metropolisHastingsSampler.hpp File Reference

Metropolis-Hastings MCMC sampling engine. More...

#include "../domains/integration_domain.hpp"
#include "../geometry.hpp"
#include <array>
#include <random>
#include <utility>
#include <functional>
#include "metropolisHastingsSampler.tpp"

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Classes
class	mc::mcmc::MetropolisHastingsSampler< dim >
	Metropolis-Hastings MCMC sampler for arbitrary target distributions. More...

Namespaces
namespace	mc
namespace	mc::mcmc

Detailed Description

Metropolis-Hastings MCMC sampling engine.

Author

Giacomo Merlo

Date

11/01/26

Implements the Metropolis-Hastings algorithm for sampling from arbitrary target probability distributions using Markov Chain Monte Carlo (MCMC).

Algorithm Overview: The Metropolis-Hastings sampler generates a sequence of correlated samples distributed according to a target probability density π(x) by:

1. Starting at an initial state x₀
2. Proposing x' = x + N(0, σ²) from a symmetric random walk
3. Computing acceptance ratio α = min(1, π(x')/π(x))
4. Accepting x' with probability α, otherwise staying at x

Advantages over rejection sampling:

• Works efficiently in high dimensions where rejection becomes infeasible
• Handles arbitrary complex distributions via their density function
• Produces unbiased samples after burn-in period

Key properties:

• Samples form a Markov chain (current sample depends only on previous)
• Asymptotically distributed according to π(x)
• Symmetric random walk proposal ensures detailed balance
• Acceptance rate should be ~23.4% in high dimensions (optimal)

Note

Requires careful burn-in and thinning for reliable estimates.

See also

Metropolis et al. (1953), Hastings (1970)

Definition in file metropolisHastingsSampler.hpp.