I was wondering if there is an option in DiffEqBayes.jl or another package to make MCMC parameter estimation that fits one of the variables as a function of the other, rather than the time series of each.

Let’s say I have a system that looks like this:

dx/dt = αx - βx

dy/dt = γx + ηy

But my observational dataset is y(x). Is there a way to use it for the parameter estimation of the ODE? (I know it’s unintuitive since there is an underlying assumption that y and x are independent, however, this is the only type of data I have)