A perspective note on likelihood approximation and inference for complex simulation models using a chain of aggregated normalizing flows
This study addresses the scalability and statistical validity bottlenecks in likelihood approximation and inference for complex simulation models by proposing a novel framework based on aggregated normalizing flow chains. Methodologically, it integrates information-theoretic formalization with sequential decision-making paradigms to construct flexible probability distributions through the sequential optimization of bijective transformation parameters. Furthermore, an empirical likelihood estimator under moment constraints is employed to iteratively update and aggregate the global flow parameters. This research establishes a surrogate model that simultaneously ensures computational feasibility and statistical power, enabling efficient parameter exploration, hypothesis testing, and uncertainty quantification. Ultimately, the proposed approach provides a reliable Bayesian inference solution for complex systems.