An MCMC-ABC practical model identification statistical optimiser software – Python implementation, preparation for commercial software development

The main aim of the study is to develop a systematic method to refine priors for non-linear error propagation in Bayesian PMI. A systematic method to refine priors for non-linear error propagation using machine-learning-enhanced Approximate Bayesian Computational (ABC) tool was developed by a subset of applicants [Mukherjee & Plosz, 2021, Proc. IWA-WRRmod2020, 1-7; Plosz et al., 2020, Water Res. 184, 116129]. In contrast to the ABC, Markov Chain Monte Carlo (MCMC) methods can produce asymptotically exact posterior samples of the parameters. A methodology based on tensor-train-driven transport maps and MCMC that allows an accurate approximation of the posterior was developed by another subset of applicants [Dolgov et al., 2022, FoCM 22, 1863].
A combination of the ABC and MCMC methods is being researched by the two applicants using Matlab implementations.