# Bayesian hierarchical temporal models

I have been asked recently to transform an already existing Bayesian hierarchical model into an non-stationary model by making the input and the latent variable time dependent(or non stationary). let x be the input that needs to be made time dependent (X vary in time i have some inputs of X at different random times so not really a continuous time series ) $$X\sim Gamma(a,z)$$ and the latent variable is $$k\sim N(X,\sigma)$$

Initially I am an engineer so I have some statistics background. I also understand a bit the basics of Bayesian models (prior etc..) I tried to look for references that can help me but all I can find in papers seems complicated . Can anyone advise me on the matter ?