Complete NNP model (power law or Pareto distribution) #1
Description
We need a better implementation of the power law or Pareto component distribution in the NNP model, which is currently disabled.
Fitting the model while holding the Pareto scale parameter m fixed is straightforward. However, sampling both the power law exponent alpha and the scale parameter m is challenging.
The problem is that we cannot use the model's gradient information in Hamiltonian MCMC samplers like NUTS. Scale-free samplers like DEMetropolisZ or DEMetropolis (multi-processing) also did not work well. I also tried sequential Monte Carlo (simulated annealing), which worked somewhat better.
I believe we need to re-parametrise the model in terms of log quantities, allowing us to switch from a Pareto distribution to an Exponential distribution.
This will take some effort.