mc::mcmc::MetropolisHastingsSampler< dim > Class Template Reference

Metropolis-Hastings MCMC sampler for arbitrary target distributions. More...

#include <metropolisHastingsSampler.hpp>

Collaboration diagram for mc::mcmc::MetropolisHastingsSampler< dim >:

Public Member Functions
	MetropolisHastingsSampler (const mc::domains::IntegrationDomain< dim > &d, const std::function< double(const mc::geom::Point< dim > &)> &p, mc::geom::Point< dim > x0, double deviation)
	Construct Metropolis-Hastings sampler with target distribution.
mc::geom::Point< dim >	next (std::mt19937 &rng)
	Generate the next sample from the Markov chain.
double	target_pdf (const mc::geom::Point< dim > &x)
	Evaluate target probability density at a point.
double	acceptance_rate () const
	Get the current acceptance rate of the Markov chain.

Detailed Description

template<size_t dim>
class mc::mcmc::MetropolisHastingsSampler< dim >

Metropolis-Hastings MCMC sampler for arbitrary target distributions.

Template Parameters

dim	Dimensionality of the sample space.

Generates a Markov chain of samples asymptotically distributed according to target_pdf(x) using the Metropolis-Hastings algorithm.

Sampling process:

• Proposal: x' = x + N(0, σ²) where σ = deviation
• Acceptance: α = min(1, π(x')/π(x))
• Update: x_{n+1} = x' with probability α, else x_{n+1} = x_n

Usage:

1. Construct sampler with target density and initial point
2. Call next() repeatedly to generate Markov chain
3. Discard initial burn-in samples
4. Use remaining samples for Monte Carlo integration
5. Monitor acceptance_rate() to tune deviation

Performance tuning:

• If acceptance_rate() is too high (>50%), increase deviation
• If acceptance_rate() is too low (<10%), decrease deviation
• Target ~23.4% for high-dimensional problems

Note

The target density should return 0 outside the domain rather than relying on explicit domain checks (for flexibility).

Warning

Samples are correlated; use thinning for variance reduction.

Definition at line 78 of file metropolisHastingsSampler.hpp.

Constructor & Destructor Documentation

MetropolisHastingsSampler()

template<size_t dim>

mc::mcmc::MetropolisHastingsSampler< dim >::MetropolisHastingsSampler ( const mc::domains::IntegrationDomain< dim > &  d, const std::function< double(const mc::geom::Point< dim > &)> &  p, mc::geom::Point< dim >  x0, double  deviation  )

explicit

Construct Metropolis-Hastings sampler with target distribution.

Parameters

d	Integration domain (defines valid region and constraints).
p	Target probability density function π(x). Should return 0 outside the domain and positive values inside. Must be finite and > 0 at x0.
x0	Initial point for the Markov chain. Must satisfy domain.isInside(x0).
deviation	Standard deviation σ of random walk proposal N(0, σ²). Tune this parameter to achieve ~23.4% acceptance rate.

Exceptions

std::invalid_argument

If x0 is outside the domain.

Initializes sampler state and validates initial conditions. The random walk proposal will use a normal distribution with standard deviation deviation for each dimension.

Member Function Documentation

acceptance_rate()

template<size_t dim>

double mc::mcmc::MetropolisHastingsSampler< dim >::acceptance_rate

(

)

const

Get the current acceptance rate of the Markov chain.

Returns

Fraction of proposed moves that were accepted: n_accept / n_steps. Returns 0.0 if no steps have been taken.

The acceptance rate indicates chain quality:

• Too high (>50%): Increase deviation to explore wider
• Optimal (~23.4%): Good for high-dimensional problems (d > 5)
• Too low (<10%): Decrease deviation to accept more proposals

Use this metric to tune the deviation parameter for efficiency. Generally aim for 20-40% in practice depending on dimensionality.

Note

This is a cumulative rate across all next() calls. Reset the sampler to start fresh statistics if needed.

next()

template<size_t dim>

mc::geom::Point< dim > mc::mcmc::MetropolisHastingsSampler< dim >::next

(

std::mt19937 &

rng

)

Generate the next sample from the Markov chain.

Parameters

rng	Random number generator (must be seeded externally).

Returns

Next point in the chain: either the proposed point or current point.

Implements one iteration of the Metropolis-Hastings algorithm:

1. Propose y = current + N(0, σ²) where σ = deviation
2. Compute target densities: π(current), π(y)
3. Compute acceptance ratio: α = min(1, π(y)/π(current))
4. Accept y with probability α, update current = y and increment counter
5. Return updated current point

Important: The target density p(x) is expected to handle domain constraints by returning 0 outside valid regions (not throwing exceptions).

Exceptions

std::runtime_error

If π(current) becomes ≤ 0 or non-finite. This indicates the algorithm entered an invalid state.

Note

Automatically tracks acceptance statistics via n_steps and n_accept.

Call acceptance_rate() to monitor chain quality.

target_pdf()

template<size_t dim>

double mc::mcmc::MetropolisHastingsSampler< dim >::target_pdf

(

const mc::geom::Point< dim > &

x

)

Evaluate target probability density at a point.

Parameters

x	Query point in the domain.

Returns

π(x), the target probability density at x.

Evaluates the target probability density function provided at construction. This is a simple accessor for the internal target.

Note

For points outside the domain, the target should return 0.

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

• src/montecarlo/mcmc/metropolisHastingsSampler.hpp