MultiBUGS VS paramonte

Oberon is awesome. I typically use a variant of it called Component Pascal. It is a very esoteric, and quite unique language.

My usage of it is in WinBUGS/OpenBUGS/MultiBUGS [1], for Markov chain Monte Carlo statistical analysis. It's really cool and works amazingly well for systems of differential equations too.

The version I recommend using is MultiBUGS [2]. I would avoid installing it in Windows, though!

[1] https://www.mrc-bsu.cam.ac.uk/software/bugs/

[2] https://github.com/MultiBUGS/MultiBUGS

The ParaMonte Machine Learning library is an actively developed package in Fortran 2018 standard. The next release of the package contains about a million lines of Fortran (along with other languages). There are many more Fortran libraries, mostly in the Aerospace, Geology, Astronomy, Civil Engineering, and Petroleum industry and academia. Many electronic structure, nuclear, and plasma physics packages have been and are still developed in Fortran. Ask this question on the Fortran Community Discourse to get a more comprehensive list of current Fortran packages.

Bayesian modeling is at the heart of scientific inference and uncertainty quantification. Whether the industry uses it or not, does not devalue this important approach. If they do not then it is likely that they have not yet realized its significance. But I suspect many do, in collaboration with Academia and they typically use their own specialized high-performance tools for such inferences since their models are far more complex than things that could be implemented via such high-level probabilistic programming languages as pymc3. Incidentally, our lab has developed (and is still developing) a High-Performance serial/parallel package for sampling and integration of Bayesian posteriors which is available from multiple programming languages including C/C++/Fortran/Python/MATLAB/...: https://github.com/cdslaborg/paramonte

https://github.com/cdslaborg/paramonte/blob/e3087ef9c9b13c53c5298e4abea2bcb5043ab8af/src/kernel/Integration_mod.f90#L108

Can you provide more information about your data? How many dimensions? 1D? Also, could you elaborate on what you mean by fitting a Gaussian to the time series data? Do you mean a Gaussian process? My lab has written a fast generic Bayesian optimizer and sampler library, in pure modern Fortran, that can not only find the best-fit parameters of your time-series model (whether polynomial, sin, ...), but can also put constraints on the uncertainties associated with the parameters. Writing a generic likelihood function for polynomial or other types of fits is quite easy. Once you write it, you simply compile and link it with this library to find the best-fit parameters of each model. The prebuilt ready-to-use versions of the library are also available on the GitHub release page.I would be happy to help you further with writing the polynomial/sin models and fitting them to your data with this library. But some further information is needed from your side to write the objective functions for different models (poly, sin, ...).