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I have written a Bayesian model in JAGS that I use to calculate the growth rates of several plant populations as well as their variance while taking into account the observation error during the sampling process. It works well and now I would like to test if those growth rates differ between populations in different habitats or with different conservation status. So far I have used the median of the posterior distributions as a point estimate for the growth rate and variance of each population but I feel that I am loosing a lot of useful information by not considering the whole posterior distribution of those parameters. So, is it correct if I use all or all values from the posterior distributions in other analysis like ANOVA?

Edit for context and clarity: My objective is to calculate the growth rates and the variance of those growth rates for about 300 plant populations. My data is the annual count of individuals, so I have one value for each year and population. In addition, and this is really the part that interest me more and the reason for using Bayesian inference, I have measured the observation error en each of those populations by counting twice some years. I am using the variance between each count as a measure of that observation error. This forces me to run the model separately for each population, so I end up with 300 different model results, each one with its own posteriors for the growth rate and its variance. So far, this works as intended, but now I would like to test if there are differences in those growth rates between populations living in different habitats, for example, those living in grasslands vs forests. So far what I have tried doing was taking the median of each posterior as a point estimate for that parameter and compare it between habitats using frequentist ANOVA but I am aware that by doing this I am loosing a lot of the information that I get from the Bayesian approach so I was thinking about using the whole posterior, or maybe just a few thousand samples from it as the data for that ANOVA.

Héctor Miranda
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  • From what I understand you're trying to use your posterior as a new quasi-prior in (the next step of) your analysis. In that case you might want to consider approximating the posterior with a Gaussian around the MAP. Also, it's just a hunch, but I think you've been using the mode rather than the median of your posterior so far (which aren't necessarily identical). – Durden Jul 20 '23 at 15:29
  • Thanks for the comment. I want to use the results from the model, in this case the individual growth rate of each population, in another test, but it doesn't have to be Bayesian so I wouldn't use it as a prior. I just want to test if those growth rates differ between habitats but I don't want to loose the information that I get from the posterior if I use a point estimate. – Héctor Miranda Jul 21 '23 at 10:57

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You could, but keep in mind that the errors would propagate, so each new model you stack adds to the uncertainty of the end result. But why would you do that? Your description lacks details, but it sounds as if you could achieve the same thing by either directly using the results you have or modifying the model to give you the result that you want. If you want to compare growth rates estimated by the model between groups, you can simply look at the overlap between posterior distributions of the estimates to get your answer directly. The simplest approach possible would be to plot the distributions of the predicted growth rates between the groups (e.g. kernel densities plotted with different colors per group), but you may also take a more formal approach and calculate some kind of Bayesian $p$-values.

Tim
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  • Thanks for the answer Tim. What do you mean by directly using the results that I have? I have thought about modifying the model because right now I estimate each population's growth rate separately but I am not sure if it would work, specially since each population has different observation error. – Héctor Miranda Jul 20 '23 at 09:05
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    @HéctorMiranda if you are estimating the models separately, you still can plot each group, or look at some statistics, like overlaps between posterior quantiles between groups. – Tim Jul 20 '23 at 09:09