[Basta-users] Kullback-Leibler divergence interpretation

[Fernando Colchero]

Hi Jelle,

    Well, you could calculate Bayesian p-values, and their interpretation is, roughly, what you calculated. The KLDC values we have in BaSTA show the mean (calibrated) Kullback-Leibler discrepancies (KL) between both distributions. The issue is that KL values are non-symetrical. For example, if you want to determine the amount of overlap between a distribution P and a distribution D, unless they have the same variance, KL(P, D) is not equal to KL(D, P). I am not sure how you calculated the percentage of overlap, but it is likely that you had one side of the overlap, say P with respect to D, but it is possible that values will be different the other way around. 

     I think it is safe to state that your 0.88 and 0.99 values indicate that there is little overlap in the first and almost none in the second, which suggests that both parameters for both groups are different. Still, I understand that it would be handy to have a clear threshold as with traditional p-values. However, if you think about it, such thresholds are somewhat arbitrary and may not apply to a specific system. That is why some Bayesian and even non-Bayesian statisticians prefer to state how likely or how probable is that x and y are related instead of having hard boundaries. 

    I hope that this is helpful. Best,

    Fernando



Fernando Colchero
Assistant Professor
Department of Mathematics and Computer Sciences
Max Planck Odense Center on the Biodemography of Aging

Tlf.               +45 65 50 46 35
Email           colchero at imada.sdu.dk
Web             www.sdu.dk/staff/colchero
Pers. web   www.colchero.com
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University of Southern Denmark





On Feb 14, 2013, at 4:36 PM, Jelle Boonekamp <jjboonekamp at gmail.com> wrote:

> Dear BaSTA users,
> 
> I am wrestling a bit with the interpretation of the Kullback-Leibler metric describing the posterior distributions of model parameters. In my example I get KLDC values of 0.88 and 0.99 for the b0 and b1 Gompertz parameters respectively, when comparing two groups of individuals. If I understood correctly then a value of 1 of this calibrated KLD indicates that there is no overlap between distributions, and a value of 0.5 indicates that they are identical. However, when I calculate by hand the percentage of overlapping (which I think can be interpreted as measure of significance since these posterior values are normally distributed) of both distributions I get 0.24 and 0.066 respectively (KLDC 0.88 and 0.99). I would have thought that at least the distributions with KLDC = 0.99, to show less overlap than what I calculated by hand (0.066). 
> 
> Can someone shed some light on this?
> 
> Best, Jelle
> 
> -- 
> Jelle Boonekamp
> Behavioural Biology
> University of Groningen
> P.O. Box 11103
> 9700 CC Groningen
> The Netherlands
> 
> tel: +31.50.363 7853
> Sent with Sparrow
> 
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