An in-depth look at highest posterior model selection

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We consider the properties of the highest posterior probability model in a linear regression setting. Under a spike and slab hierarchy we find that although highest posterior model selection is total risk consistent, it possesses hidden undesirable properties. One such property is a marked underfitting in finite samples, a phenomenon well noted for Bayesian information criterion (BIC) related procedures but not often associated with highest posterior model selection. Another concern is the substantial effect the prior has on model selection. We employ a rescaling of the hierarchy and show that the resulting rescaled spike and slab models mitigate the effects of underfitting because of a perfect cancellation of a BIC-like penalty term. Furthermore, by drawing upon an equivalence between the highest posterior model and the median model, we find that the effect of the prior is less influential on model selection, as long as the underlying true model is sparse. Nonsparse settings are, however, problematic. Using the posterior mean for variable selection instead of posterior inclusion probabilities avoids these issues.

Original languageEnglish
Pages (from-to)377-403
Number of pages27
JournalEconometric Theory
Volume24
Issue number2
DOIs
StatePublished - Apr 1 2008
Externally publishedYes

Fingerprint

Model selection
equivalence
penalty
inclusion
Bayesian information criterion
regression
Rescaling
Total risk
Finite sample
Cancellation
Variable selection
Penalty
Median
Posterior probability
Equivalence
Linear regression
Probability model
Inclusion

ASJC Scopus subject areas

  • Economics and Econometrics
  • Social Sciences (miscellaneous)

Cite this

An in-depth look at highest posterior model selection. / Dey, Tanujit; Ishwaran, Hemant; Rao, Jonnagadda S.

In: Econometric Theory, Vol. 24, No. 2, 01.04.2008, p. 377-403.

Research output: Contribution to journalArticle

@article{f72aa11aa143449fb58828f6f82c7fd7,
title = "An in-depth look at highest posterior model selection",
abstract = "We consider the properties of the highest posterior probability model in a linear regression setting. Under a spike and slab hierarchy we find that although highest posterior model selection is total risk consistent, it possesses hidden undesirable properties. One such property is a marked underfitting in finite samples, a phenomenon well noted for Bayesian information criterion (BIC) related procedures but not often associated with highest posterior model selection. Another concern is the substantial effect the prior has on model selection. We employ a rescaling of the hierarchy and show that the resulting rescaled spike and slab models mitigate the effects of underfitting because of a perfect cancellation of a BIC-like penalty term. Furthermore, by drawing upon an equivalence between the highest posterior model and the median model, we find that the effect of the prior is less influential on model selection, as long as the underlying true model is sparse. Nonsparse settings are, however, problematic. Using the posterior mean for variable selection instead of posterior inclusion probabilities avoids these issues.",
author = "Tanujit Dey and Hemant Ishwaran and Rao, {Jonnagadda S}",
year = "2008",
month = "4",
day = "1",
doi = "10.1017/S026646660808016X",
language = "English",
volume = "24",
pages = "377--403",
journal = "Econometric Theory",
issn = "0266-4666",
publisher = "Cambridge University Press",
number = "2",

}

TY - JOUR

T1 - An in-depth look at highest posterior model selection

AU - Dey, Tanujit

AU - Ishwaran, Hemant

AU - Rao, Jonnagadda S

PY - 2008/4/1

Y1 - 2008/4/1

N2 - We consider the properties of the highest posterior probability model in a linear regression setting. Under a spike and slab hierarchy we find that although highest posterior model selection is total risk consistent, it possesses hidden undesirable properties. One such property is a marked underfitting in finite samples, a phenomenon well noted for Bayesian information criterion (BIC) related procedures but not often associated with highest posterior model selection. Another concern is the substantial effect the prior has on model selection. We employ a rescaling of the hierarchy and show that the resulting rescaled spike and slab models mitigate the effects of underfitting because of a perfect cancellation of a BIC-like penalty term. Furthermore, by drawing upon an equivalence between the highest posterior model and the median model, we find that the effect of the prior is less influential on model selection, as long as the underlying true model is sparse. Nonsparse settings are, however, problematic. Using the posterior mean for variable selection instead of posterior inclusion probabilities avoids these issues.

AB - We consider the properties of the highest posterior probability model in a linear regression setting. Under a spike and slab hierarchy we find that although highest posterior model selection is total risk consistent, it possesses hidden undesirable properties. One such property is a marked underfitting in finite samples, a phenomenon well noted for Bayesian information criterion (BIC) related procedures but not often associated with highest posterior model selection. Another concern is the substantial effect the prior has on model selection. We employ a rescaling of the hierarchy and show that the resulting rescaled spike and slab models mitigate the effects of underfitting because of a perfect cancellation of a BIC-like penalty term. Furthermore, by drawing upon an equivalence between the highest posterior model and the median model, we find that the effect of the prior is less influential on model selection, as long as the underlying true model is sparse. Nonsparse settings are, however, problematic. Using the posterior mean for variable selection instead of posterior inclusion probabilities avoids these issues.

UR - http://www.scopus.com/inward/record.url?scp=39649116697&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=39649116697&partnerID=8YFLogxK

U2 - 10.1017/S026646660808016X

DO - 10.1017/S026646660808016X

M3 - Article

VL - 24

SP - 377

EP - 403

JO - Econometric Theory

JF - Econometric Theory

SN - 0266-4666

IS - 2

ER -