Estimate unknown model inputs or parameters by incorporating prior information and updating it with observed data or a design goal through Bayes’ theorem.
Bayesian calibration
Bayesian calibration is a form of inverse analysis that comprises several methods based on Bayesian probability theory, specifically the Bayes’ rule. Bayesian calibration aims to update system inputs such that the system outputs become, on average, close to experimental observations (data). The key idea is to describe all system quantities by probability densities rather than deterministic variables and to exploit Bayes’ rule. The latter provides a mathematical description for updating a prior probability density based on a likelihood model for observed data to yield a so-called posterior distribution. In the calibration setting, this concept updates a prior belief for the system inputs with the information provided by experimental data. The resulting posterior distribution for the system inputs is the solution to the Bayesian calibration problem. Samples from this distribution will lead to system outputs that follow the distribution of the observed data. Mathematically, the probabilistic treatment of the involved system quantities allows for the natural handling of uncertainties, experimental noise, and prior beliefs. Using entire densities rather than single deterministic values leads to algorithmically stable methods. The posterior density usually has no analytical description due to the implicit dependency on a (nonlinear) system input to output map. Several methods exist in QUEENS to find the posterior or an approximation to the latter by iterative procedures. Prominent examples are Markov Chain Monte Carlo (MCMC), specifically the Metropolis-Hastings algorithm, Sequential Monte Carlo (SMC), and Stochastic Variational Inference (SVI).
Features in QUEENS
- Sequential Monte Carlo (SMC)
- Markov Chain Monte Carlo (MCMC), specifically the Metropolis-Hastings algorithm
- Stochastic Variational Inference (SVI), based on the reparameterization trick
- Black-Box Variational Inference
- Bayesian Multi-Fidelity Inverse Analysis (BMFIA)