Define distribution functional constraints

[nhuurre]

@mssaw

I want to sample 8 parameters (say theta) where other 4 (say phi) are defined by functional constraints which depend on theta parameters. All parameters have to be positive as they represent some biological processes. Some of them have to by less then 1.

So your parameter space is an 8-dimensional submanifold of 12-dimensional space, defined by 4 equations and more than 12 inequalities. That’s sounds quite difficult geometry. There’s no general solution, we’ll need to see the exact functional constraints.

But regardless of that, ODE system with more than 30 equations is going to perform super slow no matter how it’s parametrized. See this earlier thread.

Costs/benefits of solving large ODE systems as systems of difference equations/in discrete time

I have been working with large systems of ordinary differential equations in a systems modelling context, similar to the ‘system dynamics’ literature of Jay Forrester, John Sterman et al. System dynamics models often include a large number of ODEs (20+ is not uncommon) and parameters, and data for some of the state variables may never be available/have a high proportion of missingness. For example, see the C-ROADS model (https://www.climateinteractive.org/tools/c-roads/). Solving large systems …