# Comparison with Marginal Density

**URL:** <https://forum.dynare.org/t/comparison-with-marginal-density/14431>\
**Category:** ML/Bayesian estimation\
**Created:** [6 September 2019 22:44 UTC](https://forum.dynare.org/t/comparison-with-marginal-density/14431 "2019-09-06T22:44:16Z")\
**Posts on this page:** 8\
**Page:** 1

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**Author:** ![mtaherizade](https://forum.dynare.org/letter_avatar_proxy/v4/letter/m/50afbb/32.png) [@mtaherizade](https://forum.dynare.org/u/mtaherizade)\
**Post date:** [6 September 2019 22:44 UTC](https://forum.dynare.org/t/comparison-with-marginal-density/14431/1 "2019-09-06T22:44:16Z")

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Hi,  
To comparing two versions of a dsge model should I consider initial value of the log posterior? I have to subtract it from marginal log-likelihood?

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**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\
**Post date:** [7 September 2019 12:32 UTC](https://forum.dynare.org/t/comparison-with-marginal-density/14431/2 "2019-09-07T12:32:55Z")

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You need to use the marginal data density, not the log posterior.

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**Author:** ![mtaherizade](https://forum.dynare.org/letter_avatar_proxy/v4/letter/m/50afbb/32.png) [@mtaherizade](https://forum.dynare.org/u/mtaherizade)\
**Post date:** [7 September 2019 14:47 UTC](https://forum.dynare.org/t/comparison-with-marginal-density/14431/3 "2019-09-07T14:47:23Z")

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Excuse me, lower marginal density value means better fit?  
What’s the difference between LaplaceApproximation and ModifiedHarmonicMean?

Thank you so much for responding.

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**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\
**Post date:** [8 September 2019 18:23 UTC](https://forum.dynare.org/t/comparison-with-marginal-density/14431/4 "2019-09-08T18:23:46Z")

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The higher the density, the better.  
Please see [Laplace approximation vs. Harmonic Mean Estimator](https://forum.dynare.org/t/laplace-approximation-vs-harmonic-mean-estimator/5178)

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**Author:** ![mtaherizade](https://forum.dynare.org/letter_avatar_proxy/v4/letter/m/50afbb/32.png) [@mtaherizade](https://forum.dynare.org/u/mtaherizade)\
**Post date:** [8 September 2019 18:35 UTC](https://forum.dynare.org/t/comparison-with-marginal-density/14431/5 "2019-09-08T18:35:20Z")

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Thank you very much, sir.

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**Author:** ![mtaherizade](https://forum.dynare.org/letter_avatar_proxy/v4/letter/m/50afbb/32.png) [@mtaherizade](https://forum.dynare.org/u/mtaherizade)\
**Post date:** [8 September 2019 20:59 UTC](https://forum.dynare.org/t/comparison-with-marginal-density/14431/6 "2019-09-08T20:59:14Z")

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Excuse me again, Can i use marginal data density for comparing DSGE-VARs with various lambda too?

Thanks in advance.

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**Author:** ![mtaherizade](https://forum.dynare.org/letter_avatar_proxy/v4/letter/m/50afbb/32.png) [@mtaherizade](https://forum.dynare.org/u/mtaherizade)\
**Post date:** [8 September 2019 21:04 UTC](https://forum.dynare.org/t/comparison-with-marginal-density/14431/7 "2019-09-08T21:04:27Z")

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Sorry, I mean the number oo\_MarginalDensity shows are minus of real value? Marginal data density must be negative or not?

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**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\
**Post date:** [9 September 2019 09:50 UTC](https://forum.dynare.org/t/comparison-with-marginal-density/14431/8 "2019-09-09T09:50:16Z")

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1. I would estimate lambda in this case.
2. It’s the log of a density, so it will be negative whenever the densities are smaller than 1. It’s not the case that it’s minus the density.