ExtremeValue

Generalized extreme value likelihood function evaluating the model goodness against experiments.

Overview

The ExtremeValue (Gumbel) likelihood function is given by:

L(θ,σΘi,M,Di)=1βexp((z+exp(z)))where, z=M(Θi)M^(θ, Θi)β \begin{aligned} &\mathcal{L}(\pmb{\theta}, \sigma | \Theta_i, \mathcal{M}, \mathcal{D}_i) = \frac{1}{\beta} \exp{\big(-(z+\exp{(-z)})\big)}\\ &\text{where,}~z = \frac{M(\pmb{\Theta}_i) - \hat{M}(\pmb{\theta},~\Theta_i)}{\beta}\\ \end{aligned}(1)

where, M^(θ, Θi)\hat{M}(\pmb{\theta},~\pmb{\Theta}_i) is the model prediction given model parameters θ\pmb{\theta} and the ithi^{\text{th}} experimental configuration Θi\pmb{\Theta}_i and M(Θi)M(\pmb{\Theta}_i) is the ithi^{\text{th}} experimental data point. β\beta above the scale of the distribution representing the model inadequacy and experimental noise uncertainties.

Input Parameters

  • noiseExperimental noise plus model deviations against experiments.

    C++ Type:ReporterName

    Unit:(no unit assumed)

    Controllable:No

    Description:Experimental noise plus model deviations against experiments.

Required Parameters

  • exp_valuesUser-specified experimental values when CSV file is not provided.

    C++ Type:std::vector<double>

    Unit:(no unit assumed)

    Controllable:No

    Description:User-specified experimental values when CSV file is not provided.

  • file_column_nameName of column in CSV file to use, by default first column is used.

    C++ Type:std::string

    Unit:(no unit assumed)

    Controllable:No

    Description:Name of column in CSV file to use, by default first column is used.

  • file_nameName of the CSV file with experimental values.

    C++ Type:FileName

    Unit:(no unit assumed)

    Controllable:No

    Description:Name of the CSV file with experimental values.

  • log_likelihoodTrueCompute log-likelihood or likelihood.

    Default:True

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:Compute log-likelihood or likelihood.

Optional Parameters

  • control_tagsAdds user-defined labels for accessing object parameters via control logic.

    C++ Type:std::vector<std::string>

    Unit:(no unit assumed)

    Controllable:No

    Description:Adds user-defined labels for accessing object parameters via control logic.

  • enableTrueSet the enabled status of the MooseObject.

    Default:True

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:Set the enabled status of the MooseObject.

Advanced Parameters