# Overview of Methods#

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Various statistical methods have been developed to deal with the challenges of data-induced and method-induced uncertainties. The aim of this chapter of the UQ Dictionary is to introduce a categorization of selected methods from different disciplines, their connections to uncertainty quantification as well as links to further readings. Applications of the methods, for instance in microbiology and surface wave tomography, can be found in the case studies chapter.

Sensitivity analysis tools reveal uncertainties of models with respect to initial conditions and input parameters.

Monte-Carlo methods propagate uncertainties of particular quantities of interest by random sampling.

UQ for dynamical models focuses on the specific challenges of processes that evolve over time, e.g stochastic processes.

Bayesian methods require adequate prior distributions, model formulations and sampling algorithms, e.g. Hamiltonian Monte Carlo.

Optimization under uncertainty introduces techniques to optimize objective functions which contain uncertain parameters.

Imputation methods for missing data are subject to uncertainties which should be addressed properly.

Uncertainty propagation studies how uncertainties affect a model.

Model selection is an uncertain procedure which can be guided by proper criteria and clever parameterization.

# Authors#

Jonas Bauer