  Varying coefficient models are useful in applications where the effect of the
covariate might depend on some other covariate such as time or location.
Various applications of these models often give rise to case-specific prior
distributions for the parameter(s) describing how much the coefficients vary.
In this work, we introduce a unified view of varying coefficients models,
arguing for a way of specifying these prior distributions that are coherent
across various applications, avoid overfitting and have a coherent
interpretation. We do this by considering varying coefficients models as a
flexible extension of the natural simpler model and capitalising on the
recently proposed framework of penalized complexity (PC) priors. We illustrate
our approach in two spatial examples where varying coefficient models are
relevant.
