Gaussian

Gaussian likelihood function evaluating the model goodness against experiments.

Overview

The Gaussian likelihood function considering $var element = document.getElementById("moose-equation-86cbefa5-0fd7-4514-ba3e-514d51d986d0");katex.render("N", element, {displayMode:false,throwOnError:false});$ experimental configurations is given by:

$(1)var element = document.getElementById("moose-equation-f0df6c27-9722-4583-924b-9377937660d1");katex.render(" \\mathcal{L} = \\prod_{i=1}^N \\mathcal{N}\\big(\\hat{M}(\\pmb{\\theta},~\\pmb{\\Theta}_i) - M(\\pmb{\\Theta}_i),~\\sigma \\big)", element, {displayMode:true,throwOnError:false});$

where, $var element = document.getElementById("moose-equation-c5984b3f-0a28-4984-85ab-5d78398e31e0");katex.render("\\hat{M}(\\pmb{\\theta},~\\pmb{\\Theta}_i)", element, {displayMode:false,throwOnError:false});$ is the model prediction given model parameters $var element = document.getElementById("moose-equation-3e65eb55-c02b-49aa-a444-56acc192c3d1");katex.render("\\pmb{\\theta}", element, {displayMode:false,throwOnError:false});$ and the $var element = document.getElementById("moose-equation-45f36a0c-0c38-4929-871c-575a9511d526");katex.render("i^{\\text{th}}", element, {displayMode:false,throwOnError:false});$ experimental configuration $var element = document.getElementById("moose-equation-0317bee8-80ec-4394-8579-fc958a5fe48b");katex.render("\\pmb{\\Theta}_i", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-d86636da-bd95-475f-adfb-b0b626d07676");katex.render("M(\\pmb{\\Theta}_i)", element, {displayMode:false,throwOnError:false});$ is the $var element = document.getElementById("moose-equation-f23fdd27-8568-4fd0-97a0-f6aea983e641");katex.render("i^{\\text{th}}", element, {displayMode:false,throwOnError:false});$ experimental data point. $var element = document.getElementById("moose-equation-93f29feb-ddc6-414c-9237-f124c4c0588a");katex.render("\\sigma", element, {displayMode:false,throwOnError:false});$ above is the scale of the distribution representing the model inadequacy and experimental noise uncertainties, while $var element = document.getElementById("moose-equation-877f1068-918b-4ad3-b24b-27ca5b579506");katex.render("\\mathcal{N}", element, {displayMode:false,throwOnError:false});$ represents a Gaussian distribution.

Example Input File Syntax

[Likelihood<<<{"href": "../../syntax/Likelihood/index.html"}>>>]
  [gaussian]
    type = Gaussian<<<{"description": "Gaussian likelihood function evaluating the model goodness against experiments.", "href": "Gaussian.html"}>>>
    noise<<<{"description": "Experimental noise plus model deviations against experiments."}>>> = 'noise_specified/noise_specified'
    file_name<<<{"description": "Name of the CSV file with experimental values."}>>> = 'exp1.csv'
    log_likelihood<<<{"description": "Compute log-likelihood or likelihood."}>>> = true
  []
[]

Input Parameters

noiseExperimental noise plus model deviations against experiments.
C++ Type:ReporterName
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
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
Controllable:No
Description:Name of the CSV file with experimental values.
log_likelihoodTrueCompute log-likelihood or likelihood.
Default:True
C++ Type:bool
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>
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
Controllable:No
Description:Set the enabled status of the MooseObject.

Advanced Parameters

(moose/modules/stochastic_tools/test/tests/likelihoods/gaussian_derived/main.i)

[StochasticTools]
[]

[Distributions]
  [mu1]
    type = Normal
    mean = 0.0
    standard_deviation = 0.5
  []
[]

[Samplers]
  [sample]
    type = MonteCarlo
    distributions = 'mu1 mu1'
    num_rows = 3
    seed = 2547
  []
[]

[MultiApps]
  [sub]
    type = SamplerFullSolveMultiApp
    input_files = sub.i
    sampler = sample
  []
[]

[Transfers]
  [param]
    type = SamplerParameterTransfer
    to_multi_app = sub
    sampler = sample
    parameters = 'BCs/left/value BCs/right/value'
    # to_control = 'stochastic'
  []
  [reporter_transfer]
    type = SamplerReporterTransfer
    from_reporter = 'average/value'
    stochastic_reporter = 'constant'
    from_multi_app = sub
    sampler = sample
  []
[]

[Reporters]
  [constant]
    type = StochasticReporter
  []
  [noise_specified]
    type = ConstantReporter
    real_names = 'noise_specified'
    real_values = '0.2'
  []
  [likelihoodtest]
    type = TestLikelihood
    likelihoods = 'gaussian'
    model_pred = constant/reporter_transfer:average:value
    sampler = sample
  []
[]

[Likelihood]
  [gaussian]
    type = Gaussian
    noise = 'noise_specified/noise_specified'
    file_name = 'exp1.csv'
    log_likelihood=true
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  file_base ='loglikelihood_scalar'
  [out]
    type = JSON
    execute_system_information_on = NONE
  []
[]

Overview
Example Input File Syntax
Input Parameters