Having problems defining random function for custom distribution with mixture of observed and random variables

Thanks for your answer @junpenglao. The problem I am trying to solve is to predict alpha and beta given a set of covariates. Also, it is essential to predict alpha and beta separately as one is proportional to fitness of individual at t=0 and beta is related to “aging” rate of the individual (i.e., the rate at which fitness reduces with time). Ideally, I would like to have both alpha and beta individually rather than just alpha + beta*time.

Is there no way to do this with pymc? In general, it would be great to have a few examples of how random function is written for custom functions within pymc (or maybe I just haven’t found them). For example, could I make logalpha and beta observed but make all of it missing values?

Again, thanks in advance.