mc::integrators::MHMontecarloIntegrator< dim > Class Template Reference

Metropolis-Hastings MCMC integrator for complex domains. More...

#include <MHintegrator.hpp>

Inheritance diagram for mc::integrators::MHMontecarloIntegrator< dim >:

Collaboration diagram for mc::integrators::MHMontecarloIntegrator< dim >:

Public Types
using	Point = mc::geom::Point< dim >
using	Func = std::function< double(const Point &)>

Public Member Functions
	MHMontecarloIntegrator (const mc::domains::IntegrationDomain< dim > &d)
	Construct an MH-based integrator for a domain.
double	integrate (const Func &f, int n_samples, const mc::proposals::Proposal< dim > &proposal, std::uint32_t seed) override
	Compute the integral using MH sampling combined with volume estimation.
void	setConfig (std::size_t burn_in_, std::size_t thinning_, std::size_t n_samples_volume_, double deviation_, Func p_, Point x0_)
	Configure the MCMC sampler parameters.
Public Member Functions inherited from mc::integrators::Integrator< dim >
	Integrator (const mc::domains::IntegrationDomain< dim > &d)
	Constructs an integrator for a specific domain.
virtual double	integrate (const std::function< double(const mc::geom::Point< dim > &)> &f, int n_samples, const mc::proposals::Proposal< dim > &proposal, std::uint32_t seed)=0
virtual	~Integrator ()=default
	Virtual destructor for proper polymorphic cleanup.

Additional Inherited Members
Protected Member Functions inherited from mc::integrators::Integrator< dim >
std::vector< mc::geom::Point< dim > >	initializeRandomizer (int numbers)
	Initializes random samples uniformly distributed in the domain.
Protected Attributes inherited from mc::integrators::Integrator< dim >
const mc::domains::IntegrationDomain< dim > &	domain
	Reference to the integration domain.
std::vector< std::mt19937 >	randomizer
	Per-thread random number generators.

Detailed Description

template<std::size_t dim>
class mc::integrators::MHMontecarloIntegrator< dim >

Metropolis-Hastings MCMC integrator for complex domains.

Template Parameters

dim	Dimensionality of the integration domain.

Two-stage integration approach:

1. Volume Estimation: Hit-or-Miss MC to estimate V_Ω
2. Mean Estimation: MH sampler with target density p(x) to estimate E[f]

Integral: ∫_Ω f(x) dx ≈ V̂_Ω · (1/M) ∑ᵢ f(xᵢ) where xᵢ ~ π(x) ∝ p(x)

This approach is especially effective for:

• Complex domains with intricate boundaries
• Multimodal or highly non-uniform integrands
• Cases where uniform sampling has poor convergence

Note

Configuration must be set via setConfig() before integrate().

Definition at line 43 of file MHintegrator.hpp.

Member Typedef Documentation

Func

template<std::size_t dim>

using mc::integrators::MHMontecarloIntegrator< dim >::Func = std::function<double(const Point&)>

Definition at line 46 of file MHintegrator.hpp.

Point

template<std::size_t dim>

using mc::integrators::MHMontecarloIntegrator< dim >::Point = mc::geom::Point<dim>

Definition at line 45 of file MHintegrator.hpp.

Constructor & Destructor Documentation

MHMontecarloIntegrator()

template<std::size_t dim>

mc::integrators::MHMontecarloIntegrator< dim >::MHMontecarloIntegrator ( const mc::domains::IntegrationDomain< dim > &  d )

explicit

Construct an MH-based integrator for a domain.

Parameters

d	Reference to the integration domain.

Member Function Documentation

integrate()

template<std::size_t dim>

double mc::integrators::MHMontecarloIntegrator< dim >::integrate ( const Func &  f, int  n_samples, const mc::proposals::Proposal< dim > &  proposal, std::uint32_t  seed  )

override

Compute the integral using MH sampling combined with volume estimation.

Parameters

f	Integrand function: ℝⁿ → ℝ.
n_samples	Number of post-burn-in, post-thinning samples to keep.
proposal	Unused (MH uses internal sampler).
seed	Random seed for reproducibility.

Returns

Estimated integral ∫_Ω f(x) dx.

Exceptions

std::runtime_error	if setConfig() not called first.
std::invalid_argument	if n_samples ≤ 0.
std::runtime_error	if all samples yield non-finite f(x).

setConfig()

template<std::size_t dim>

void mc::integrators::MHMontecarloIntegrator< dim >::setConfig	(	std::size_t	burn_in_,
		std::size_t	thinning_,
		std::size_t	n_samples_volume_,
		double	deviation_,
		Func	p_,
		Point	x0_
	)

Configure the MCMC sampler parameters.

Parameters

burn_in_	Number of initial samples to discard (warmup).
thinning_	Keep every k-th sample (k=thinning_) for autocorrelation reduction.
n_samples_volume_	Number of samples for volume estimation.
deviation_	Proposal standard deviation (controls MH acceptance rate).
p_	Target density: π(x) ∝ p(x); should be proportional to integrand.
x0_	Initial point in the domain (burn-in starting point).

Exceptions

std::invalid_argument

if parameters are invalid (e.g., thinning=0, x0 ∉ Ω).

Note

Must be called before integrate().

---

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

• src/montecarlo/integrators/MHintegrator.hpp