Exploration of nonlinear parallel heterogeneous reaction pathways through Bayesian variable selection

Abstract Inversion is a key method for extracting nonlinear dynamics governed by heterogeneous reaction that occur in parallel in the natural sciences. Therefore, in this study, we propose a Bayesian statistical framework to determine the active reaction pathways using only the noisy observable spatial distribution of the solid phase. In this method, active reaction pathways were explored using a Widely Applicable Bayesian Information Criterion (WBIC), which is used to select models within the framework of Bayesian inference. Plausible reaction mechanisms were determined by maximizing the posterior distribution. This conditional probability is obtained through Markov chain Monte Carlo simulations. The efficiency of the proposed method is then determined using simulated spatial data of the solid phase. The results show that active reaction pathways can be identified from the redundant candidates of reaction pathways. After these redundant reaction pathways were excluded, the controlling factor of the reaction dynamics was estimated with high accuracy. Graphic Abstract