This file is part of IDEAS, which uses RePEc data


[ Papers | Articles | Software | Books | Chapters | Authors | Institutions | JEL Classification | NEP reports | Search | New papers by email | Author registration | Rankings | Volunteers | FAQ | Blog | Help! ]

On the dangers of modelling through continuous distributions: A Bayesian perspective

Author info | Abstract | Publisher info | Download info | Related research | Statistics
Author Info
Carmen Fernandez
M. F. J. Steel

Additional information is available for the following registered author(s):

Abstract

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.

Download Info
To download:

If you experience problems downloading a file, check if you have the proper application to view it first. Information about this may be contained in the File-Format links below. 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.

File URL: http://www2.warwick.ac.uk/fac/sci/statistics/staff/academic/steel/steel_homepage/fs4fi2.ps
File Format: application/postscript
File Function:
Download Restriction: no

Publisher Info
Paper provided by Edinburgh School of Economics, University of Edinburgh in its series ESE Discussion Papers with number 22.

Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Length: 16
Date of creation: Oct 2004
Date of revision:
Handle: RePEc:edn:esedps:22

Contact details of provider:
Postal: 50 George Square, EH8 9JY, Edinburgh
Phone: +44(0)1316508361
Fax: +44(0)1316504514
Web page: http://www.econ.ed.ac.uk/
More information through EDIRC

For technical questions regarding this item, or to correct its listing, contact: (Santiago Sanchez-Pages).

Related research
Keywords: Location-scale model; Rounding; Scale Mixtures of Normals; Skewness; Student-T.;

Other versions of this item:

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.:
  1. 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. [Downloadable!] (restricted)
    Other versions:
  2. Ball, Clifford A, 1988. " Estimation Bias Induced by Discrete Security Prices," Journal of Finance, American Finance Association, vol. 43(4), pages 841-65, September. [Downloadable!] (restricted)
  3. 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.
    Other versions:
  4. Fernandez, C. & Steel, M., 1996. "On Bayesian inference under sampling from scale mixtures of normals," Discussion Paper 2, Tilburg University, Center for Economic Research. [Downloadable!]
  5. 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. [Downloadable!] (restricted)
  6. Fernandez, C. & Steel, M.F.J., 1995. "reference Priors in Non-Normal Location Problems," Papers 9591, Tilburg - Center for Economic Research.
  7. Fernandez, C. & Steel, M.F.J., 1996. "On Bayesian modelling of fat tails and skewness," Discussion Paper 58, Tilburg University, Center for Economic Research. [Downloadable!]
  8. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Blackwell Publishing, vol. 61(2), pages 247-64, April. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, 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.)

  1. Fernandez, C. & Steel, M.F.J., 1997. "Multivariate student-T regression models : pitfalls and inference," Discussion Paper 8, Tilburg University, Center for Economic Research. [Downloadable!]
Statistics
Access and download statistics

Did you know? RePEc also has a blog.

This page was last updated on 2009-12-1.

This information is provided to you by IDEAS at the Department of Economics, College of Liberal Arts and Sciences, University of Connecticut using RePEc data on a server sponsored by the Society for Economic Dynamics.