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Abstract

Model comparison and selection is an important
problem in many model-based signal processing applications.
Often, very simple information criteria such as the Akaike
information criterion or the Bayesian information criterion are
used despite their shortcomings. Compared to these methods,
Djuric’s asymptotic MAP rule was an improvement, and in this
paper we extend the work by Djuric in several ways. Specifically,
we consider the elicitation of proper prior distributions, treat
the case of real- and complex-valued data simultaneously in
a Bayesian framework similar to that considered by Djuric,
and develop new model selection rules for a regression model
containing both linear and non-linear parameters. Moreover,
we use this framework to give a new interpretation of the
popular information criteria and relate their performance to the
signal-to-noise ratio of the data. By use of simulations, we also
demonstrate that our proposed model comparison and selection
rules outperform the traditional information criteria both in
terms of detecting the true model and in terms of predicting
unobserved data. The simulation code is available online.
Original languageEnglish
JournalI E E E Transactions on Signal Processing
Volume62
Issue number1
Pages (from-to)225-238
Number of pages14
ISSN1053-587X
DOIs
Publication statusPublished - 1 Jan 2014

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Signal processing

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@article{9b7ccd660f96463f839dc0c19cf6367d,
title = "Bayesian Model Comparison With the g-Prior",
abstract = "Model comparison and selection is an importantproblem in many model-based signal processing applications.Often, very simple information criteria such as the Akaikeinformation criterion or the Bayesian information criterion areused despite their shortcomings. Compared to these methods,Djuric’s asymptotic MAP rule was an improvement, and in thispaper we extend the work by Djuric in several ways. Specifically,we consider the elicitation of proper prior distributions, treatthe case of real- and complex-valued data simultaneously ina Bayesian framework similar to that considered by Djuric,and develop new model selection rules for a regression modelcontaining both linear and non-linear parameters. Moreover,we use this framework to give a new interpretation of thepopular information criteria and relate their performance to thesignal-to-noise ratio of the data. By use of simulations, we alsodemonstrate that our proposed model comparison and selectionrules outperform the traditional information criteria both interms of detecting the true model and in terms of predictingunobserved data. The simulation code is available online.",
author = "Nielsen, {Jesper Kj{\ae}r} and Christensen, {Mads Gr{\ae}sb{\o}ll} and Cemgil, {Ali Taylan} and Jensen, {S{\o}ren Holdt}",
year = "2014",
month = "1",
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doi = "10.1109/TSP.2013.2286776",
language = "English",
volume = "62",
pages = "225--238",
journal = "I E E E Transactions on Signal Processing",
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}

Bayesian Model Comparison With the g-Prior. / Nielsen, Jesper Kjær; Christensen, Mads Græsbøll; Cemgil, Ali Taylan; Jensen, Søren Holdt.

In: I E E E Transactions on Signal Processing, Vol. 62, No. 1, 01.01.2014, p. 225-238.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Bayesian Model Comparison With the g-Prior

AU - Nielsen, Jesper Kjær

AU - Christensen, Mads Græsbøll

AU - Cemgil, Ali Taylan

AU - Jensen, Søren Holdt

PY - 2014/1/1

Y1 - 2014/1/1

N2 - Model comparison and selection is an importantproblem in many model-based signal processing applications.Often, very simple information criteria such as the Akaikeinformation criterion or the Bayesian information criterion areused despite their shortcomings. Compared to these methods,Djuric’s asymptotic MAP rule was an improvement, and in thispaper we extend the work by Djuric in several ways. Specifically,we consider the elicitation of proper prior distributions, treatthe case of real- and complex-valued data simultaneously ina Bayesian framework similar to that considered by Djuric,and develop new model selection rules for a regression modelcontaining both linear and non-linear parameters. Moreover,we use this framework to give a new interpretation of thepopular information criteria and relate their performance to thesignal-to-noise ratio of the data. By use of simulations, we alsodemonstrate that our proposed model comparison and selectionrules outperform the traditional information criteria both interms of detecting the true model and in terms of predictingunobserved data. The simulation code is available online.

AB - Model comparison and selection is an importantproblem in many model-based signal processing applications.Often, very simple information criteria such as the Akaikeinformation criterion or the Bayesian information criterion areused despite their shortcomings. Compared to these methods,Djuric’s asymptotic MAP rule was an improvement, and in thispaper we extend the work by Djuric in several ways. Specifically,we consider the elicitation of proper prior distributions, treatthe case of real- and complex-valued data simultaneously ina Bayesian framework similar to that considered by Djuric,and develop new model selection rules for a regression modelcontaining both linear and non-linear parameters. Moreover,we use this framework to give a new interpretation of thepopular information criteria and relate their performance to thesignal-to-noise ratio of the data. By use of simulations, we alsodemonstrate that our proposed model comparison and selectionrules outperform the traditional information criteria both interms of detecting the true model and in terms of predictingunobserved data. The simulation code is available online.

U2 - 10.1109/TSP.2013.2286776

DO - 10.1109/TSP.2013.2286776

M3 - Journal article

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SP - 225

EP - 238

JO - I E E E Transactions on Signal Processing

JF - I E E E Transactions on Signal Processing

SN - 1053-587X

IS - 1

ER -