I have seen several examples of people performing bayesian linear regression in python packages such as stan or pymc3 where they have the parameters/distributions as exponents w.r.t the variables.
def transform(x, ec, slope): return 1 / (1 + (x / ec)**(-slope))
Where slope follows lets say an normal distribution with some mean and sd. This is clearly not linear w.r.t to the parameters and i am wondering how it is possible that we can derive the posterior from this since bayesian linear regression assumes linearity w.r.t to parameters?
I have clearly missed an vital and basic part of bayesian linear regression.
Can someone point it out?