Compare posterior distribution across different models

General
1

Hello!
I recently came across this post about calculating similarity between two posterior distributions:

and was wondering, if the provided solutions (estimate degree of overlap/ probability of superiority) would be an option for posterior distributions from DIFFERENT models as well.

Model 1: probability of a bird species being active during day, night, twilight during summer
Model 2: same species, same time periods, but during spring

Unfortunately, the raw data from spring are not available anymore for one particular species, so running one joint model with summer and spring data is not an option. But, I have the posterior samples of spring and summer separately. Priors were the same for both models in case that matters.

Now could I for example compare day activity summer vs day activity spring by estimating overlap of the posterior distributions or is this a absolute no go, because the distributions come from two different models?
If the mentioned solutions do not work, would there be others that might?

Any thought on this would really help!
Thanks in advance!

Kate

format_code(like_this, if_applicable)

If you need to use math formula, use Latex syntax:

Y \sim N(\mu, \sigma)

Don’t forget to attach tags (top right of this form) for application area/class of models or other general subject areas your topic touches on.

2

From what you describe you don’t seem to have different models, but the same model with different data, is that right?

Also, I’d say your main interest is in the model parameters, which say something about the ecology you are interested in, so you can see the difference between these parameters in each case.

In the case where you actually have different models, but the same data, you can (and should) still look at the parameters of interest, but presumably you added some parameters of somewhat less interest, and you’d need to check how that affects the overall fit using LOO or WAIC.

If you have different data and models, I’d say that would be very difficult to compare.