Reparameterising ODE model: How to incorporate prior information on original parameters?



I recently was able to rewrite my ODE model and simplify it by combining several parameter into a few single parameter.

Since the new parameters don’t bare any direct biological meaning, it is slightly bit tricky to define reasonable priors.

Thus I am wondering: Is there a coherent way of integrating prior knowledge of the “original” parameter into the “new” parameters after re-parametrisation.

Thanks for all your comments already.


Depending on how the parameters are being combined, and how strict you need to be about the actual distribution of the new parameters, you could use the properties of the mean and variance of random variables get some ballpark values for the priors of the new parameters.

If that’s too loos, maybe that can be improved by using a convolution or product of distributions to arrive at a distribution that is formally related to those of the original model.