mc::estimators::ISMeanEstimator< dim > Class Template Reference

Importance sampling mean estimator with variance reduction. More...

#include <ISMeanEstimator.hpp>

Collaboration diagram for mc::estimators::ISMeanEstimator< dim >:

Public Member Functions
ImportanceEstimate< dim >	estimate (const mc::domains::IntegrationDomain< dim > &domain, std::uint32_t seed, std::size_t n_samples, const mc::proposals::Proposal< dim > &proposal, const std::function< double(const mc::geom::Point< dim > &)> &f) const
	Estimate the weighted mean using importance sampling.

Detailed Description

template<std::size_t dim>
class mc::estimators::ISMeanEstimator< dim >

Importance sampling mean estimator with variance reduction.

Template Parameters

dim	Dimensionality of the space.

Estimates the mean using importance sampling:

1. Sample N points from proposal q(x): x₁, ..., xₙ ~ q
2. Filter to domain points with q > 0
3. Compute weighted average: μ̂ = (1/N) ∑ᵢ [f(xᵢ)/q(xᵢ)]
4. Estimate variance and standard error

Variance Reduction: If q(x) ≈ f(x), the weights [f(x)/q(x)] are roughly constant, reducing variance compared to uniform sampling.

Usage: For integration over Ω: ∫_Ω f(x) dx ≈ (mean result) [no volume factor—importance weight handles normalization]

Note

Uses OpenMP for parallel sampling from proposal.

Proposal must support sample() and pdf() methods.

Definition at line 59 of file ISMeanEstimator.hpp.

Member Function Documentation

estimate()

template<std::size_t dim>

ImportanceEstimate< dim > mc::estimators::ISMeanEstimator< dim >::estimate	(	const mc::domains::IntegrationDomain< dim > &	domain,
		std::uint32_t	seed,
		std::size_t	n_samples,
		const mc::proposals::Proposal< dim > &	proposal,
		const std::function< double(const mc::geom::Point< dim > &)> &	f
	)		const

Estimate the weighted mean using importance sampling.

Parameters

domain	The integration domain.
seed	Random seed for reproducibility.
n_samples	Number of samples to draw from proposal.
proposal	Sampling distribution q(x) (should resemble |f(x)|).
f	Function to evaluate.

Returns

ImportanceEstimate with weighted mean, stderr, and sample counts.

Exceptions

std::invalid_argument

if n_samples == 0.

Algorithm:

• Each thread samples n_local points from proposal (parallel)
• Keeps only points inside domain with q(x) > 0
• Accumulates weighted sum ∑ [f(x)/q(x)] and sum of squares
• Returns (mean / N, stderr, n_inside)

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

• src/montecarlo/estimators/ISMeanEstimator.hpp