My model is y=a+bx_1+cx_2, when i used prior distributions a\sim N(0,10), b\sim N(0,10), c\sim N(0,10), the result of modelling is acceptable. Now my changed model is y=a+bx_1+c\frac{\lambda^{x_2}}{x_2 !}e^{-\lambda}, and my question is what prior distributions for c and \lambda could be better?

I think the current recommendation is to do prior prediction checks. Just put normals on things unless you have a reason to do something else, make predictions from the model without data, and try to at least get everything on the right scale.

Here’s a video from one of the Stancon’s concerning this: https://www.youtube.com/watch?v=ZRpo41l02KQ&feature=youtu.be&t=2694

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ok, i will try, thank you a lot.

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There’s also the prior choice wiki.

Your model won’t be identified because c \cdot e^{-\lambda} shows up as a regression coefficient on \lambda^{x_2}. The posterior will only be proper with priors on c and \lambda, but it’d be better to reformulate the model to be identifiable.