Gaussian

Gaussian likelihood function evaluating the model goodness against experiments.

Overview

The Gaussian likelihood function considering NN experimental configurations is given by:

L=i=1NN(M^(θ, Θi)M(Θi), σ) \mathcal{L} = \prod_{i=1}^N \mathcal{N}\big(\hat{M}(\pmb{\theta},~\pmb{\Theta}_i) - M(\pmb{\Theta}_i),~\sigma \big)(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. σ\sigma above is the scale of the distribution representing the model inadequacy and experimental noise uncertainties, while N\mathcal{N} represents a Gaussian distribution.

Example Input File Syntax

[Likelihood]
  [gaussian]
    type = Gaussian
    noise = 'noise_specified/noise_specified'
    file_name = 'exp1.csv'
    log_likelihood = true
  []
[]
(contrib/moose/modules/stochastic_tools/test/tests/likelihoods/gaussian_derived/main.i)

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