High fidelity mathematical model building with experimental data: A Bayesian approach

摘要: Abstract Mathematical models of physicochemical systems are usually built in an iterative fashion during the course experimental investigation. In this paper, a novel Bayesian approach to model building is presented. This now feasible because breakthroughs Monte Carlo sampling procedures and high performance computing, that make it possible deal directly with nonlinear mathematical themselves instead their linear approximations. By including error for data, further use statistical concepts test given adequacy against data prior knowledge, place realistic confidence limits on resulting parameters. paper work flow takes advantage these recent advances enable fidelity modeling proposed. A set parameters needed initiate process. Probability distributions based available quantitative subjective information must also be supplied. Finally, describing heteroscedasticity along probability generated from exploratory data. Then experiments designed collected. Using Bayes’ theorem, (MC) or Markov Chain (MCMC) methods used generate sequence samples parameter values each postulated model. These sets then discriminate among using criteria introduced paper. Once discrimination achieved, global lack fit determine adequacy. After single adequate selected, highest density (HPD) intervals determined individual HPD regions constructed all pairs. Experiments reduce uncertainty joint posterior regions. procedure described properly represent uncertainties predictions made The proposed demonstrated by illustrative problem where three simple discriminated most suitable ones estimated rigorously.