MCMC¶

class
MCMC
(*args)¶ MonteCarlo Markov Chain.
 Available constructor:
MCMC(prior, conditional, observations, initialState)
MCMC(prior, conditional, model, parameters, observations, initialState)
Parameters: prior :
Distribution
Prior distribution of the parameters of the underlying Bayesian statistical model.
conditional :
Distribution
Required distribution to define the likelihood of the underlying Bayesian statistical model.
model :
NumericalMathFunction
Function required to define the likelihood.
observations : 2d sequence of float
Observations required to define the likelihood.
initialState : sequence of float
Initial state of the MonteCarlo Markov chain on which the Sampler is based.
parameters : 2d sequence of float
Parameters of the model to be fixed.
Notes
MCMC provides a implementation of the concept of sampler, using a MonteCarlo Markov Chain (MCMC) algorithm starting from initialState. More precisely, let be the PDF of its target distribution and its dimension, be the PDF of the prior distribution, be the PDF of the conditional distribution when its parameters are set to , be the number of scalar parameters of conditional distribution (which corresponds to the dimension of the above ), be the function corresponding to model and be the sample observations (of size ):
In the first usage, it creates a sampler based on a MCMC algorithm whose target distribution is defined by:
In the first usage, it creates a sampler based on a MCMC algorithm whose target distribution is defined by:
where the () are such that:
In fact, the first usage is a particular case of the second.
The MCMC method implemented in OpenTURNS is the Random Walk MetropolisHastings algorithm. A sample can be generated only through the MCMC’s derived class:
RandomWalkMetropolisHastings
.Methods
computeLogLikelihood
(currentState)Compute the logarithm of the likelihood w.r.t. getBurnIn
()Get the length of the burnin period. getClassName
()Accessor to the object’s name. getConditional
()Get the conditional distribution. getDimension
()Get the dimension of the samples generated. getHistory
()Get the history storage. getId
()Accessor to the object’s id. getModel
()Get the model. getName
()Accessor to the object’s name. getNonRejectedComponents
()Get the components to be always accepted. getObservations
()Get the observations. getParameters
()Get the parameters. getPrior
()Get the prior distribution. getRealization
()Return a realization. getSample
(size)Return several realizations. getShadowedId
()Accessor to the object’s shadowed id. getThinning
()Get the thinning parameter. getVerbose
()Tell whether the verbose mode is activated or not. getVisibility
()Accessor to the object’s visibility state. hasName
()Test if the object is named. hasVisibleName
()Test if the object has a distinguishable name. setBurnIn
(burnIn)Set the length of the burnin period. setHistory
(strategy)Set the history storage. setName
(name)Accessor to the object’s name. setNonRejectedComponents
(nonRejectedComponents)Set the components to be always accepted. setObservations
(observations)Set the observations. setParameters
(parameters)Set the parameters. setPrior
(prior)Set the prior distribution. setShadowedId
(id)Accessor to the object’s shadowed id. setThinning
(thinning)Set the thinning parameter. setVerbose
(verbose)Set the verbose mode. setVisibility
(visible)Accessor to the object’s visibility state. 
__init__
(*args)¶

computeLogLikelihood
(currentState)¶ Compute the logarithm of the likelihood w.r.t. observations.
Parameters: currentState : sequence of float
Current state.
Returns: logLikelihood : float
Logarithm of the likelihood w.r.t. observations .

getBurnIn
()¶ Get the length of the burnin period.
Returns: lenght : int
Length of the burnin period, that is the number of first iterates of the MCMC chain which will be thrown away when generating the sample.

getClassName
()¶ Accessor to the object’s name.
Returns: class_name : str
The object class name (object.__class__.__name__).

getConditional
()¶ Get the conditional distribution.
Returns: conditional :
Distribution
Distribution taken into account in the definition of the likelihood, whose PDF with parameters corresponds to in the equations of the target distribution’s PDF.

getDimension
()¶ Get the dimension of the samples generated.
Returns: dimension : int
Dimension of the samples that the Sampler can generate.

getHistory
()¶ Get the history storage.
Returns: history :
HistoryStrategy
Used to record the chain.

getId
()¶ Accessor to the object’s id.
Returns: id : int
Internal unique identifier.

getModel
()¶ Get the model.
Returns: model :
NumericalMathFunction
Model take into account in the definition of the likelihood, which corresponds to , that is the functions () in the equation of the target distribution’s PDF.

getName
()¶ Accessor to the object’s name.
Returns: name : str
The name of the object.

getNonRejectedComponents
()¶ Get the components to be always accepted.
Returns: nonRejectedComponents :
Indices
The indices of the components that are not tuned, and sampled according to the prior distribution in order to take into account the intrinsic uncertainty, as opposed to the epistemic uncertainty corresponding to the tuned variables.

getObservations
()¶ Get the observations.
Returns: observations :
NumericalSample
Sample taken into account in the definition of the likelihood, which corresponds to the tuple of the () in equations of the target distribution’s PDF.

getParameters
()¶ Get the parameters.
Returns: parameters :
NumericalPoint
Fixed parameters of the model required to define the likelihood.

getPrior
()¶ Get the prior distribution.
Returns: prior :
Distribution
The prior distribution of the parameter of the underlying Bayesian statistical model, whose PDF corresponds to in the equations of the target distribution’s PDF.

getRealization
()¶ Return a realization.
Returns: realization :
NumericalPoint
A new realization.

getSample
(size)¶ Return several realizations.
Parameters: size : int,
Number of realizations needed.
Returns: realizations :
NumericalSample
Sequence composed of size new realizations.

getShadowedId
()¶ Accessor to the object’s shadowed id.
Returns: id : int
Internal unique identifier.

getThinning
()¶ Get the thinning parameter.
Returns: thinning : int
Thinning parameter: storing only every point after the burnin period.
Notes
When generating a sample of size , the number of MCMC iterations performed is where is the burnin period length and the thinning parameter.

getVerbose
()¶ Tell whether the verbose mode is activated or not.
Returns: isVerbose : bool
The verbose mode is activated if it is True, desactivated otherwise.

getVisibility
()¶ Accessor to the object’s visibility state.
Returns: visible : bool
Visibility flag.

hasName
()¶ Test if the object is named.
Returns: hasName : bool
True if the name is not empty.

hasVisibleName
()¶ Test if the object has a distinguishable name.
Returns: hasVisibleName : bool
True if the name is not empty and not the default one.

setBurnIn
(burnIn)¶ Set the length of the burnin period.
Parameters: lenght : int
Length of the burnin period, that is the number of first iterates of the MCMC chain which will be thrown away when generating the sample.

setHistory
(strategy)¶ Set the history storage.
Parameters: history :
HistoryStrategy
Used to record the chain.

setName
(name)¶ Accessor to the object’s name.
Parameters: name : str
The name of the object.

setNonRejectedComponents
(nonRejectedComponents)¶ Set the components to be always accepted.
Parameters: nonRejectedComponents : sequence of int
The indices of the components that are not tuned, and sampled according to the prior distribution in order to take into account the intrinsic uncertainty, as opposed to the epistemic uncertainty corresponding to the tuned variables.

setObservations
(observations)¶ Set the observations.
Parameters: observations : 2d sequence of float
Sample taken into account in the definition of the likelihood, which corresponds to the tuple of the () in the equations of the target distribution’s PDF.

setParameters
(parameters)¶ Set the parameters.
Parameters: parameters : sequence of float
Fixed parameters of the model required to define the likelihood.

setPrior
(prior)¶ Set the prior distribution.
Parameters: prior :
Distribution
The prior distribution of the parameter of the underlying Bayesian statistical model, whose PDF corresponds to in the equations of the target distribution’s PDF.

setShadowedId
(id)¶ Accessor to the object’s shadowed id.
Parameters: id : int
Internal unique identifier.

setThinning
(thinning)¶ Set the thinning parameter.
Parameters: thinning : int,
Thinning parameter: storing only every point after the burnin period.
Notes
When generating a sample of size , the number of MCMC iterations performed is where is the burnin period length and the thinning parameter.

setVerbose
(verbose)¶ Set the verbose mode.
Parameters: isVerbose : bool
The verbose mode is activated if it is True, desactivated otherwise.

setVisibility
(visible)¶ Accessor to the object’s visibility state.
Parameters: visible : bool
Visibility flag.