Reference Priors for the General Location-Scale Model

C. Fernández, M.F.J. Steel

Research output: Working paperDiscussion paperOther research output

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Abstract

The reference prior algorithm (Berger and Bernardo 1992) is applied to multivariate location-scale models with any regular sampling density, where we establish the irrelevance of the usual assumption of Normal sampling if our interest is in either the location or the scale. This result immediately extends to the linear regression model. On the other hand, an essentially arbitrary step in the reference prior algorithm, namely the choice of the nested sequence of sets in the parameter space is seen to play a role. Our results lend an additional motivation to the often used prior proportional to the inverse of the scale parameter, as it is found to be both the independence Jeffreys' prior and the reference prior under variation independence in the sequence of sets, for any choice of the sampling density. However, if our parameter of interest is not a one-to-one transformation of either location or scale, the choice of the sampling density is generally shown to intervene.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages10
Volume1997-105
Publication statusPublished - 1997

Publication series

NameCentER Discussion Paper
Volume1997-105

Fingerprint

Location-scale Model
Reference Prior
Jeffreys Prior
Multivariate Models
Scale Parameter
Linear Regression Model
Immediately
Parameter Space
Directly proportional
Arbitrary
Independence

Keywords

  • Jeffreys' prior
  • multivariate regression model
  • posterior existence
  • scale mixture of normals

Cite this

Fernández, C., & Steel, M. F. J. (1997). Reference Priors for the General Location-Scale Model. (CentER Discussion Paper; Vol. 1997-105). Tilburg: Econometrics.
Fernández, C. ; Steel, M.F.J. / Reference Priors for the General Location-Scale Model. Tilburg : Econometrics, 1997. (CentER Discussion Paper).
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Fernández, C & Steel, MFJ 1997 'Reference Priors for the General Location-Scale Model' CentER Discussion Paper, vol. 1997-105, Econometrics, Tilburg.

Reference Priors for the General Location-Scale Model. / Fernández, C.; Steel, M.F.J.

Tilburg : Econometrics, 1997. (CentER Discussion Paper; Vol. 1997-105).

Research output: Working paperDiscussion paperOther research output

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AB - The reference prior algorithm (Berger and Bernardo 1992) is applied to multivariate location-scale models with any regular sampling density, where we establish the irrelevance of the usual assumption of Normal sampling if our interest is in either the location or the scale. This result immediately extends to the linear regression model. On the other hand, an essentially arbitrary step in the reference prior algorithm, namely the choice of the nested sequence of sets in the parameter space is seen to play a role. Our results lend an additional motivation to the often used prior proportional to the inverse of the scale parameter, as it is found to be both the independence Jeffreys' prior and the reference prior under variation independence in the sequence of sets, for any choice of the sampling density. However, if our parameter of interest is not a one-to-one transformation of either location or scale, the choice of the sampling density is generally shown to intervene.

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Fernández C, Steel MFJ. Reference Priors for the General Location-Scale Model. Tilburg: Econometrics. 1997. (CentER Discussion Paper).