On the Dangers of Modelling through Continuous Distributions

A Bayesian Perspective

C. Fernández, M.F.J. Steel

Research output: Working paperDiscussion paperOther research output

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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.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages24
Volume1997-05
Publication statusPublished - 1997

Publication series

NameCentER Discussion Paper
Volume1997-05

Fingerprint

sampling
modeling
sampler
student
distribution
freedom

Keywords

  • Coarse data
  • posterior existence
  • location-scale model
  • rounding
  • scale mixtures of normals
  • skewness
  • student-t

Cite this

Fernández, C., & Steel, M. F. J. (1997). On the Dangers of Modelling through Continuous Distributions: A Bayesian Perspective. (CentER Discussion Paper; Vol. 1997-05). Tilburg: Econometrics.
Fernández, C. ; Steel, M.F.J. / On the Dangers of Modelling through Continuous Distributions : A Bayesian Perspective. Tilburg : Econometrics, 1997. (CentER Discussion Paper).
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Fernández, C & Steel, MFJ 1997 'On the Dangers of Modelling through Continuous Distributions: A Bayesian Perspective' CentER Discussion Paper, vol. 1997-05, Econometrics, Tilburg.

On the Dangers of Modelling through Continuous Distributions : A Bayesian Perspective. / Fernández, C.; Steel, M.F.J.

Tilburg : Econometrics, 1997. (CentER Discussion Paper; Vol. 1997-05).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - On the Dangers of Modelling through Continuous Distributions

T2 - A Bayesian Perspective

AU - Fernández, C.

AU - Steel, M.F.J.

N1 - Pagination: 24

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N2 - 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.

AB - 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.

KW - Coarse data

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KW - location-scale model

KW - rounding

KW - scale mixtures of normals

KW - skewness

KW - student-t

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VL - 1997-05

T3 - CentER Discussion Paper

BT - On the Dangers of Modelling through Continuous Distributions

PB - Econometrics

CY - Tilburg

ER -

Fernández C, Steel MFJ. On the Dangers of Modelling through Continuous Distributions: A Bayesian Perspective. Tilburg: Econometrics. 1997. (CentER Discussion Paper).