Trying it out of the box on an HPC led to, at best, 6 hours of running for a single chain, and, at worst, 384 hours, again, for a single chain, depending on the synthetic data used. My likelihood function requires arbitrary precision and utilizes the higher-order chain rule a la Faa Di Bruno, which necessitates many operations even with using lookup tables because very very high derivatives are necessary in just the likelihood calculation. Because of that, all calculations are very precious and time consuming. Giving NUTS even a slightly perturbed ML-esimtated start position should lead it into a better direction hopefully. I anticipate with real data, the time could be much longer. Thank you so much for your remarks! I appreciate it. My other option is, instead, to code up the likelihood function in C++ and have NUTS call that function.
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