Bayesian model updating method removes sampling noise for faster inference
A Bayesian Model Updating Framework for Systems Under Hybrid Uncertainties via Probability Integral Transform and Maximum Mean Discrepancy
Computational Engineering, Finance, and Science
Summary
Updating models with uncertain inputs is tricky because results are not fixed numbers but probabilities, making exact calculations very hard. The authors propose a new technique that transforms random outputs into fixed ones, avoiding extra random errors in the calculations. This approach uses known math tools to speed up and improve how we estimate model parameters and their likely values. They tested their method on benchmarks including a NASA challenge and ran analyses quickly on regular computers.
What this means in practice
- •For engineering simulation teams: Improve posterior estimates in uncertain models by eliminating resampling noise, enabling faster and more accurate uncertainty quantification in simulations.
- •For aerospace design teams: Use the framework to efficiently analyze uncertainty in complex aerospace system models, as demonstrated on NASA’s uncertainty quantification challenge.
Authors
Shijie Zhong, Jiangfeng Fu
Abstract
Model updating under hybrid uncertainty is challenging because aleatory input variability makes the simulator output a probability distribution rather than a scalar, rendering the likelihood analytically intractable. Existing Approximate Bayesian Computation (ABC) methods typically employ nested Monte Carlo sampling, where aleatory samples are redrawn for each epistemic parameter evaluation, introducing sampling noise into the discrepancy and consequently affecting posterior inference and model evidence. This paper eliminates this resampling noise by construction. The probability integral transform (PIT) converts the stochastic simulator into a deterministic map of distribution-free latent variables and epistemic parameters. By freezing a set of stratified quantile particles, the resulting discrepancy becomes a deterministic, sampling-noise-free function of the unknown parameters. Transitional Markov Chain Monte Carlo (TMCMC) is then employed for posterior inference and model evidence estimation. The framework is validated on a two-dimensional benchmark, a high-dimensional transient oscillator, and Subproblem A of the NASA Langley Multidisciplinary Uncertainty Quantification Challenge. The complete Bayesian analysis is achieved in approximately half a minute on a standard desktop workstation.