MetropolisHastings¶

class MetropolisHastings(*args)¶

Base class for Metropolis-Hastings algorithms.

Refer to Bayesian calibration, The Metropolis-Hastings Algorithm.

Methods

`computeLogLikelihood`(state)	Compute the logarithm of the likelihood w.r.t.
`computeLogPosterior`(currentState)	Compute the logarithm of the unnormalized posterior density.
`getAcceptanceRate`()	Get acceptance rate.
`getClassName`()	Accessor to the object's name.
`getConditional`()	Get the conditional distribution.
`getCovariates`()	Get the parameters.
`getDimension`()	Accessor to the dimension of the RandomVector.
`getHistory`()	Get the history storage.
`getId`()	Accessor to the object's id.
`getImplementation`()	Accessor to the underlying implementation.
`getInitialState`()	Get the initial state.
`getLinkFunction`()	Get the model.
`getMarginalIndices`()	Get the indices of the sampled components.
`getName`()	Accessor to the object's name.
`getObservations`()	Get the observations.
`getRealization`()	Compute one realization of the RandomVector.
`getTargetDistribution`()	Get the target distribution.
`getTargetLogPDF`()	Get the target log-pdf.
`getTargetLogPDFSupport`()	Get the target log-pdf support.
`setHistory`(strategy)	Set the history storage.
`setLikelihood`(*args)	Set the likelihood.
`setName`(name)	Accessor to the object's name.

See also

openturns.RandomVector.getSample

Examples

>>> import openturns as ot
>>> distribution = ot.Normal([0.0, 0.0], [1.0, 1.0], ot.CorrelationMatrix(2))
>>> randomVector = ot.RandomVector(distribution)
>>> ot.RandomGenerator.SetSeed(0)
>>> print(randomVector.getRealization())
[0.608202,-1.26617]
>>> print(randomVector.getRealization())
[-0.438266,1.20548]

getTargetDistribution()¶

Get the target distribution.

Returns:

targetDistributionDistribution: The targetDistribution argument provided to the constructor

getTargetLogPDF()¶

Get the target log-pdf.

Returns:

targetLogPDFFunction: The targetLogPDF argument provided to the constructor

getTargetLogPDFSupport()¶

Get the target log-pdf support.

Returns:

supportInterval: The support argument provided to the constructor

setHistory(strategy)¶

Set the history storage.

Parameters:

historyHistoryStrategy: Used to record the chain.

setLikelihood(*args)¶

Set the likelihood.

Parameters:

conditionalDistribution: Required distribution to define the likelihood of the underlying Bayesian statistical model.
observations2-d sequence of float: Observations $\vect y^i$ required to define the likelihood.
linkFunctionFunction, optional: Function $g$ that maps the chain into the conditional distribution parameters. If provided, its input dimension must match the chain dimension and its output dimension must match the conditional distribution parameter dimension. Else it is set to the identity.
covariates2-d sequence of float, optional: Parameters $\vect c^i$ of the linkFunction for each observation $\vect y^i$ . If provided, their dimension must match the parameter dimension of linkFunction.

Notes

Once this method is called, the class no longer samples from the distribution targetDistribution or from the distribution defined by targetLogPDF and support, but considers that distribution as being the prior. Let $\pi(\vect \theta)$ be the PDF of the prior at the point $\vect \theta$ . The class now samples from the posterior, whose PDF is proportional to $L(\vect\theta) \, \pi(\vect\theta)$ , the likelihood $L(\vect \theta)$ being defined from the arguments of this method.

The optional parameters linkFunction and covariates allow several options to define the likelihood $L(\vect \theta)$ . Letting $f$ be the PDF of the distribution conditional:

Without linkFunction and covariates the likelihood term reads:

$L(\vect \theta) = \prod_{i=1}^n f(\vect{y}^i|\vect{\theta})$
If only the linkFunction is provided:

$L(\vect \theta) = \prod_{i=1}^n f(\vect{y}^i|g(\vect{\theta}))$
If both the linkFunction and covariates are provided:

$L(\vect \theta) = \prod_{i=1}^n f(\vect{y}^i|g_{\vect c^i}(\vect{\theta}))$