of creation:||1998|
|Date of revision:|
|Contact details of provider:|| Postal: |
Web page: http://www.econ.ed.ac.uk/
More information through EDIRC
References listed on IDEAS
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.:
- 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.
- Geweke, J, 1993. "Bayesian Treatment of the Independent Student- t Linear Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S19-40, Suppl. De.
- 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.
- Fernandez, C. & Steel, M.F.J., 1995.
"reference Priors in Non-Normal Location Problems,"
9591, Tilburg - Center for Economic 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.
- 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.
- Éric Jacquier & Nicholas G. Polson & Peter E. Rossi, 1999. "Stochastic Volatility: Univariate and Multivariate Extensions," CIRANO Working Papers 99s-26, CIRANO.
- Ball, Clifford A, 1988. " Estimation Bias Induced by Discrete Security Prices," Journal of Finance, American Finance Association, vol. 43(4), pages 841-65, September.
- 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.
- 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, Jerry A. & Lo, Andrew W. & MacKinlay, Archie Craig, 1955-, 1990. "An ordered probit analysis of transaction stock prices," Working papers 3234-90., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- 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.
When requesting a correction, please mention this item's handle: RePEc:edn:esedps:22. See general information about how to correct material in RePEc.
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.