Probabilistic Input Modeling

Unique to uncertainty quantification (UQ) test functions is the representation of the input variables as random variables. This is because in a UQ problem, each of the relevant input variables is considered uncertain and they are modeled probabilistically.

In such a setting, each input variable is represented as a random variable whose distribution is described (in the case of a continuous random variable) by a probability density function (PDF). Multiple input variables are represented as a multivariate random variable whose distribution is described by a joint PDF. The random variables in such a multivariate random variable may or may not be statistically independent.

For more flexible and powerful probabilistic input modeling capabilities, please refer to a complete UQ framework such as UQLab or ChaosPy.

UQTestFuns includes some basic probabilistic input modeling capabilities that allows the built-in test functions to be specified without extensive dependencies1. These capabilities, however, are not designed to be a flexible suite of tools to handle the representation of a wide range of distributions for practical applications. Density functions and dependency structures are only made available when a specific UQ test function requires them. The list of supported univariate distributions can be found here.

This section of the documentation explains in more detail how to specify a probabilistic input in UQTestFuns. In UQTestFuns, a probabilistic input consists of one or more input variables, each of which is represented as a univariate random variable with a prescribed distribution:

• To learn more about how to create a univariate random variable, check out the Creating a Univariate Random Variable page.

• To learn more about how to model one or more input variables probabilistically, check out the Creating a Probabilistic Input Model page.

• To get an overview on the basic concepts in probability relevant to UQTestFuns, check out the Preliminaries page.

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1

that is, outside the common numerical Python environment (NumPy and SciPy). In fact, the univariate distributions in UQTestFuns wrap around the ones from scipy.stats with parametrization that is more consistent with the applied UQ literature.