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On the Dangers of Modelling through Continuous Distributions: A Bayesian Perspective

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  • Fernández, C.
  • Steel, M.F.J.

    (Tilburg University, Center for Economic Research)

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 its empirical relevance is linked to coarse gathering of data, such as rounding. A solution, inspired by the way observations are recorded, is proposed. 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 data set of stock returns.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 1997-05.

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Date of creation: 1997
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Handle: RePEc:dgr:kubcen:199705

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Web page: http://center.uvt.nl

Related research

Keywords: Coarse data; posterior existence; location-scale model; rounding; scale mixtures of normals; skewness; student-t;

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References

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  1. Éric Jacquier & Nicholas G. Polson & Peter E. Rossi, 1999. "Stochastic Volatility: Univariate and Multivariate Extensions," CIRANO Working Papers 99s-26, CIRANO.
  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.
  3. 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.
  4. 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.
  5. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  6. 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.
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