2021/06/17 by David John, David N. John, Livia Stohrer +9
Computer Science · Decision Sciences · Mathematics · Physics and Astronomy · #Applications (stat.AP) #Data Analysis #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Gaussian Processes and Bayesian Inference #Machine Learning and Algorithms #Markov Chains and Monte Carlo Methods #Methodology (stat.ME) #Optimization and Control (math.OC) #Probabilistic and Robust Engineering Design #Statistics and Probability (physics.data-an) #math.OC #physics.data-an #stat.AP #stat.ME
paper · pdf · doi:10.48550/arxiv.2106.09597
arxiv created 2021/06/17 · openalex publication_date 2021/06/17 · arxiv updated 2021/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Inferring parameter distributions of complex industrial systems from noisy time series data requires methods to deal with the uncertainty of the underlying data and the used simulation model. Bayesian inference is well suited for these uncertain inverse problems. Standard methods used to identify uncertain parameters are Markov Chain Monte Carlo (MCMC) methods with explicit evaluation of a likelihood function. However, if the likelihood is very complex, such that its evaluation is computationally expensive, or even unknown in its explicit form, Approximate Bayesian Computation (ABC) methods provide a promising alternative. In this work both methods are first applied to artificially generated data and second on a real world problem, by using data of an electric motor test bench. We show that both methods are able to infer the distribution of varying parameters with a Bayesian hierarchical approach. But the proposed ABC method is computationally much more efficient in order to achieve results with similar accuracy. We suggest to use summary statistics in order to reduce the dimension of the data which significantly increases the efficiency of the algorithm. Further the simulation model is replaced by a Polynomial Chaos Expansion (PCE) surrogate to speed up model evaluations. We proof consistency for the proposed surrogate-based ABC method with summary statistics under mild conditions on the (approximated) forward model.