A class for storing and working with the results of Markov chain Monte Carlo algorithms. More...

#include <MarkovChain.h>

Inheritance diagram for muq::SamplingAlgorithms::MarkovChain:

Detailed Description

A class for storing and working with the results of Markov chain Monte Carlo algorithms.

The MarkovChain class is a child of SampleCollection where the sample weights correspond to the number of consecutive steps taking the same value, and the weights are unnormalized (i.e., do not sum to one). This is a useful class for storing the chain produced by an MCMC algorithm without storing the duplicate points that result from rejected proposals.

Definition at line 19 of file MarkovChain.h.

Public Member Functions
	MarkovChain ()=default

virtual	~MarkovChain ()=default

virtual Eigen::VectorXd	ESS (std::string const &method="Batch") const override

virtual Eigen::VectorXd	ESS (int blockDim) const override

virtual Eigen::VectorXd	ESS (int blockDim, std::string const &method) const override

virtual Eigen::VectorXd	StandardError (std::string const &method="Batch") const override

virtual Eigen::VectorXd	StandardError (int blockDim) const override

virtual Eigen::VectorXd	StandardError (int blockDim, std::string const &method) const override

Eigen::VectorXd	WolffESS (int blockDim) const

Eigen::VectorXd	WolffError (int blockDim) const

virtual std::shared_ptr< SampleCollection >	segment (unsigned int startInd, unsigned int length, unsigned int skipBy=1) const override

Public Member Functions inherited from muq::SamplingAlgorithms::SampleCollection
	SampleCollection ()=default

virtual	~SampleCollection ()=default

virtual void	Add (std::shared_ptr< SamplingState > newSamp)

virtual std::shared_ptr< SamplingState >	at (unsigned i)

virtual const std::shared_ptr< SamplingState >	at (unsigned i) const

virtual unsigned int	size () const

virtual std::shared_ptr< SampleCollection >	head (unsigned int N) const

virtual std::shared_ptr< SampleCollection >	tail (unsigned int N) const

virtual const std::shared_ptr< SamplingState >	back () const

virtual Eigen::VectorXd	CentralMoment (unsigned order, Eigen::VectorXd const &mean, int blockNum=-1) const override
	Computes the componentwise central moments (e.g., variance, skewness, kurtosis, etc..) of a specific order given that we already know the mean. More...

virtual Eigen::VectorXd	CentralMoment (unsigned int order, int blockNum=-1) const override

virtual Eigen::VectorXd	Mean (int blockInd=-1) const override

virtual Eigen::MatrixXd	Covariance (int blockInd=-1) const override

virtual Eigen::MatrixXd	Covariance (Eigen::VectorXd const &mean, int blockInd=-1) const override

virtual std::vector< Eigen::MatrixXd >	RunningCovariance (int blockInd=-1) const

virtual std::vector< Eigen::MatrixXd >	RunningCovariance (Eigen::VectorXd const &mean, int blockInd=-1) const

Eigen::VectorXd	BatchESS (int blockInd=-1, int batchSize=-1, int overlap=-1) const

double	MultiBatchESS (int blockInd=-1, int batchSize=-1, int overlap=-1) const

virtual Eigen::VectorXd	BatchError (int blockInd=-1, int batchSize=-1, int overlap=-1) const

virtual Eigen::VectorXd	MultiBatchError (int blockInd=-1, int batchSize=-1, int overlap=-1) const

virtual Eigen::MatrixXd	AsMatrix (int blockDim=-1) const

virtual Eigen::VectorXd	Weights () const

virtual Eigen::VectorXd	Rhat (int blockDim, unsigned int numSegments=4, boost::property_tree::ptree options=boost::property_tree::ptree()) const

virtual Eigen::VectorXd	Rhat (unsigned int numSegments=4, boost::property_tree::ptree options=boost::property_tree::ptree()) const

Public Member Functions inherited from muq::SamplingAlgorithms::SampleEstimator
virtual	~SampleEstimator ()=default

virtual unsigned int	BlockSize (int blockInd) const =0

virtual unsigned int	NumBlocks () const =0

virtual Eigen::VectorXd	CentralMoment (unsigned int order, Eigen::VectorXd const &mean, int blockNum=-1) const

virtual Eigen::VectorXd	StandardizedMoment (unsigned int order, int blockInd=-1) const

virtual Eigen::VectorXd	StandardizedMoment (unsigned int order, Eigen::VectorXd const &mean, int blockInd=-1) const

virtual Eigen::VectorXd	StandardizedMoment (unsigned int order, Eigen::VectorXd const &mean, Eigen::VectorXd const &stdDev, int blockInd=-1) const

virtual Eigen::VectorXd	Variance (int blockInd=-1) const

virtual Eigen::VectorXd	Variance (Eigen::VectorXd const &mean, int blockInd=-1) const

virtual Eigen::VectorXd	Skewness (int blockInd=-1) const

virtual Eigen::VectorXd	Skewness (Eigen::VectorXd const &mean, int blockInd=-1) const

virtual Eigen::VectorXd	Skewness (Eigen::VectorXd const &mean, Eigen::VectorXd const &stdDev, int blockInd=-1) const

virtual Eigen::VectorXd	Kurtosis (int blockInd=-1) const

virtual Eigen::VectorXd	Kurtosis (Eigen::VectorXd const &mean, int blockInd=-1) const

virtual Eigen::VectorXd	Kurtosis (Eigen::VectorXd const &mean, Eigen::VectorXd const &stdDev, int blockInd=-1) const

virtual Eigen::VectorXd	ExpectedValue (std::shared_ptr< muq::Modeling::ModPiece > const &f, std::vector< std::string > const &metains=std::vector< std::string >()) const =0

Static Public Member Functions
static double	SingleComponentWolffESS (Eigen::Ref< const Eigen::VectorXd > const &trace)

Static Public Member Functions inherited from muq::SamplingAlgorithms::SampleCollection
static std::shared_ptr< SampleCollection >	FromMatrix (Eigen::MatrixXd const &samps)

Constructor & Destructor Documentation

◆ MarkovChain()

muq::SamplingAlgorithms::MarkovChain::MarkovChain ( )

default

◆ ~MarkovChain()

virtual muq::SamplingAlgorithms::MarkovChain::~MarkovChain ( )

virtualdefault

Member Function Documentation

◆ ESS() [1/3]

virtual Eigen::VectorXd muq::SamplingAlgorithms::MarkovChain::ESS ( int blockDim ) const

inlineoverridevirtual

Parameters

[in] blockDim The block of the SampleState that we want to use in the ESS computation.

Returns: Either a vector of length \(D\) containing an ESS estimate for each component or a vector of length 1 containing a single multivariate ESS estimate.

Reimplemented from muq::SamplingAlgorithms::SampleCollection.

Definition at line 42 of file MarkovChain.h.

References ESS().

Referenced by ESS().

◆ ESS() [2/3]

Eigen::VectorXd MarkovChain::ESS	(	int	blockDim,
		std::string const &	method
	)		const

overridevirtual

Parameters

[in]	blockDim	The block of the SampleState that we want to use in the ESS computation.
[in]	method	A string specifying the method used to estimate the ESS. Options in SampleCollection are "Batch" or "MultiBatch". The MarkovChain class also supports a "Wolff" method.

Returns: Either a vector of length \(D\) containing an ESS estimate for each component or a vector of length 1 containing a single multivariate ESS estimate.

Reimplemented from muq::SamplingAlgorithms::SampleCollection.

Definition at line 7 of file MarkovChain.cpp.

References muq::SamplingAlgorithms::SampleCollection::BatchESS(), muq::SamplingAlgorithms::SampleCollection::MultiBatchESS(), and WolffESS().

◆ ESS() [3/3]

virtual Eigen::VectorXd muq::SamplingAlgorithms::MarkovChain::ESS ( std::string const & method = "Batch" ) const

inlineoverridevirtual

Computes the effective sample size of the Markov chain.

If method=="Wolff", the spectral method described in "Monte Carlo errors with less error" by Ulli Wolff is employed. This returns an ESS for each component of the chain.

If method=="Batch" (default) The overlapping batch method (OBM) described in [Flegal2010] is used. This method is also applied to each component independently, resulting in an ESS estimate for each component.

If method=="MultiBatch", The multivariate method of [Vats2019] is employed. This method takes into account the joint correlation of all components of the chain and returns a single ESS. This approach is preferred in high dimensional settings.

Reimplemented from muq::SamplingAlgorithms::SampleCollection.

Definition at line 41 of file MarkovChain.h.

References ESS().

Referenced by ESS().

◆ segment()

std::shared_ptr< SampleCollection > MarkovChain::segment	(	unsigned int	startInd,
		unsigned int	length,
		unsigned int	skipBy = `1`
	)		const

overridevirtual

Returns a new sample collection containing a segment of this sample collection. The Equivalent to a python command like list[startInd:startInd+length:skipBy]

Reimplemented from muq::SamplingAlgorithms::SampleCollection.

Definition at line 158 of file MarkovChain.cpp.

References muq::SamplingAlgorithms::SampleCollection::at(), and muq::SamplingAlgorithms::SampleCollection::size().

◆ SingleComponentWolffESS()

double MarkovChain::SingleComponentWolffESS ( Eigen::Ref< const Eigen::VectorXd > const & trace )

static

Computes the effective sample size given a vector containing a single component of the Markov chain.

Definition at line 58 of file MarkovChain.cpp.

References muq::SamplingAlgorithms::SampleCollection::size().

Referenced by WolffESS().

◆ StandardError() [1/3]

virtual Eigen::VectorXd muq::SamplingAlgorithms::MarkovChain::StandardError ( int blockDim ) const

inlineoverridevirtual

Reimplemented from muq::SamplingAlgorithms::SampleCollection.

Definition at line 60 of file MarkovChain.h.

References StandardError().

Referenced by StandardError().

◆ StandardError() [2/3]

Eigen::VectorXd MarkovChain::StandardError	(	int	blockInd,
		std::string const &	method
	)		const

overridevirtual

Returns an estimate of the the Monte Carlo standard error (MCSE) \(\hat{\sigma}\) for a Monte Carlo estimate of the mean derived using this SampleEstimator. Recall at the MCSE is the standard deviation of the estimator variance employed in the Central Limit Theorem.

Parameters

[in]	blockInd	Specifies the block of the sampling state we're interested in. Defaults to -1, which will result in all blocks of the sampling state being concatenated in the MCSE estimate.
[in]	method	A string describing what method should be used to estimate the MCSE. Defaults to "Batch". Options are the same as the ESS function: "Batch", "MultiBatch", and "Wolff". The "Wolff" option is only valid for the "MarkovChain" and "MultiIndexEstimator" classes.

Returns: A vector containing either the MCSE for each component.

Reimplemented from muq::SamplingAlgorithms::SampleCollection.

Definition at line 24 of file MarkovChain.cpp.

References muq::SamplingAlgorithms::SampleCollection::BatchError(), muq::SamplingAlgorithms::SampleCollection::MultiBatchError(), and WolffError().

◆ StandardError() [3/3]

virtual Eigen::VectorXd muq::SamplingAlgorithms::MarkovChain::StandardError ( std::string const & method = "Batch" ) const

inlineoverridevirtual

Computes the Monte Carlo standard error (MCSE) of the Markov chain.

If method=="Wolff", the spectral method described in "Monte Carlo errors with less error" by Ulli Wolff [Wolff2004] is employed. This returns an MCSE for each component of the chain.

If method=="Batch" (default) The overlapping batch method (OBM) described in [Flegal2010] is used. This method is also applied to each component independently, resulting in an MCSE estimate for each component.

If method=="MultiBatch", The multivariate method of [Vats2019] is employed. This method takes into account the joint correlation of all components of the chain and returns a single generalized MCSE. This approach is preferred in high dimensional settings.

Reimplemented from muq::SamplingAlgorithms::SampleCollection.

Definition at line 59 of file MarkovChain.h.

References StandardError().

Referenced by StandardError().

◆ WolffError()

Eigen::VectorXd MarkovChain::WolffError ( int blockDim ) const

Computes the MCSE based on the effective sample size returned by WolffESS

Parameters

[in] blockInd Specifies the block of the sampling state we're interested in. Defaults to -1, which will result in all blocks of the sampling state being concatenated in the MCSE estimate.

Returns: A vector containing the MCSE for each component of the chain.

Definition at line 40 of file MarkovChain.cpp.

References muq::SamplingAlgorithms::SampleEstimator::Variance(), and WolffESS().

Referenced by StandardError().

◆ WolffESS()

Eigen::VectorXd MarkovChain::WolffESS ( int blockDim ) const

Computes the effective sample size using the spectral method of [Wolff2004]

Parameters

[in] blockInd Specifies the block of the sampling state we're interested in. Defaults to -1, which will result in all blocks of the sampling state being concatenated in the ESS estimate.

Returns: A vector containing the ESS for each component of the chain.

Definition at line 47 of file MarkovChain.cpp.

References muq::SamplingAlgorithms::SampleCollection::AsMatrix(), and SingleComponentWolffESS().

Referenced by ESS(), and WolffError().

Member Data Documentation

◆ meta

std::vector<std::unordered_map<std::string, boost::any> > muq::SamplingAlgorithms::MarkovChain::meta

private

Definition at line 85 of file MarkovChain.h.

The documentation for this class was generated from the following files:

doxygen_prep/MUQ/SamplingAlgorithms/MarkovChain.h
doxygen_prep/modules/SamplingAlgorithms/src/MarkovChain.cpp

Detailed Description

Public Member Functions

Static Public Member Functions

Constructor & Destructor Documentation

◆ MarkovChain()

◆ ~MarkovChain()

Member Function Documentation

◆ ESS() [1/3]

◆ ESS() [2/3]

◆ ESS() [3/3]

◆ segment()

◆ SingleComponentWolffESS()

◆ StandardError() [1/3]

◆ StandardError() [2/3]

◆ StandardError() [3/3]

◆ WolffError()

◆ WolffESS()

Member Data Documentation

◆ meta