Bayesian parameter estimation of miss-specified models

TL;DR

This paper introduces a Bayesian method for estimating parameters and model errors in simplified models fitted to complex real data, enabling better insights despite model misspecification.

Contribution

It presents a novel Bayesian approach that simultaneously infers model parameters, model error, and measurement errors using multiple data sets.

Findings

Effective in absorbing measurement instrument errors into model error

Allows for simultaneous estimation of parameters and errors in complex models

Improves robustness of parameter inference in misspecified models

Abstract

Fitting a simplifying model with several parameters to real data of complex objects is a highly nontrivial task, but enables the possibility to get insights into the objects physics. Here, we present a method to infer the parameters of the model, the model error as well as the statistics of the model error. This method relies on the usage of many data sets in a simultaneous analysis in order to overcome the problems caused by the degeneracy between model parameters and model error. Errors in the modeling of the measurement instrument can be absorbed in the model error allowing for applications with complex instruments.