### Abstract

Original language | English |
---|---|

Place of Publication | Tilburg |

Publisher | Econometrics |

Number of pages | 24 |

Volume | 1997-05 |

Publication status | Published - 1997 |

### Publication series

Name | CentER Discussion Paper |
---|---|

Volume | 1997-05 |

### Fingerprint

### Keywords

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

### Cite this

*On the Dangers of Modelling through Continuous Distributions: A Bayesian Perspective*. (CentER Discussion Paper; Vol. 1997-05). Tilburg: Econometrics.

}

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

Research output: Working paper › Discussion paper › Other 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

PY - 1997

Y1 - 1997

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

KW - posterior existence

KW - location-scale model

KW - rounding

KW - scale mixtures of normals

KW - skewness

KW - student-t

M3 - Discussion paper

VL - 1997-05

T3 - CentER Discussion Paper

BT - On the Dangers of Modelling through Continuous Distributions

PB - Econometrics

CY - Tilburg

ER -