Bayesian inference is a powerful tool for probabilistic model calibration and inverse problems. UQ[py]Lab offers a flexible and intuitive way to set-up and solve Bayesian inverse problems.

• Intuitive definition of prior knowledge, forward model and data
• State-of-the-art Markov Chain Monte Carlo (MCMC) algorithms
• Customizable discrepancy between model and measurements
• Support for user-specified custom likelihood
• Support for multiple forward models and multiple discrepancy models (joint inversion)
• Fully integrated with UQLab (e.g. surrogate models, complex priors, etc.)

Polynomial Chaos-Kriging (PC-Kriging) associates the global approximation behavior of polynomial chaos expansions and the local accuracy of Kriging to provide a highly accurate surrogate model at low computational costs.

• Support for sequential and optimal construction of PC-Kriging
• Full control on both levels of approximation: polynomial chaos expansions and Kriging directly use the corresponding dedicated UQLab modules
• Support for sparse, adaptive and arbitrary polynomial chaos expansions
• Gradient-based, global and hybrid optimization  methods for Kriging

Gaussian process modeling is a flexible and robust technique to build fast surrogate models based on small experimental designs

• Simple, ordinary, and universal Kriging
• Highly customizable trend and correlation functions
• Maximum-likelihood- and cross-validation-based hyperparameter estimation
• Gradient-based, global, and hybrid optimization methods
• Interpolation (noise-free response) and regression (noisy response) modes

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When the performance of a system is affected by uncertainties on its characteristics and/or its environment, reliability can be assessed by computing probabilities of failure.
UQLab offers state-of-the-art reliability algorithms and a powerful modular framework
for active learning reliability.

• FORM/SORM approximation methods
• Sampling methods (Monte Carlo, importance sampling, subset simulation)
• Modular framework to build custom active learning solution schemes
• Kriging-based adaptive methods (AK-MCS, APCK-MCS)

Probabilistic modelling lies at the core of uncertainty quantification. Full support for complex probabilistic models based on copula and marginal representation. Powerful data-driven inference module.

• Support for many common marginal distributions
• Support for standard copulas, as well as complex vine-copula constructions
• Fully automatic inference of both marginal distributions and copula
• Advanced sampling schemes, including latin hypercube sampling, quasi-random sequences

Sensitivity analysis can identify the driving factors that most influence the response of a model

• Approximation- and simulation- based methods
• Advanced variance decomposition techniques (e.g. Sobol' indices)
• Support for metamodel-based sensitivity analysis
• Support for sensitivity analysis of dependent input variables

Polynomial chaos expansions (PCE), one of the most powerful and versatile surrogate models available today

• Non-intrusive PCE facilities
• State-of-the-art sparse regression solvers, including least angle regression, subspace pursuit, Bayesian compressing sensing and much more
• Support for classical polynomials, as well as polynomials orthogonal to user-defined input distributions
• Support also fully data-driven, arbitrary PCE