IndependentMHDecision (Independent Metropolis-Hastings Decision)

Perform decision making for independent Metropolis-Hastings MCMC.

Overview

The IndependentMHDecision derives from PMCMCDecision and overrides both the computeEvidence and the computeTransitionVector functions. This is due to the fact that Metropolis-Hastings samplers use a single seed to compute the next $var element = document.getElementById("moose-equation-f503f91a-b4d3-4687-bcf7-dbba1dfc3c52");katex.render("P", element, {displayMode:false,throwOnError:false});$ proposals and the evidences for all these samples need to be evaluated in reference to the seed sample. As such, any MCMC sampler that follows this single seed principle should derive from IndependentMHDecision and should typically only override the computeTransitionVector function, depending upon its mathematical construction.

Parallelized Metropolis-Hastings class of samplers is proposed by Calderhead (2014). The sampling procedure is similar to that of a serial Metropolis-Hastings sampler with some modifications to account for the parallelization. At each serial step, a seed state $var element = document.getElementById("moose-equation-42d9b271-c2b6-4a7f-b5cb-f68675c19c5b");katex.render("\\mathcal{S}_x", element, {displayMode:false,throwOnError:false});$ is defined. Using this seed state, $var element = document.getElementById("moose-equation-bedd5f52-1688-41c7-b4ad-dbebbf2c6805");katex.render("P", element, {displayMode:false,throwOnError:false});$ parallel proposals are made using a proposal distribution $var element = document.getElementById("moose-equation-848afea6-5349-4148-b812-7b9f8f597914");katex.render("\\mathcal{G}", element, {displayMode:false,throwOnError:false});$ . The computational model is evaluated in parallel for these proposals and likelihood function is computed. Then, a transition probability vector $var element = document.getElementById("moose-equation-f2a7b964-f54f-4a79-ae5e-03fe9c3d844b");katex.render("\\pmb{t}_{xy}", element, {displayMode:false,throwOnError:false});$ is computed whose elements are defined as:

$(1)var element = document.getElementById("moose-equation-749fe61d-c63b-44ff-bad3-96f366b84cfe");katex.render(" \\pmb{t}_{xy} = \\begin{cases} \\frac{1}{P} \\min{(1,~t_{xy^p})} & \\text{ if } x\\neq y \\\\ 1-\\sum_{x\\neq y} \\pmb{t}_{xy} & \\text{ otherwise} \\end{cases}", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-66035839-a34a-4447-8012-6eeba2d6f6cf");katex.render("t_{xy^p}", element, {displayMode:false,throwOnError:false});$ is the transition probability defined as shown in the above equation for the $var element = document.getElementById("moose-equation-9c05320a-4c93-453d-9d3e-1e9e2c96a002");katex.render("p^{\\text{th}}", element, {displayMode:false,throwOnError:false});$ parallel proposal. Each of the $var element = document.getElementById("moose-equation-f107f152-2e3a-456f-81ed-83d1a1869c42");katex.render("P", element, {displayMode:false,throwOnError:false});$ parallel proposals is accepted or rejected with a probability defined by the corresponding index in the vector $var element = document.getElementById("moose-equation-097b7ee6-7d48-4ba2-86d5-a5fc487b4d90");katex.render("\\pmb{t}_{xy}", element, {displayMode:false,throwOnError:false});$ . Calderhead (2014) proved the theoretical convergence of this parallelized Metropolis-Hastings construction to the required posterior. In addition, the proposal distribution $var element = document.getElementById("moose-equation-6da8ab4f-89fc-4563-a330-364539204c49");katex.render("\\mathcal{G}", element, {displayMode:false,throwOnError:false});$ can be defined in a flexible way in that it can be a random-walk proposal, Langevin dynamics Cheng et al. (2022) proposal, or Hamiltonian dynamics Betancourt (2017) proposal.

Input Parameters

likelihoodsNames of likelihoods.
C++ Type:std::vector<UserObjectName>
Unit:(no unit assumed)
Controllable:No
Description:Names of likelihoods.
output_valueValue of the model output from the SubApp.
C++ Type:ReporterName
Unit:(no unit assumed)
Controllable:No
Description:Value of the model output from the SubApp.
samplerThe sampler object.
C++ Type:SamplerName
Unit:(no unit assumed)
Controllable:No
Description:The sampler object.

Required Parameters

execute_onTIMESTEP_ENDThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
Default:TIMESTEP_END
C++ Type:ExecFlagEnum
Unit:(no unit assumed)
Options:NONE, INITIAL, LINEAR, NONLINEAR_CONVERGENCE, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM
Controllable:No
Description:The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
inputsinputsUncertain inputs to the model.
Default:inputs
C++ Type:ReporterValueName
Unit:(no unit assumed)
Controllable:No
Description:Uncertain inputs to the model.
noisenoiseModel noise term to pass to Likelihoods object.
Default:noise
C++ Type:ReporterValueName
Unit:(no unit assumed)
Controllable:No
Description:Model noise term to pass to Likelihoods object.
outputs_requiredoutputs_requiredModified value of the model output from this reporter class.
Default:outputs_required
C++ Type:ReporterValueName
Unit:(no unit assumed)
Controllable:No
Description:Modified value of the model output from this reporter class.
prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
seed_inputseed_inputThe seed vector input for proposing new samples.
Default:seed_input
C++ Type:ReporterValueName
Unit:(no unit assumed)
Controllable:No
Description:The seed vector input for proposing new samples.
tpmtpmThe transition probability matrix.
Default:tpm
C++ Type:ReporterValueName
Unit:(no unit assumed)
Controllable:No
Description:The transition probability matrix.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
variancevarianceModel variance term.
Default:variance
C++ Type:ReporterValueName
Unit:(no unit assumed)
Controllable:No
Description:Model variance term.

Optional Parameters

allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
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:Yes
Description:Set the enabled status of the MooseObject.
execution_order_group0Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
Default:0
C++ Type:int
Unit:(no unit assumed)
Controllable:No
Description:Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
force_postauxFalseForces the UserObject to be executed in POSTAUX
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Forces the UserObject to be executed in POSTAUX
force_preauxFalseForces the UserObject to be executed in PREAUX
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Forces the UserObject to be executed in PREAUX
force_preicFalseForces the UserObject to be executed in PREIC during initial setup
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Forces the UserObject to be executed in PREIC during initial setup
outputsVector of output names where you would like to restrict the output of variables(s) associated with this object
C++ Type:std::vector<OutputName>
Unit:(no unit assumed)
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

References

M. Betancourt. A conceptual introduction to Hamiltonian Monte Carlo. arXiv preprint, 2017. doi:10.48550/arXiv.1701.02434.

@article{Betancourt2017a,
    author = "Betancourt, M.",
    title = "{A conceptual introduction to Hamiltonian Monte Carlo}",
    journal = "arXiv preprint",
    volume = "arXiv:1701.02434",
    year = "2017",
    doi = "10.48550/arXiv.1701.02434"
}

B. Calderhead. A general construction for parallelizing Metropolis-Hastings algorithms. Proceedings of the National Academy of Sciences, 111(49):17408–17413, 2014. doi:10.1073/pnas.1408184111.

@article{Calderhead2014a,
    author = "Calderhead, B.",
    title = "{A general construction for parallelizing Metropolis-Hastings algorithms}",
    journal = "Proceedings of the National Academy of Sciences",
    volume = "111",
    number = "49",
    pages = "17408--17413",
    year = "2014",
    doi = "10.1073/pnas.1408184111"
}

X. Cheng, J. Zhang, and S. Sra. Efficient Sampling on Riemannian Manifolds via Langevin MCMC. Advances in Neural Information Processing Systems, 35:5995–6006, 2022.

@article{Cheng2022a,
    author = "Cheng, X. and Zhang, J. and Sra, S.",
    title = "{Efficient Sampling on Riemannian Manifolds via Langevin MCMC}",
    journal = "Advances in Neural Information Processing Systems",
    volume = "35",
    pages = "5995--6006",
    year = "2022"
}

Overview
Input Parameters
References