BayesianEcosystems_IAP

I am far from an expert on the pros/cons between the two, but with Stan I can do systems of differential equations a lot easier. In some cases, it is infinitely easier. There are some really good examples for Stan on this, and the language structure just handles this easier: https://github.com/gregbritten/BayesianEcosystems_IAP/blob/m... Julia also does better with differential equations in MCMC in general, in my experience compared to pymc3, but it can still be problematic. In some cases, it is most ideal to use the wrapper DiffEqBayes, but it has been somewhat abandoned in support for a neural differential equations package, DiffEqFlux. In some cases if you have a lot of data input, it simply is not possible to use DiffEqBayes. Stan allows for a lot of data input too alongside the system of differential equations, without any issue at a

Stan uses MCMC (specifically NUTS, which is a Hamiltonian Monte Carlo sampler) to optimize parameter fitting, so it can be used for things like ODEs. Here is an example from a class taught last January that uses stan to fit a simple ODE (using the `integrate_ode_rk45` function in stan): https://github.com/gregbritten/BayesianEcosystems_IAP/blob/m...