cmp::mcmc::EvolutionaryMarkovChain Class Reference

Implements an Evolutionary Markov Chain Monte Carlo sampler. More...

#include <mcmc.h>

Public Member Functions
	EvolutionaryMarkovChain ()=default
	EvolutionaryMarkovChain (std::vector< Eigen::VectorXd > initialSamples, std::vector< double > initialScores, double nugget=1e-6)
	Constructs an EvolutionaryMarkovChain sampler.
void	step (const score_t &getScore, std::default_random_engine &rng, double gamma=0.2)
	Performs one crossover and mutation step for all chains.
std::vector< Eigen::VectorXd >	getCurrent () const
	Gets the current states of all chains.
std::vector< double >	getScores () const
	Gets the current log probability scores of all chains.

Protected Attributes
size_t	nChains_ {0}
	Number of active parallel chains.
size_t	dim_ {0}
	Dimension of the parameter space.
std::vector< Eigen::VectorXd >	chainSamples_
	Current parameter samples for each chain.
std::vector< double >	chainScores_
	Current score (log probability) for each chain.
std::uniform_int_distribution< size_t >	distChain_
	Discrete uniform distribution helper to pick random chain.
std::uniform_real_distribution< double >	distU_ {0, 1}
	Uniform distribution helper.
std::normal_distribution< double >	distN_ {0, 1}
	Normal distribution helper.
double	nugget_ {1e-6}
	Crossover mutation noise scaling.

Detailed Description

Implements an Evolutionary Markov Chain Monte Carlo sampler.

Mathematical Formulation Uses differential evolution crossover proposals. For each chain \(i\), candidate states \(\boldsymbol{\theta}_i^*\) are generated using states from two other distinct, randomly selected chains \(j\) and \(k\):

\[ \boldsymbol{\theta}_i^* = \boldsymbol{\theta}_i + \gamma (\boldsymbol{\theta}_j - \boldsymbol{\theta}_k) + \mathbf{e} \]

where \(\gamma\) is the scale factor and \(\mathbf{e} \sim \mathcal{N}(\mathbf{0}, \sigma_e^2 \mathbf{I})\) represents small mutation noise. The candidate state is accepted according to the Metropolis-Hastings probability:

\[ \alpha = \min\left(1, \exp\left(\log \pi(\boldsymbol{\theta}_i^*) - \log \pi(\boldsymbol{\theta}_i)\right)\right) \]

Implementation Algorithm

1. For each chain \(i\), randomly selects distinct partner chains \(j\) and \(k\).
2. Evaluates mutated crossover states.
3. Applies Metropolis-Hastings rejection step based on the likelihood evaluations.

Constructor & Destructor Documentation

EvolutionaryMarkovChain() [1/2]

cmp::mcmc::EvolutionaryMarkovChain::EvolutionaryMarkovChain ( )

default

EvolutionaryMarkovChain() [2/2]

cmp::mcmc::EvolutionaryMarkovChain::EvolutionaryMarkovChain	(	std::vector< Eigen::VectorXd >	initialSamples,
		std::vector< double >	initialScores,
		double	nugget = 1e-6
	)

Constructs an EvolutionaryMarkovChain sampler.

Parameters

initialSamples	Initial parameter states for each chain.
initialScores	Initial log probability scores for each chain.
nugget	Standard deviation scaling for crossover mutation noise.

Member Function Documentation

getCurrent()

std::vector< Eigen::VectorXd > cmp::mcmc::EvolutionaryMarkovChain::getCurrent ( ) const

inline

Gets the current states of all chains.

Returns

Vector of chain samples.

getScores()

std::vector< double > cmp::mcmc::EvolutionaryMarkovChain::getScores ( ) const

inline

Gets the current log probability scores of all chains.

Returns

Vector of chain scores.

step()

void cmp::mcmc::EvolutionaryMarkovChain::step	(	const score_t &	getScore,
		std::default_random_engine &	rng,
		double	gamma = 0.2
	)

Performs one crossover and mutation step for all chains.

Parameters

getScore	The log posterior probability evaluator.
rng	Random number engine.
gamma	Scale factor for difference vector in differential evolution.

Member Data Documentation

chainSamples_

std::vector<Eigen::VectorXd> cmp::mcmc::EvolutionaryMarkovChain::chainSamples_

protected

Current parameter samples for each chain.

chainScores_

std::vector<double> cmp::mcmc::EvolutionaryMarkovChain::chainScores_

protected

Current score (log probability) for each chain.

dim_

size_t cmp::mcmc::EvolutionaryMarkovChain::dim_ {0}

protected

Dimension of the parameter space.

distChain_

std::uniform_int_distribution<size_t> cmp::mcmc::EvolutionaryMarkovChain::distChain_

protected

Discrete uniform distribution helper to pick random chain.

distN_

std::normal_distribution<double> cmp::mcmc::EvolutionaryMarkovChain::distN_ {0, 1}

protected

Normal distribution helper.

distU_

std::uniform_real_distribution<double> cmp::mcmc::EvolutionaryMarkovChain::distU_ {0, 1}

protected

Uniform distribution helper.

nChains_

size_t cmp::mcmc::EvolutionaryMarkovChain::nChains_ {0}

protected

Number of active parallel chains.

nugget_

double cmp::mcmc::EvolutionaryMarkovChain::nugget_ {1e-6}

protected

Crossover mutation noise scaling.

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

• include/mcmc.h
• src/mcmc.cpp